Abstract
This review reports on the advances achieved in these fields of the natural sciences in connection with the discovery of the heavy isotope of hydrogen. We shall see that not only is the study of the properties of the heavy hydrogen isotope of interest, but that its applications as an auxiliary tool are also highly valuable for research.
Full Text
HEAVY ISOTOPE OF HYDROGEN *
L. Farkas, Cambridge
The discovery of the heavy isotope of hydrogen by Urey, Brickwedde, and Murphy \(^{151—154}\) in the spring of 1932, and the preparation of pure heavy water by G. N. Lewis and Macdonald \(^{97,108}\) in February 1933, aroused extraordinary activity in physics, chemistry, and biology. **
In the present review we report on the advances achieved in these fields of the natural sciences in connection with the discovery of the heavy isotope of hydrogen. We shall see that not only is the study of the properties of the heavy hydrogen isotope of interest, but its applications as an auxiliary agent are also extremely valuable for research.
Contents. § 1. Properties of the heavy hydrogen nucleus and its nuclear reactions. § 2. Spectroscopic investigations. § 3. Thermodynamics of compounds of heavy hydrogen. § 4. Ortho- and para-modifications of the molecule. § 5. Elasticity of \(D_2\) vapors. § 6. Electrolytic preparation of heavy water. § 7. Properties of heavy water. § 8. Methods for determining the concentration of \(D\) in a mixture of both isotopes. § 9. Distribution of the heavy isotope of hydrogen in nature. § 10. Causes of the different reaction rates in compounds containing \(H\) and \(D\). § 11. Exchange reactions in a homogeneous gas space. § 12. Exchange reactions in a homogeneous solution. § 13. Catalytic exchange reactions. § 14. Certain gas reactions of \(H_2\), \(HD\), and \(D_2\), and their rates. § 15. Preparation of both hydrogen isotopes from aqueous solutions. § 16. Comparison of catalytic reactions of both hydrogen isotopes. § 17. Reactions in solutions, rates of fermentation processes. § 18. Biological experiments with heavy water.
§ 1. Properties of the heavy hydrogen nucleus and its nuclear reactions
The mass of the heavy hydrogen nucleus (hereafter we shall denote the light isotope by \(H\), the heavy isotope \((H^2)\) by \(D\)) was measured with extraordinary accuracy by K. T. Bainbridge \(^{3—5}\) using a mass spectrograph. Table 1 gives the numerical values of the masses, with \(O^{16}\) taken as \(16.00000\); the observational error is not indicated; for the numbers printed in bold it is not greater than \(1:20000\).
The energy of formation (mass defect) of the nucleus \(D\) from a proton and a neutron *** is, according to the formula
\[ {}_{1}H^{1} + {}_{0}n^{1} \rightarrow {}_{1}D^{2} + \Delta E \]
\[ 1.007775 + 1.0080 = 2.01363 + 0.00212 \tag{1} \]
* Naturwiss. 22, 613, 637, 653, 1934.
** The history of the discovery of the heavy isotope of hydrogen has recently been set forth by Frerichs in Naturwiss. 22, 113, 1934.
*** The splitting of the \(D\) nucleus by \(\gamma\)-rays according to the reaction \({}_{1}D^{2}+h\nu \rightarrow {}_{1}H^{1}+{}_{0}n^{1}\) was proved by J. Chadwick and M. Goldhaber and gives for the neutron the mass indicated in Table 1, with an accuracy of \(\pm 0.0005\). The reverse reaction was observed by Lea \(^{96}\). He found, upon bombarding paraffin or liquid hydrogen with neutrons from Be, particles emitted in the direction of the incident neutrons and hard \(\gamma\)-radiation with an energy of the expected magnitude.
comparatively small* (2 million V), and therefore it could be assumed that the nucleus D is readily split. For this reason Rutherford and Kempton^137 made attempts to split heavy hydrogen by bombardment with α-particles or protons. It turned out that neither polonium α-particles nor protons up to 300,000 V produce a reaction with the nucleus D.
The possible spontaneous decay of the nucleus D was investigated by P. Ladenburg^94, who attempted to detect the weak radioactivity of heavy water. Since no noticeable radioactivity was found, it follows from these measurements that the mean lifetime of the nucleus D is greater than \(10^{15}\) years.
TABLE 1
| Designation | Weight | Designation | Weight |
|---|---|---|---|
| \(e\) | 0.00055 | \({}_{2}\mathrm{He}^{3}\) | 3.0165 |
| Neutron | 1.0080 | \({}_{2}\mathrm{He}^{4}\) | 4.00216 |
| Proton | 1.007225 | \({}_{8}\mathrm{O}^{16}\) | 16.00000 |
| \({}_{1}\mathrm{H}^{1}\) | 1.007775 | \(\mathrm{H}^{2}\) | 2.01555 |
| \({}_{1}\mathrm{D}^{+}\) | 2.01308 | \(\mathrm{DH}\) | 3.02146 |
| \({}_{1}\mathrm{D}^{2}\) | 2.01363 | \(\mathrm{D}^{2}\) | 4.02723 |
| \({}_{1}\mathrm{H}^{3}\) | 3.0151 |
Recently Oliphant, Harteck, and Lord Rutherford^122,123 investigated the reaction of D nuclei with D, bombarding heavy ammonium chloride \((\mathrm{ND}_{4}\mathrm{Cl})\) and ammonium sulfate \((\mathrm{ND}_{4}\mathrm{SO}_{4})\) with \(\mathrm{D}^{+}\) rays at velocities of 2,000–100,000 V. In this case the D nucleus proved to be readily split, and two nuclear reactions occur:**
\[ {}_{1}\mathrm{D}^{2}+{}_{1}\mathrm{D}^{2}\longrightarrow({}_{2}\mathrm{He}^{4})\longrightarrow{}_{1}\mathrm{H}^{1}+{}_{1}\mathrm{H}^{3} \tag{2} \]
\[ {}_{1}\mathrm{D}^{2}+{}_{1}\mathrm{D}^{2}\longrightarrow({}_{2}\mathrm{He}^{4})\longrightarrow{}_{2}\mathrm{He}^{3}+{}_{0}\mathrm{n}^{1} \tag{3} \]
In the first case, protons arise with a range of 14.3 cm \((3\cdot10^{6}\ \mathrm{V})\) and hydrogen isotope II with a range of 1.6 cm. The mass of this new hydrogen isotope can be calculated from the law of conservation of energy and momentum in the collision; the value obtained is given in Table 1.
The reaction leading to the new isotope of hydrogen occurs very
* The small mass defect of the nucleus D (in comparison with the mass defect of the nucleus He) can be understood on the basis of Wigner’s theory^164,47. In the nucleus D the potential energies of the neutron and proton almost compensate their kinetic energy. In the nucleus He, however, against the four potential energies of two neutrons and two protons there are only the kinetic energies of these particles, as a result of which a considerable binding energy remains.
** The existence of these reactions was also proved by direct photographs with the aid of a Wilson chamber^41.
often: at a \(D\)-ray energy of \(100\,000\) e-V, at least \(10^{-6}\) of the nuclei \(D\) incident on \(ND_4Cl\) are transformed according to (2) and (3).
The isotope of hydrogen with mass 3 occurs in nature only in very insignificant concentrations; according to Bleakney, Lozier, and Smith\({}^{115}\), the upper limit of its concentration relative to ordinary hydrogen is \(1:10^9\). In pure heavy water, however, \(H^3\) occurs in the ratio \(1:200\,000\), and Harnwell, Smith, Van Voorhis, and Kuiper\({}^{77}\) succeeded, by means of nuclear reaction (2), in obtaining a certain quantity of hydrogen with an \(H^3\) content of \(1:5000\). For this purpose pure \(D_2\) was bombarded with canal \(D\)-rays of energy \(70\,000\) e-V, the enrichment of \(H^3\) from \(1:2\cdot 10^5\) to \(1:5\cdot 10^3\) occurring after a short operation of the canal tube. From the energetic point of view \(H^3\) is more stable than \(D\), and the possibility is not excluded of obtaining \(H^3\) in large quantities by means of the indicated nuclear reaction.
Nuclear reaction (3) also gives a new isotope of He with mass 3.0163, the second product of the reaction being a neutron with energy about \(2\cdot 10^6\) V. This reaction proceeds with a yield analogous to the yield of \(H^3\) in reaction (2), and the neutron radiation thereby obtained is at present the most powerful source of neutrons at our disposal. Because of the ease of the reaction \(D\) with \(D\), it is a source of errors in experiments on the splitting of heavy nuclei. The decay products observed when heavy metals are bombarded may arise from the reaction of \(D\) with \(D\), since hydrogen isotope in small concentrations (in water films, etc.) can hardly be avoided.
Cockcroft and Walton\({}^{34}\) investigated a number of nuclear reactions of heavy hydrogen with light nuclei, for example:
\[
{}_{3}\mathrm{Li}^{6}+{}_{1}\mathrm{D}^{2}\rightarrow{}_{3}\mathrm{Li}^{7}+{}_{1}\mathrm{H}^{1}
\]
\[
{}_{3}\mathrm{Li}^{6}+{}_{1}\mathrm{D}^{2}\rightarrow 2\,{}_{2}\mathrm{He}^{4}
\]
\[
{}_{6}\mathrm{C}^{12}+{}_{1}\mathrm{D}^{2}\rightarrow{}_{6}\mathrm{C}^{13}+{}_{1}\mathrm{H}^{1}
\]
\[
{}_{5}\mathrm{B}^{10}+{}_{1}\mathrm{D}^{2}\rightarrow{}_{5}\mathrm{B}^{11}+{}_{1}\mathrm{H}^{1}+h\nu
\]
\[
{}_{5}\mathrm{B}^{10}+{}_{1}\mathrm{D}^{2}\rightarrow 3\,{}_{2}\mathrm{He}^{4}
\]
\[
{}_{8}\mathrm{O}^{16}+{}_{1}\mathrm{D}^{2}\rightarrow{}_{8}\mathrm{O}^{17}+{}_{1}\mathrm{H}^{1}
\]
Thus it turns out that \(D\) enters into reactions with the majority of nuclei, and comparison with the corresponding proton reactions leads to important conclusions concerning the structure of the nucleus and the thermal effects of nuclear reactions.*
Further essential features characterizing the \(D\) nucleus are: the spin of the nucleus, its statistics, and its magnetic moment. For the proton, Fermi statistics are valid, as can be shown from the alternation of intensities in molecular spectra and from
* See also the works on nuclear reactions\({}^{2,36,37,42,46,138}\).
equilibrium between para- and orthohydrogen; its mechanical moment is \(\frac{1}{2}\frac{h}{2\pi}\). The investigation of the spectrum of \(D_2\) (see below), carried out by Eshleman and Lewis\(^{101}\), and the investigation of the equilibrium between ortho- and parahydrogen \(D_2\) by A. Farkas, L. Farkas, and P. Harteck\(^{57}\) revealed Bose statistics and the mechanical moment \(1\frac{h}{2\pi}\).*
Apparently, with the determination of the statistics of the \(D\) nucleus, a rule regulating nuclear statistics has been found: for odd atomic weight Fermi statistics holds, for even atomic weight—Bose statistics, independently of whether the atomic number of the nucleus is even or odd.
The magnetic moment of the proton was determined by Stern, Frisch, and Estermann** by means of the deflection of a molecular beam of \(H_2\) in an inhomogeneous field. The moment of the nucleus turned out, unexpectedly, to be equal to 2.5 nuclear magnetons \((2.5 \cdot 0.5 \cdot 10^{-23}\) CGS units). A. Farkas, L. Farkas, and P. Harteck\(^{57}\) attempted to determine the magnetic moment of the nucleus, in relation to the moment of the proton \(D\), by another method. They compared the rate of the ortho-\(D_2\) conversion over catalyst \(O\) into ordinary \(D\) with the corresponding reaction in the \(H_2\)-conversion (see § 4) and derived from this the ratio
\[ \frac{\text{magnetic moment of the proton}}{\text{magnetic moment of }D}=5.5, \]
i.e. for \(\mu_D\) about 0.5 nuclear magnetons.
A value of the same order for \(\mu_D\) was recently obtained by Stern and Estermann by the molecular-beam method, namely 0.7 nuclear magnetons. Thus both methods agree sufficiently with one another that the magnetic moment of the \(D\) nucleus is very small, in contrast to the moment of the proton, which is very large. The moment of the \(D\) nucleus is of great importance for the systematics of the magnetic moments of complex nuclei, especially since for other nuclei with the number of protons equal to the number of neutrons, determination of the magnetic moments is as yet impossible.*
§ 2. Spectroscopic Investigations
The displacement of the Balmer lines of the heavy hydrogen atom relative to the lines of the light isotope served as the first proof of the existence of the new isotope of hydrogen (see Urey, Brickwedde, and Murphy\(^{153}\)).
* See also\(^{12}\) and Clusius and Bartholomé\(^{35}\).
* Estermann, Nature 132, 169, 1933; Z. Physik 85, 1933.
* Rabi, Kellogg, and Zacharias\(^{129, 190}\) obtained for \(\mu_P\) \(3.1 + 0.2\), for \(\mu_D\) \(0.75 \pm 0.1\).
*** In these nuclei, for example in \(N^{14}\), no hyperfine structure has so far been observed, whence it may be concluded that the magnetic moment of the nucleus is at least very small.
The difference in wavelengths arises from the different motion of the nucleus in the atoms H and D, as a result of which the Rydberg constant \(R\) changes somewhat:
\[ \nu_{\mathrm H}=R_{\mathrm H}\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right); \qquad R_{\mathrm H}=\frac{2\pi^2 m_e e^4}{h^3\left(1+\frac{m_e}{M_{\mathrm H}}\right)} \]
\[ \nu_{\mathrm D}=R_{\mathrm D}\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right); \qquad R_{\mathrm D}=\frac{2\pi^2 m_e e^4}{h^3\left(1+\frac{m_e}{M_{\mathrm D}}\right)} \]
where \(R_{\mathrm H}=109677.76\ \mathrm{cm}^{-1}\) and \(R_{\mathrm D}=109707.56\ \mathrm{cm}^{-1}\).
The wavelengths of the Balmer lines in D are shorter than in light hydrogen: the measured difference in wavelengths is in very good agreement with theory.*
\[ D_{\alpha}-H_{\alpha}\ 2.79\ \text{\AA};\qquad D_{\beta}-H_{\beta}\ 1.33\ \text{\AA};\qquad D_{\gamma}-H_{\gamma}\ 1.19\ \text{\AA}. \]
The molecular spectra of a large number of compounds containing D have also been investigated; for example, the band spectra of the molecules \(D_2^{44,91}\), \(HD^{1,15,43}\), \(OD^{33,92}\), \(AlD^{83,84}\), the infrared spectra \(DCl^{76}\), \(C_2D_2^{131,170}\), \(ND_3^{26}\), and the infrared and Raman spectra of \(HOD\) and \(D_2O^{10,31,166,167}\).
The observed differences with respect to the spectra of the corresponding light hydrogen compounds, since they concern the “isotopic” effect of rotational terms and vibrational levels, can be well explained by theoretical formulas.***
For the constants of rotational terms
\[ \left(B=\frac{h}{8\pi^2 c\mu r^2}\right) \]
the relation holds
\[ \frac{B_e}{B_e^{(i)}}=\rho^2, \tag{1} \]
where \(B_e^{(i)}\) refers to the heavy isotope, and
\[ \rho^2=\frac{\mu}{\mu^{(i)}}= \frac{M_{\mathrm H}\cdot M_X}{M_{\mathrm H}+M_X}: \frac{M_{\mathrm D}\cdot M_X}{M_{\mathrm D}+M_X}. \tag{2} \]
— the ratio of the reduced masses of the molecules HX and DX.
The ratio for the fundamental frequencies:
\[ \frac{\omega_e}{\omega_e^{(i)}}=\rho; \tag{3} \]
* Thus the ionization potential for D is greater by \(84.5\) cal than for H.
* The fine structure of the lines of heavy hydrogen is also in agreement with theory \(^{141,165}\).
** See also \(^{171}\).
\(\rho\) for hydrogen is equal to 0.7–0.8 (for other molecules \(\rho\) is from 0.95 to 0.99), so that for heavy hydrogen compounds the isotope shift reaches a very considerable magnitude. In Table 2 some molecular constants are given for \(H_2\), HD, and \(D_2\). In the last row the “zero-point” energy is given:
\[ \varepsilon^{(0)}=hc\left(\frac{1}{2}\widetilde{\omega}_e-\frac{1}{4}\widetilde{\omega}_e x\right). \tag{4} \]
It plays, as we shall see, a decisive role in questions of equilibria in which heavy and light hydrogen participate, and then in the question of the reaction rates of both isotopes.
TABLE 2*
| \(H_2\) | HD | \(D_2\) | |
|---|---|---|---|
| \(\widetilde{\omega}_e\) | \(4\,403\ \mathrm{cm}^{-1}\) | \(3\,813.75\ \mathrm{cm}^{-1}\) | \(3\,114.95\ \mathrm{cm}^{-1}\)** |
| \(\widetilde{\omega}_e x\) | 120.5 | 90.4 | 60.3 |
| \(B_e\) | 60.871 | 45.670 | 30.466*** |
| \(\alpha\) | 3.124 | 2.0302 | 1.106 |
| \(\varepsilon^0\) | \(6\,175.5\ \mathrm{cal.}\) | \(5\,3589\ \mathrm{cal.}\) | \(4\,886.6\ \mathrm{cal.}\)**** |
In the bands of the \(D_2\) molecule lying in the visible region, an alternation of intensities was observed. From it Ashley and Lewis\(^{101}\) and Murphy and Johnston\(^{120}\) concluded that the spin \(i_D=1\). Since in the \(D_2\) molecule those rotational lines are strong which in \(H_2\) are weak, Bose statistics holds in the \(D_2\) nucleus.
In addition to the vibrational and rotational frequencies of the molecule, which according to (1) and (3) depend strongly on mass, on passing from light to heavy hydrogen compounds the frequency of the “pure” electronic jump also changes. But this change does not exceed \(0.1\%\).
§ 3. Thermodynamics of Heavy-Hydrogen Compounds
The possibility of calculating the molecular constants of heavy-hydrogen compounds by the formulas of isotope shift makes it possible to approach theoretically the question of equilibria in which heavy and light hydrogen participate.
* For more accurate constants (with allowance also for upper rotational and vibrational states), see works 31, 15, 43, 105.
** \(\omega_v=\omega_e\left(v+\frac{1}{2}\right)-\omega_e x\left(v+\frac{1}{2}\right)^2\).
*** \(B_v \simeq B_c-a\left(v+\frac{1}{2}\right)\).
**** Owing to this difference in zero-point energies, the convergence point of the Lyman bands in HD and D should have approximately a \(285\ \mathrm{cm}^{-1}\) and \(560\ \mathrm{cm}^{-1}\) higher frequency than in \(H_2\). The heat of dissociation in HD and \(D_2\) is also greater than that of the \(H_2\) molecule,
\[ D_2=102\,800\pm1\,000\ \mathrm{cal.},\qquad D_{\mathrm{HD}}=103\,617\pm1\,000\ \mathrm{cal.}, \]
\[ D_{\mathrm{D}_2}=104\,589\pm1\,000\ \mathrm{cal.} \]
As an example, let us consider the equilibrium between the molecules H₂, HD, and D₂, which can be formed by the atoms H and D. The equilibrium constant (see Urey and Rittenberg^155^)
\[ K=\frac{[\mathrm{HD}]^2}{[\mathrm{H}_2][\mathrm{D}_2]} \]
of the reaction
\[ \mathrm{H}_2+\mathrm{D}_2 \rightleftarrows 2\mathrm{HD} \tag{1} \]
is equal (since the vibrations are not excited) to:
\[ \lg K_1=-\frac{\Delta E_0^0}{2.3RT}+\frac{3}{2}\lg\frac{M_{\mathrm{HD}}^2}{M_{\mathrm{H}_2}M_{\mathrm{D}_2}}+\lg\frac{Z_{\mathrm{HD}}^2}{Z_{\mathrm{H}_2}Z_{\mathrm{D}_2}} . \tag{2} \]
The first term of the sum on the right-hand side takes into account the difference in the zero-point energies of the molecules participating in the reaction, and \(\Delta E_0^0\) is equal to
\[ \Delta E_0^0=2\varepsilon_{\mathrm{HD}}^0-\varepsilon_{\mathrm{H}_2}^0-\varepsilon_{\mathrm{D}_2}^0=155\ \text{cal.} \]
The second term arises from the “translational” sum of states* and is equal to \(\frac{3}{2}\lg\frac{9}{8}\). The third term depends on the “rotational” sum of states and, in the temperature interval between 200 and 700°K, is equal to \(\lg 4\cdot\frac{8}{9}\), where \(\lg\frac{8}{9}\) is determined by the ratio of the moments of inertia
\[ \frac{J_{\mathrm{HD}}^2}{J_{\mathrm{H}_2}J_{\mathrm{D}_2}}=\frac{8}{9}, \]
and \(\lg 4\) enters because in reaction (1) two molecules with identical nuclei pass into two asymmetric HD molecules. At temperatures below 200°K, when the rotational degrees of freedom are incompletely excited, the rotational sums of states must be calculated separately
\[ Z=\sum_j g(2j+1)e^{-E_j/kT} \tag{3} \]
for the three molecules at each temperature. In doing so it should be taken into account that for H₂ \(\left(i_{\mathrm{H}}=\frac{1}{2}\right)\)
for even rotational terms (para states) the statistical weight of the nucleus is
\[ g_p=i(2i+1)=1, \]
and for odd terms (ortho states)
\[ g_o=(i+1)(2i+1)=3, \]
whereas for D₂ \((i_{\mathrm{D}}=1)\) the even ones have \(g_o=6\),
* See, for example, the review article by G. E. Uhlenbeck, “Spectral Physics and Thermodynamics,” Z. Elektrochemie 39, 758, 895, 1933.
odd \(g_p=3\), and in HD all rotational states have the statistical weight of the nucleus:*
\[ g_{\mathrm{HD}}=(2i+1)(2i_D+1)=6. \]
Table 3 contains the equilibrium constant \(K_1\) of reaction (1) at different temperatures.
Equilibrium (1) was experimentally investigated by A. Farkas and L. Farkas \(^{35,36}\), and then more precisely by Urey, Rittenberg, and Bleakney \(^{134}\), by measuring the ratio \(\mathrm{H_2}:\mathrm{HD}:\mathrm{D_2}\) at various temperatures with the aid of the thermal conductivity of the gas and mass-spectroscopically. In this, complete agreement with theory was found; in particular, the “relative” independence of \(K_1\) from temperature was established.
TABLE 3
| \(T^0\) | \(K_1\) |
|---|---|
| 20,4 | 0,152 |
| 50,0 | 1,345 |
| 100,0 | 1,265 |
| 200,0 | 2,903 |
| 298,0 | 3,269 |
| 400,0 | 3,429 |
| 575,0 | 3,710 |
| 700,0 | 3,800 |
Just as equilibrium (1), other simple equilibria can also be calculated theoretically in which light and heavy hydrogen take part. For the equilibria
\[ \mathrm{H_2}+\mathrm{DCl}\rightleftarrows \mathrm{HD}+\mathrm{HCl} \]
\[ \mathrm{H_2}+\mathrm{DJ}\rightleftarrows \mathrm{HD}+\mathrm{HJ} \]
one obtains at \(20^\circ\mathrm{C}\)
\[ K_4\frac{[\mathrm{HD}]\cdot[\mathrm{HCl}]}{[\mathrm{H_2}]\cdot[\mathrm{DCl}]}=1,28 \]
and \(K_5=1,98\).** In more complicated reactions the calculation of the equilibrium constant is no longer so simple, but it is known that in very many cases of double exchange substitution of the type
\[ \mathrm{A}_{\text{light}}+\mathrm{B}_{\text{heavy}}\rightleftarrows \mathrm{A}_{\text{heavy}}+\mathrm{B}_{\text{light}} \tag{6} \]
there are significant deviations of the equilibrium constant from 1, in contrast to analogous substitutions for other isotopes, for which the equilibrium constants are practically always equal to 1. The most important and, experimentally, so far best-investigated case is the equilibrium:
\[ [\mathrm{H_2O}]_{\text{liq}}+\mathrm{HD}\rightleftarrows[\mathrm{HOD}]_{\text{liq}}+\mathrm{H_2}, \tag{7} \]
* At high temperature, where \(\sum(2j+1)e^{-E_j/kT}=\sum(2j+1)e^{-E_j/kT}\), the expression
\[ \frac{g_{\mathrm{HD}}^2}{\dfrac{g_{p\mathrm{H}_2}+g_{o\mathrm{H}_2}}{2}}\cdot \frac{1}{\dfrac{g_{p\mathrm{D}_2}+g_{o\mathrm{D}_2}}{2}} \]
gives a factor of 4, which was derived before the introduction of nuclear weights from symmetry considerations.
** Equilibrium (5) has also been investigated experimentally, and the agreement with theory proved brilliant \(^{135}\).
constant of which was first determined by Bonhoeffer and K. Rummel \(^{21,25}\), then by A. Farkas and L. Farkas \(^{58}\).*
The equilibrium constant
\[ K_7=\frac{[\mathrm{HOD}]_{\mathrm{liquid}}\cdot[\mathrm{H}_2]} {[\mathrm{HD}]\cdot[\mathrm{H}_2\mathrm{O}]_{\mathrm{liquid}}} \]
is equal at \(20^\circ\mathrm{C}\) to 3.3, at \(40^\circ\mathrm{C}\)—3.0, and at \(100^\circ\mathrm{C}\)—2.2 (approximate values). On the basis of these values one can derive from theoretical formulas (in the first approximation) the mean differences of zero-point energies—\(\varepsilon_{\mathrm{H_2O}}-\varepsilon_{\mathrm{HOD}}\)—of about \(1\,750\) cal.
In the theoretical calculation of equilibrium (7), one must take into account the different vibrational frequencies and the moment of inertia of water; on the basis of known data (Raman frequencies of \(\mathrm{H_2O}\) and \(\mathrm{HDO}\)) satisfactory agreement with the experimental value is obtained.** The thermal effect of reaction (7) is \(+930\pm20\) cal.
Attention should be drawn to the fact that, in water at low temperatures, the heavy isotope in equilibrium is predominantly bound to the O atom, whereas in a hydrogen halide acid the equilibrium is shifted in favor of “free” heavy hydrogen.
For a complete study of equilibria in which water participates, it is necessary to know the equilibrium constant of the reaction
\[ \mathrm{H_2O}+\mathrm{D_2O}\rightleftarrows 2\,\mathrm{HOD}. \tag{8} \]
At present it is not yet known experimentally, but it can be calculated theoretically in the same way as \(K_1\).
\[ K_8=\frac{[\mathrm{HOD}]^2}{[\mathrm{H_2O}]\cdot[\mathrm{D_2O}]} \]
Tepley and Eyring \(^{149}\) obtained \(K_8=3.26\) at \(20^\circ\mathrm{C}\), and, since the difference of zero-point energies is almost zero, \(K_8\), like \(K_1\), depends very little on temperature. From \(K_1\), \(K_7\), and \(K_8\) all equilibrium reactions between water and hydrogen can be calculated. Thus, for example,
\[ \mathrm{H_2O}+\mathrm{D_2}\rightleftarrows \mathrm{D_2O}+\mathrm{H_2}. \tag{9} \]
\[ K_9=\frac{K_1^{\,2}}{K_8}\,K_7^{\,2} \]
An equilibrium of type (6) is the reaction:
\[ \mathrm{CH_3COCH_3}+\mathrm{HOD}\rightleftarrows \mathrm{CH_3COCH_2D}+\mathrm{H_2O}, \tag{10} \]
which was studied by Halford, Anderson, and Bates \(^{73}\). The equilibrium constant at \(20^\circ\mathrm{C}\):
\[ K_{10}=\frac{[\mathrm{CH_3COCH_2D}]\,[\mathrm{H_2O}]} {[\mathrm{CH_3COCH_3}]\,[\mathrm{HOD}]}\sim 2. \]
* The latter obtained for the gas equilibrium (Trans. Farad. Soc.; in press) at \(20^\circ\mathrm{C}\)—\(2.65\pm0.07\), at \(100^\circ\mathrm{C}\)—\(1.80\pm0.10\).
** From the infrared frequencies of water vapors (Bartholomew and Clusius \(^{10}\)) one obtains \(\varepsilon_{\mathrm{H_2O}}-\varepsilon_{\mathrm{HOD}}\) approximately \(1\,700\) cal.
The study of analogous equilibria would undoubtedly lead to an understanding of the different chemical and biological properties of light and heavy hydrogen compounds. In §§ 10 and 15 we shall return to this question.
§ 4. Ortho- and para-modifications of the molecule D₂.
Since the nucleus D has spin, the molecule D₂ (as a symmetric one) has, just like the molecule H₂, alternating para- and ortho-rotational states, between which there are no transitions under radiation or under ordinary impact.
At high temperature the distribution between the para- and ortho-states (by ortho-states are meant states with the greater nuclear statistical weight) is determined by
\[ \frac{[\mathrm{pD}_2]}{[\mathrm{oD}_2]}=\frac{i_{\mathrm{D}}}{i_{\mathrm{D}}+1} \tag{1} \]
where \(i_{\mathrm{D}}\) denotes the spin of the nucleus.
As the temperature is lowered this ratio shifts noticeably, when \(kT\) becomes smaller than the energy of the rotational state, i.e. for D₂ below \(80^\circ\mathrm{K}\). Of course, the establishment of equilibrium, just as in the case of the reaction \(\mathrm{pH}_2 \rightleftarrows \mathrm{oH}_2\), is delayed owing to the prohibition of the transition; however, as A. Farkas, L. Farkas, and P. Harteck\(^{57}\) showed, equilibrium can be established by activated charcoal and other catalysts. To detect the displacement of the equilibrium, the thermal-conductivity method developed by A. Farkas* was used.
It turned out that, as the temperature is lowered, \(\mathrm{oD}_2\) accumulates; whence it follows that Bose statistics is valid for the D nucleus and that the temperature dependence of the observed shifts in the concentrations of D₂ agrees best with the value \(i_{\mathrm{D}}=1\).
This result is in agreement with the analysis of the spectrum of D₂ and is also confirmed by measurements of the rotational heat of D₂ at low temperatures carried out by Clusius and Bartholomé\(^{35}\). Therefore, at high temperatures ordinary D₂ (\(\mathrm{nD}_2\)) consists of
\[ \frac{2}{3}\mathrm{oD}_2 \ \text{and}\ \frac{1}{3}\mathrm{pD}_2, \]
whereas at \(20.4^\circ\mathrm{C}\) D₂ in equilibrium consists of almost pure \(\mathrm{oD}_2\). The lowest state of the D₂ molecule (absence of rotation) is the ortho-state, in contrast to H₂, for which the para-state is the lowest.
The rotational specific heat of the different kinds of hydrogen is shown in Fig. 1, where the curves \(\mathrm{nH}_2\) and \(\mathrm{nD}_2\), according to Dennison, are considered as mixtures of ortho- and para-molecules. The asymmetric molecule HD has no ortho- and para-states.
As regards the orientation of the nuclear spin, the ortho-state (even rotational state) in D₂ is sixfold degen-
* Z. physik. Chem. 22, 344, 1933.
expected, the para state is expressed threefold, whereas the entire HD state is expressed sixfold. But this expression appears only at extremely low temperatures, when the nuclear magnets begin to orient themselves relative to one another in the crystal lattice.
The kinetics of the mutual conversion \(oD_2 \rightleftarrows pD_2\) is exactly the same as in the conversion \(pH_2 \rightleftarrows oH_2\). Of special interest are the rate constants of such conversion reactions caused by paramagnetic substances (see L. Farkas and H. Sachse, Z. phys. Chem. 23, 1 and 18, 1933). From the ratio of the rate constants, for example of the reaction \(pH_2 + O_2 \to oD_2 + O_2\), and the reaction \(pD_2 + O_2 \to oD_2 + O_2\), one can calculate the ratio of the magnetic moments of H and D. Experiment shows that the \(O_2\)-catalyzed reaction \(oD_2 \rightleftarrows pD_2\) at \(20^\circ\mathrm{C}\) proceeds 16 times more slowly than the reaction \(pH_2 \rightleftarrows oH_2\), and theoretically it follows from this that:
Fig. 1.
\[ \frac{\mu_P^2}{\mu_D^2} =16\cdot\frac{J_{D_2}}{J_{H_2}} \sqrt{\frac{36}{2\cdot34}}\cdot 1.39=32. \]
\(J_{D_2}\) and \(J_{H_2}\) are the moments of inertia of \(D_2\) and \(H_2\); the expression under the radical takes into account the different number of collisions of \(H_2\) and \(D_2\) with \(O_2\).* Thus the magnetic moment of D is 5.6 times smaller than that of the proton.
§ 5. Elasticity of \(D_2\) Vapors
The vapor pressure of heavy hydrogen \(\left(nD_2=\dfrac{2}{3}oD+\dfrac{1}{3}pD_2\right)\) was measured by Brickwedde, Scott, Urey, and Wahl \({}^{28}\), and subsequently by Lewis and Hanson et al. \({}^{104,105}\) (Table 4).
The large difference in the vapor pressures of the two isotopes is explained on the basis of a theoretical formula. In first approximation the ratio of the vapor pressures at a temperature of \(13.92^\circ\mathrm{K}\) is determined by the expression
\[ 2.3\lg\frac{P_{H_2}}{P_{D_2}} = -\frac{\varepsilon_{H_2}-\varepsilon_{D_2}}{RT} + \frac{\Phi_{H_2}-\Phi_{D_2}}{R} + \frac{3}{2}\lg\frac{M_{H_2}}{M_{D_2}}, \tag{1} \]
where \(\varepsilon_{H_2}-\varepsilon_{D_2}\) is the difference of the zero-point energies of the two condensates and \(\Phi_{H_2}-\Phi_{D_2}\) are the Debye functions, calculated for characteristic
\[ \text{* Regarding the factor }1.39\text{ see }{}^{57},\text{ where, however, on p. 492 one should read:} \]
\[ \frac{Z^{H_2}_{p\to0}}{Z^{D_2}_{p\to0}}=\frac{\mu_p^2}{\mu_D^2}. \]
temperatures \(\theta_{\mathrm{H}_2}=91\) and \(\theta_{\mathrm{D}_2}=100\) for the crystals of \(\mathrm{H}_2\) and \(\mathrm{D}_2\) at constant pressure. \(\theta_{\mathrm{D}_2}\) and the difference of the zero-point energies \(\varepsilon_{\mathrm{H}_2}-\varepsilon_{\mathrm{D}_2}\)* are taken from experimentally obtained vapor-pressure curves for \(\mathrm{H}_2\) and \(\mathrm{D}_2\); \(\varepsilon_{\mathrm{H}_2}-\varepsilon_{\mathrm{D}_2}\) proves to be equal to 93 cal. The heat of evaporation of \(\mathrm{D}_2\) at \(0^\circ\mathrm{K}\) is 276 cal, whereas for \(\mathrm{H}_2\) it is 183 cal.
The heat of fusion of \(\mathrm{D}_2\) is 53 cal, that of \(\mathrm{H}_2\) 28 cal. The vapor-pressure curve of \(\mathrm{D}_2\) thus reveals the existence of “zero-point” vibrations of the crystal lattice, which occur alongside the vibrations of individual molecules in the gas and in the crystal.
TABLE 4
| Temperature | Vapor pressure in mm | Vapor pressure in mm | Note |
|---|---|---|---|
| Normal \(\mathrm{H}_2\) | Normal \(\mathrm{D}_2\) | ||
| 23.5 | 1740 | 760 | Boiling point of n\(\mathrm{D}_2\) |
| 20.38 | 760 | 257 | ” ” n\(\mathrm{H}_2\) |
| 18.58 | 429 | 121 | ” melting of n\(\mathrm{D}_2\) |
| 13.92 | 54 | 5 | ” ” n\(\mathrm{H}_2\) |
The vapor pressure of mixtures \(\mathrm{H}_2+\mathrm{D}_2\) can be interpolated linearly from the vapor pressures of the pure substances. The compound HD behaves like \(50\%\mathrm{H}_2+50\%\mathrm{D}_2\) (within the limits of observational error). In addition, it should be noted that between the vapor pressures of n\(\mathrm{D}_2\) and pure o\(\mathrm{D}_2\) there is a small difference, since o\(\mathrm{D}_2\) at the boiling point of n\(\mathrm{H}_2\) has a vapor pressure 5 mm higher than n\(\mathrm{D}_2\).
Urey, Murphy, and Brickwedde \(^{153}\) theoretically predicted a large difference in the vapor pressures of \(\mathrm{H}_2\), HD, and \(\mathrm{D}_2\), and used it in the fractionation of liquid hydrogen in the first enrichment of heavy hydrogen carried out by them. In this way they succeeded in raising the normal ratio \(\mathrm{H}:\mathrm{D}\) from \(1:5000\) to \(1:800\).
Fractional distillation at present has no significance for the practical preparation of \(\mathrm{D}_2\); however, it should be mentioned that Keesom and coworkers \(^{93}\), in a very perfect fractionating apparatus, starting from ordinary hydrogen, obtained a heavy isotope concentrated to \(1.5\%\).
* From the theoretical equations
\[
\varepsilon_{\mathrm{H}_2}-\varepsilon_{\mathrm{D}_2}
=
\frac{9}{8}R\left(\theta_{\mathrm{H}_2(v)}-\theta_{\mathrm{D}_2(v)}\right)
\]
and
\[
\frac{\theta_{\mathrm{H}_2(v)}}{\theta_{\mathrm{D}_2(v)}}
=
\sqrt{\frac{M_{\mathrm{D}_2}}{M_{\mathrm{H}_2}}}
\]
one obtains the characteristic temperatures \(\theta_{\mathrm{H}_2(v)}=142.4\) and \(\theta_{\mathrm{D}_2(v)}=100.7\) for the Debye functions of the specific heat at constant volume of \(\mathrm{H}_2\) and \(\mathrm{D}_2\).
§ 6. Electrolytic Production of Heavy Water
The increase in the concentration of heavy hydrogen occurring as a result of the electrolysis of water was discovered by Washburn and Urey^157 and was then used by Lewis and Macdonald^108 for obtaining pure D₂O. This unexpected possibility of obtaining pure heavy water proved extremely valuable for investigations with the new isotope of hydrogen, and electrolysis is still the best method for isolating the heavy isotope of hydrogen.*
It was established experimentally that the hydrogen formed at the cathode always contains a lower concentration of D₂ than the water from which it is evolved. If we denote by \((\mathrm H)\) and \((\mathrm D)\) the concentrations of H and D in water, and by \((\mathrm H)v=a_{\mathrm H}\) and \((\mathrm D)v=a_{\mathrm D}\) the total contents of H and D in the volume \(v\), then the relation holds
\[ d \ln a_{\mathrm H}=s\,d \ln a_{\mathrm D}, \tag{1} \]
if the heavy isotope of hydrogen is formed \(s\) times more slowly than the light one. Integration of equation (1) shows that the concentration of heavy hydrogen during electrolysis is expressed by the so-called Rayleigh formula of fractional distillation
\[ \frac{(\mathrm H_0)}{(\mathrm H)}\cdot \left[\frac{(\mathrm D_0)}{(\mathrm D)}\right]^s = \left(\frac{v_a}{v}\right)^{s-1}; \tag{2} \]
\(s\) is determined from (1) and (2):
\[ \frac{[(\mathrm H)/(\mathrm D)]_{\text{gas}}} {[(\mathrm H)/(\mathrm D)]_{\text{water}}} =s. \tag{3} \]
This equation relates the isotopic composition of the gas obtained to the composition of the liquid.
The first experiments with electrolysis, carried out by Lewis and Macdonald, showed that \(s\) in formula (1) is of the order of 5. Fig. 2 shows the increase in the concentration of heavy water as a function of the ratio of the volumes \(\frac{v_a}{v}\). From it one sees that, in order to obtain pure D₂O from ordinary water, the initial volume must be reduced by electrolysis to \(10^{-6}\) of its value. The current consumption for one g of D₂O is thus \(10^9\) A-sec. at a voltage of 3.6 V, i.e. 100 kWh per 1 g of heavy water.**
Fig. 2.
* In spectroscopically pure form, D₂ was obtained by H. Gerth^60 by means of his diffusion method.
** The thermodynamic work for isolating 1 g of D₂O is only
\[ \frac{RT}{18}\ln 5000=2\cdot 10^{-5}\ \mathrm{kWh}. \]
Lewis and Macdonald carried out the electrolysis of water in several stages in an alkaline solution with nickel electrodes; at each stage the alkaline solution, which at first was approximately \(0.5\)-normal, was brought to \(0.1\)-normal, then neutralized with the aid of \(\mathrm{CO}_2\), and after distillation was again made alkaline. When the water already contains several percent of D, it seems advantageous to burn the hydrogen formed during electrolysis, so that in the course of further concentration there are no longer any losses of D.*
Owing to the fact that, during the electrolysis of water, separation of isotopes occurs, electrolytic residues (for example, the acid from old accumulators) have a higher content of D than ordinary water, and they can be used as starting material for obtaining heavy water.** With a separation coefficient of about 5 in the stationary state, with repeated replenishment by ordinary water, the water in the bath will obviously contain \(0.0002 \cdot 5 = 0.001\) \((0.1\%)\) D. The point is that at this concentration of D in the water the hydrogen escaping contains the same amount of D as ordinary water. This stationary state is reached when the water used to replenish the electrolytic liquid is approximately 10 times the volume of the electrolyte.
Electrolytic separation of heavy hydrogen can also be carried out in an acid solution and with an analogous separation coefficient on other metals (Table 5 and works 12, 147, 148).
TABLE 5
| Cathode | Separation coeff. *** |
|---|---|
| Lead | 6.3—7.4 |
| Platinum | 4.7—7.6 |
| Activated platinum | 3.4—4.7 |
| Iron | 6.9—7.6 |
| Nickel | 4.0—6.5 |
| Copper | 5.5—6.8 |
| Silver | 5.3—6.0 |
| Mercury | 2.8—2.9 |
The separation coefficient, apparently, depends almost not at all on the concentration of D. P. Harteck \(^{79}\), at different degrees of concentration \((0.33\%\,\mathrm{D} \to 5.3\%\,\mathrm{D},\ 0.48\%\,\mathrm{D} \to 27.0\%\,\mathrm{D}\) and \(12\%\,\mathrm{D} \to 91.5\%\,\mathrm{D})\), obtained \(s = 5.5\) to 6.5.
The mechanism of the electrolytic separation of both hydrogen isotopes is undoubtedly very complex. Three different processes must play a role here:***
- The rate of discharge of \(\mathrm{H}^{+}\) and \(\mathrm{D}^{+}\) ions at the cathode.
- The rate of conversion of H and D atoms into molecular gases on the cathode metal.
* For relatively suitable apparatus for electrolysis and combustion of detonating gas containing D, see, for example, the works of Harteck \(^{79}\), Topley and Eyring \(^{149, 143, 168, 173}\).
** From Fig. 2 it is evident that precisely at the beginning concentration requires large quantities of liquid.
*** Differences in the rates of transfer of \(\mathrm{H}^{+}\) and \(\mathrm{D}^{+}\) ions can hardly cause separation. This could occur only in acid solutions, since the rate of diffusion of ions is usually greater than the rate of transfer.
**** The current density in electrolysis is approximately \(0.7\ \mathrm{A}/\mathrm{cm}^{2}\).
3. Establishment of the equilibrium
\[ [\mathrm{H_2O}]_{\mathrm{liquid}}+\mathrm{HD}\rightleftarrows[\mathrm{HOD}]+\mathrm{H_2} \tag{4} \]
at the cathode.
The first process is associated with overvoltage. According to modern views, overvoltage depends on the fact that the discharge of ions on the metal requires heat of activation. According to the views of Volmer, Erdey, and Grusz, the proton overcomes a potential barrier which lies between the hydrated ion and the electrode before it is discharged on the electrode surface; hence it is clear that, depending on the height of this potential barrier, a greater voltage must be applied for the discharge of the ion than for a “reversible” discharge. According to Gurney, overvoltage is likewise determined by the potential barrier between the hydrated ion and the cathode surface, but, in the opinion of the latter, discharge occurs through the passage of electrons across this potential barrier. According to both views, the cause of isotope separation may be the different rates of discharge of the hydrated ions H\(^+\) and D\(^+\).
A number of theoretical works (Polanyi \(^{127}\), Topley and Eyring \(^{149}\), Fowler \(^{66}\), Bell \(^{13}\)) deal with the connection between overvoltage and the electrolytic separation of both hydrogen isotopes. The separation coefficients obtained theoretically are usually larger than those actually observed, which speaks in favor of the fact that, in addition to process 1, other processes also play a role, for example, process 3. However, the experimental material is too scanty to permit a definitive judgment, and above all it is necessary to study the connection between overvoltage and the electrolytic separation of isotopes by direct experiments.
The role of equilibrium 4 in the electrolysis of water was indicated by A. Farkas and L. Farkas \(^{58,62}\). Since the equilibrium constant of process (4) at room temperature is 3.3 (§ 3, 7), then, upon establishment of this equilibrium, the hydrogen formed at the cathode contains less D than the water. It can be shown by direct calculation that the separation coefficient defined by equation (3) is approximately equal to the equilibrium constant of reaction (4), i.e.
\[ s \approx K_4. \]
The separation coefficient in obtaining hydrogen from water should therefore, at room temperature, be approximately 3.3.
A. and L. Farkas \(^{58}\) did indeed show that equilibrium (4) is established during electrolysis on the surface of the cathode: water with a 26% D content was subjected to electrolysis in a 0.2-n alkaline solution in a small U-shaped tube with nickel electrodes, yielding hydrogen with a 9.9% D content. This hydrogen did not change its D content if it was stored together with the same water in the presence of palladium black, whereas
ordinary hydrogen in the presence of palladium and water with a 26.2% D content after some time reached the same concentration as electrolytically obtained hydrogen.
The separation coefficients measured by Topley and Eyring^149 on activated platinum (3.4–3.6) likewise correspond to “equilibrium separation,” and it should generally be expected that complete establishment of equilibrium will occur precisely on very active metallic surfaces.
Of course, in these experiments the rate of the equilibrium reaction was sufficiently high to bring about complete establishment of equilibrium; in this case kinetic considerations are inapplicable for determining the magnitude of the separation.
The electrochemically equilibrium constant \(K = 3.3\) signifies a higher “discharge potential” for the ion \(\mathrm{D}^+\). However, when both isotopes are evolved, the situation is different from the electrolytic separation of two metals. On the other hand, as a consequence of the exchange reaction (4), the evolution of both isotopes at equilibrium occurs at a voltage considerably higher than their “discharge potential,” in the ratio corresponding to their equilibrium constant (4). From a practical point of view this is important because enrichment in the heavy isotope during the electrolysis of water occurs, of necessity, with a separation coefficient of 3.3 without taking precautionary measures.
The magnitudes of the equilibrium reaction during electrolysis in those cases where the separation coefficient is greater than the equilibrium constant cannot be indicated. In § 15 this question will be discussed further. Under what conditions (besides those already considered) equilibrium is established remains to be investigated.
§ 7. Properties of Heavy Water
Of the compounds of heavy hydrogen, the properties of heavy water have been investigated best of all. Pure heavy water was first obtained by Lewis and Macdonald^108–110 by repeated electrolysis of water, the density reaching the limiting value 1.1056 at 20° C. Table 6 contains the results of investigations of the properties of \(\mathrm{D_2O}\).
Qualitatively, the properties of \(\mathrm{D_2O}\) can be understood on the basis of Bernal and Fowler’s theory^14. According to this theory, cold water consists of four molecules associated in the form of a regular pyramid, which to a certain degree are oriented relative to one another, so that water should in essence be regarded as “soft ice.” In \(\mathrm{D_2O}\) this association and orientation are somewhat stronger because of the lower zero-point energy, so that the melting and boiling points and the temperature of maximum density are higher. The quantitative side of this theory has not yet been developed, but the possibility of studying the same properties in a molecule with a different isotope facilitates the theoretical treatment.
TABLE 6
Properties of D\(_2\)O
| Properties | H\(_2\)O | D\(_2\)O | Literature |
|---|---|---|---|
| 1. Ice lattice constant near the melting point, \(a\) | 4.525 Å | 4.505 Å | 65 |
| 1. Ice lattice constant near the melting point, \(c\) | 7.39 Å | 7.36 Å | — |
| 2. Volume of the unit cell | \(131\cdot 10^{-24}\ \mathrm{cm}^3\) | \(128\cdot 10^{-24}\ \mathrm{cm}^3\) | 65 |
| 3. Density at 20° C | 0.9982 | 1.1056 | 107, 116, 145 |
| 4. Relative molar volume at 20° C | 1 | 1.0037 | — |
| 5. Melting point | 0 | 3.82 | 109 |
| 6. Boiling point | 100 | 101.42 | 109 |
| 7. Maximum density | 4 | 11.6 | 109 |
| 8. Heat of vaporization | \(L\) | \(L\)—259 | 109 |
| 9. Dielectric constant | 82 | 80.5 | 112 |
| 10. Viscosity at 20° C | 10.09 | 12.6 | 110 |
| 11. Surface tension | 72.75 | 67.8 | 139 |
| 12. Magnetic susceptibility | \(-0.72\cdot 10^{-6}\) | \(-0.65\cdot 10^{-6}\) | 139 |
| 13. Refractive index \(n_{20}^{D}\) | 1.33300 | 1.32844 | 30 |
| 14. Transport velocity at 18° C, K\(^+\) | 64.2 | 54.5 | 116, 139 |
| 14. Transport velocity at 18° C, Cl\(^-\) | 65.2 | 55.3 | 103 |
| 15. H\(^+\) or D\(^+\) | 315.2 | 213.7 | |
| 16. Solubility at 25° C (g/2 water), NaCl | 0.359 | 0.305 | 142 |
| 16. Solubility at 25° C (g/2 water), BaCl | 0.357 | 0.289 |
Density \(^{107}\), melting point \(^{95}\), refractive index \(^{116}\), vapor pressure \(^{109}\) of diluted heavy water may be obtained by interpolation (almost linear) between the constants for H\(_2\)O and D\(_2\)O. However, the exact formulas contain quadratic terms, which is due to the fact that, on the one hand, HOD does not behave as 50% H\(_2\)O + 50% D\(_2\)O, and, on the other, certain interactions occur among HOD, H\(_2\)O, and D\(_2\)O in the mixture.
Table 7 gives the vapor pressure of H\(_2\)O and D\(_2\)O between 20 and 100° C \(^{109}\).*
TABLE 7
Vapor pressure of D\(_2\)O
| °C | \(p_{\mathrm{H_2O}}\) | \(p_{\mathrm{D_2O}}\) |
|---|---|---|
| 20 | 17.5 | 16.2 |
| 30 | 31.8 | 27.9 |
| 40 | 55.3 | 49.2 |
| 50 | 95.5 | 83.4 |
| 60 | 149.2 | 136.1 |
| 70 | 233.5 | 215.5 |
| 80 | 355.1 | 331.2 |
| 90 | 525.8 | 495.1 |
| 100 | 760.0 | 721.6 |
The decrease of vapor pressure with increasing D content is the reason that water containing D,
* Lewis and Cornish used the different vapor pressures of H\(_2\)O and D\(_2\)O for fractionating water. It turned out that the density of the water at the top
is very hygroscopic. This should be borne in mind when working with heavy water.
The vapor pressures have also been investigated, besides heavy water, for ND₃, CH₃COOD, DCl, and DCN. ND₃ has a lower vapor pressure, CH₃COOD a higher one, and DCl and DCN almost the same vapor pressure as the corresponding H compounds. This shows that the vapor pressure of compounds containing H and D is affected by various factors, and the matter is more complicated here than for H₂ and D₂ (see § 5). According to Lewis and Schutz¹¹⁴ᵃ, the low vapor pressure of D₂O and ND₃ is explained by stronger association owing to stronger D bonds in the liquid as compared with H₂O and NH₃; in CH₃COOD the same circumstance causes a higher vapor pressure. In DCl and DCN this effect plays no role, as a result of which, to a first approximation, the vapor pressure in the H and D compounds is the same.
§ 8. Methods for Determining the Concentration of D in a Mixture of Both Isotopes
A number of methods have been developed for determining the content of D in water and in hydrogen; however, they cannot be considered in detail here.
The most accurate method, applicable also to large quantities of water, is the determination of the density of water.* From the formula of Lewis and Luten¹⁰⁷ for the specific gravity of water with different D content, it follows, for the fraction \(x_D\) at 25°C, that
\[ x_D = 9.579\,\Delta s - 1.03\,(\Delta s^2), \tag{1} \]
where \(\Delta s\) is the difference between the specific gravities of the water being studied and ordinary water.
The density of water is determined pycnometrically or by the float method. In the best case the density can be determined with an accuracy up to \(2:10^7\), which corresponds, in round numbers, to a \(2\cdot 10^{-6}\) fraction of D (see Briscoe and co-workers⁴⁸).
For determining water in small quantities (about 10 mg), Gilfillan and Polanyi⁶⁹ developed a micropynometric method (see also⁷¹).
In principle, besides density determination, any constant of water may be used for determining the content, provided only that its value differs sufficiently for H₂O and D₂O. Analysis of D in water on the basis of the different refractive indices of H₂O and D₂O has so far found little application. This method was developed by Lewis and Luten¹⁰⁷ and by Crist, Murphy, and Urey³⁹, ³⁹ᵃ.
and at the bottom of the 7-m fractionating column differed by 70 per mille, the content of D and O¹⁸ in the water at the bottom being greater. See also, concerning the fractional distillation of water, works⁷⁵ and¹⁶⁰.
* Heavy water has a lower refractive index.
HEAVY ISOTOPE OF HYDROGEN
The change in the refractive index for the yellow sodium line (5893 Å) at 25°C is proportional to the content of D in water:
\[ x_D=-\frac{\Delta R}{0.00449}. \]
It should be noted that, by measuring the refractive index and density of water, one can determine, in addition to the content of D, also the change in the ratio \(O^{16}:O^{18}\). In fractional distillation of water, this method can be used to determine the shift in the ratio of both isotopes.
For determining the concentration of D in hydrogen, two methods have been developed: Bleakney’s mass-spectroscopic method \(^{17-19}\) and the micromethod of thermal conductivity of A. and L. Farkas \(^{55,56}\).
Bleakney’s method is based on comparison of the intensities of \(H_2^+\) ions with \(HD^+\) ions in the mass spectroscope and is especially important for determining small concentrations of D \((<0.02\%)\) and for absolute determinations of the content of D in ordinary water and hydrogen, since in these cases the density-determination method cannot be directly applied.
The thermal-conductivity micromethod is based on the different change in the specific heat of various kinds of hydrogen at low temperatures (Fig. 1); it was originally developed by A. Farkas for measuring the concentration of para- and orthohydrogen (for details see Z. physik. Chem. 22, 344, 1933). The method of measurement requires empirical calibration with hydrogen of known D content; it can be applied only for concentrations above 1%. The advantage of this method is that within several minutes in \(1—2\cdot 10^{-3}\ \text{cm}^3\) of gas at atmospheric pressure one can determine not only the content of D with an accuracy of several per mille, but also the ratios \(H_2:HD:D_2\); sometimes also \(pH_2\), \(oH_2\), \(HD\), \(pD_2\), \(oD_2\).
The possibility of determining the content of D in a small sample of gas is important in studying reaction kinetics, so that this method is especially suitable for such work.
The determination of D in water (other compounds with hydrogen are first converted into water) is carried out in such a way that water vapor, with the aid of a clean tungsten wire, is converted into hydrogen and \(WO_3\) \(^{56}\). This decomposition method has the advantage that the tungsten wire can readily be degassed at high temperature and the heat capacity of the hydrogen obtained can be determined without further purification.
The usual thermal-conductivity method of Schleiermacher, in the form in which it was applied by Bonhoeffer and Harteck (Z. physik. Chem. 4, 113, 1928) for determining the concentrations of \(pH_2\) and \(oH_2\), can also be used in determining the content of D.
Owing to the difference in the masses of the molecules \(H_2\), \(HD\), and \(D_2\), their molecular velocities are related as
\[ C_{H_2}:C_{HD}:C_{D_2}=\frac{1}{\sqrt{2}}:\frac{1}{\sqrt{3}}:\frac{1}{\sqrt{4}}; \]
are in the same ratio as their coefficients of thermal conductivity. Hence it is clear that, in determining the content, this method can be very sensitive, provided only that one has at one’s disposal a sufficient quantity of gas (1–2 cm³ at atmospheric pressure).
§ 9. Distribution of the Heavy Isotope of Hydrogen in Nature
The first determination of the concentration of D in ordinary water was made by Urey, Brickwedde, and Murphy[^153]. Comparing the intensities of the Balmer lines H and D, they obtained a ratio of 1 : 4,500. The same ratio of H to D was proposed by Birge and Menzel[^16] to explain the discrepancy between the values of the atomic weight of hydrogen determined mass-spectroscopically and chemically. At the present time the most accurate value of the ratio of D to H in water is 1 : 5,000; it was obtained by means of mass-spectroscopic analysis by Bleakney and Gould[^18][^19].
The distribution of the heavy isotope in nature has been investigated by various authors. Table 8 gives some results concerning the specific gravity of various water samples.
TABLE 8
| Origin | $\Delta s \cdot 10^6$ | Author |
|---|---|---|
| Rain water in Princeton . . . | $\dfrac{\mathrm{H}}{\mathrm{D}}=\dfrac{1}{5000}$ | Bleakney and Gould[^18][^19] |
| Water on the surface of the sea near London, Wales, and Sumatra . | 0 | Briscoe and co-workers[^48] |
| Water from the Dead Sea . . . . | +3.0 | Same |
| Sea water from a depth of 3,000 m | +2.3 | Gilfillan[^70] |
| Water in human blood . . . . | +1.5 | » |
| » in milk . . . . | +3.0 | » |
| » in urine . . . . | +0 | » |
| Water in the sap of weeping willow . . . | +2.8 | Washburn[^163] |
| » » fibers . . . . | +5.4 | » |
| » » fruits . . . . | +0 to 5.0 | Briscoe[^48] |
| » » honey . . . . | +4.0 | Dole[^45] |
| Crystalline water in various minerals . . . . | +3.0 to 7.5 | Briscoe and co-workers[^48] |
The D content in water on the surface of the earth is not subject to any appreciable fluctuations, which is quite natural, since, owing to exchange with atmospheric moisture, the concentration is everywhere equalized.
A change in the specific gravity of this standard water is observed in the investigation of water from living organisms or minerals.
The deviation reaches several units per million, which means approximately the same number of units of D per 100,000 parts of water. Deviations in the concentration of D from the norm (1:5,000) have various causes. For example, enrichment may occur because of fractional evaporation (as, for example, in the Dead Sea), since light water has a somewhat greater vapor pressure than heavy water, or because of the position of equilibrium in which light and heavy water participate. This, apparently, takes place in the crystalline water of various salts, where heavy water is bound to the crystal somewhat more strongly than light water. The same cause apparently brings about a greater content of D in liquids found in the bodies of various organisms, especially in those cases where a higher content of D is found in the hydrogen of organic compounds (for example, the acetone—water equilibrium in § 3).
Of special interest is the content of D in hydrogen. The equilibrium constant \(K = 3.3\) at \(20^\circ\mathrm{C}\) for the reaction \(\mathrm{H_2O} + \mathrm{HD} \rightleftarrows \mathrm{HOD} + \mathrm{H_2}\) is the reason that hydrogen in equilibrium with water contains only from 1:15,000 to 1:20,000 D, whereas hydrogen obtained by complete decomposition of water has the normal D content of water. Discrepancies in the first determinations of D by different authors in hydrogen were caused by this difference in D content.
It should be borne in mind that hydrogen obtained by partial decomposition of water at low temperatures (electrolysis, dissolution of metal in water or acid) usually shows a lower concentration than 1:5,000.
§ 10. Causes of the Different Reaction Rates of Compounds Containing H and D
One of the numerous areas of application of the heavy isotope of hydrogen is the kinetics of inorganic and organic reactions. Hydrogen takes part in almost all important reactions, and, by replacing light hydrogen (wholly or partially) with the heavy isotope, it is possible to study the rate of the “isotopic reaction.”
A change in rate and, in particular, the study of the path of hydrogen during the course of a reaction in many cases gives indications concerning the mechanism of the reaction. Replacement of the atom H by an atom D in some compound corresponds to labeling the molecule, which is especially important in biological and physiological chemistry, since it is sometimes possible to follow the path and transformations of the labeled substance in the organism.
Also very important are cases in which some compound loses the atom D as a result of exchange for the atom H of another compound; investigations of such an exchange reaction shed light on transformations that could not have been studied without isotopic substitution.
The various possibilities for applying heavy hydrogen in kine-
such reactions have been investigated in a whole series of works. Let us first consider the various phenomena that can give rise to different reaction rates of the two isotopes. Along with the comparison of the rates of reactions of pure H and D compounds with a third substance, separation in the reactions of their compounds also plays a role. The separation coefficient was determined by us in § 6 by equations (1) and (3); in the general case \(s\) cannot be calculated from the reaction rates of the pure substances, since the separation also depends on reverse reactions and on exchange reactions of the H and D compounds.
The simplest case is the comparison of the rates of two bimolecular reactions:
\[ A_{\text{light}} + X \to B_{\text{light}} + Y \tag{1} \]
\[ A_{\text{heavy}} + X \to B_{\text{heavy}} + Y, \tag{1a} \]
where the rate constants in the first approximation are given by the expressions
\[ k_{\mathrm H}=C\sqrt{\mu_{\mathrm H}a_{\mathrm H}^{2}}\,e^{-\frac{Q_{\mathrm H}}{RT}} \]
and
\[ k_{\mathrm D}=C\sqrt{\mu_{\mathrm D}}\cdot a_{\mathrm D}^{2}\cdot e^{-\frac{Q_{\mathrm D}}{RT}} \]
(the subscripts H and D refer to the light and heavy hydrogen compound). Thus three quantities affect the reaction rate: the reduced mass \(\mu\), the collision distance \(a\), and the heat of activation \(Q\).
The difference in the reduced masses in reactions of H and D, or \(H_2\) and \(D_2\), appears most strongly; their ratio in this case is 2. A heavy atom or molecule of hydrogen, for equal \(a_{\mathrm H}=a_{\mathrm D}\) and \(Q_{\mathrm H}=Q_{\mathrm D}\), should react 1.4 times more slowly than H and \(H_2\), since the numbers of impacts differ from one another by this factor.
As for the influence of different collision distances, here one can expect only insignificant differences; in collisions of \(H_2\), HD, and \(D_2\) with X or with one another, owing to the smaller amplitude of the zero-point energy in heavy hydrogen, the collision distance may be somewhat smaller, as may also the number of collisions. In general, however, one may assume \(a_{\mathrm H}=a_{\mathrm D}\).
The heats of activation of two neighboring reactions are, in general, not identical; namely, as Cremer and Polanyi \(^{38}\) and Eyring \(^{51}\) have shown, light hydrogen compounds have a lower heat of activation. Owing to the greater zero-point energy of light hydrogen compounds, they possess a greater store of energy, and, in the adiabatic course of the reaction, this energy goes toward overcoming the potential barrier separating the configuration \(A+X\) from the configuration \(B+Y\). Therefore the activation energy—the difference between the potential barrier and the initial state—will be, for light hydro-
...hydrogen is less by the difference of the zero-point energies, and for the ratio of the rate constants of the reactions we obtain:
\[ \frac{k_{\mathrm H}}{k_{\mathrm D}} = \sqrt{\frac{\mu_{\mathrm H}}{\mu_{\mathrm D}}}\, e^{-\frac{\varepsilon_{\mathrm H}-\varepsilon_{\mathrm D}}{RT}} . \tag{2} \]
It follows from this that, from the theoretical point of view, the bimolecular reaction of \(\mathrm{H}_2\) with any \(X\) should proceed at room temperature \(\sqrt{2}\cdot e^{\frac{1789}{RT}}\sim 28\) times faster than the corresponding reaction of \(\mathrm{D}_2\).
Some exceptions are the reactions of H and D. Since they have no zero-point energies, the heats of activation of their reactions are, in the first approximation, equal to one another. The rate of reaction of the light hydrogen atom is also greater in this case than that of the heavy one (by a factor of 2), but here the ratio of rates does not depend on temperature.
In the second approximation, as Polanyi has pointed out\(^{128}\), the bimolecular reaction of the D atom may be accelerated in comparison with the corresponding reaction of the H atom owing to the circumstance that the “saddle” of the potential barrier lying between the initial and final states has, for the D reaction, a more favorable configuration (for details see in 11). Up to now, however, not a single example of such behavior of D has been found.
Wigner showed (Z. physik. Chem. 19, 203, 1933) that some of the H atoms during the exchange reaction \(\mathrm{H}+\mathrm{H}_2\to \mathrm{H}_2+\mathrm{H}\) react not mechanically, i.e. do not overcome the potential barrier, but penetrate through it (tunnel effect). In all reactions which proceed wholly or partly non-mechanically, one can observe a lower rate arising as a consequence of the greater mass of heavy hydrogen (see, for example, Cremer and Polanyi\(^{38}\)).
Further, one can predict the “separation” of two isotopic compounds in certain substitutions proceeding under equilibrium conditions.
In § 3 it was indicated that the equilibrium constants of the reactions
\[ \mathrm{A}_{\text{light}}+X \rightleftarrows \mathrm{B}_{\text{light}}+Y \tag{3} \]
\[ \mathrm{A}_{\text{heavy}}+X \rightleftarrows \mathrm{B}_{\text{heavy}}+Y \tag{3a} \]
are in general not identical. If, for example, \(\mathrm{B}_1+\mathrm{B}_s\) is removed from the reacting mass \(A, B, X, Y\) in such a way that the equilibria (3) and (3a), and also the equilibrium
\[ \mathrm{A}_{\text{light}}+\mathrm{B}_{\text{heavy}} \rightleftarrows \mathrm{A}_{\text{heavy}}+\mathrm{B}_{\text{light}} \tag{4} \]
can continually be established, then separation of the isotopes will occur in accordance with the constant \(K\): the D content in \(\mathrm{B}_1+\mathrm{B}_s\) differs from the D content in \(\mathrm{A}_1+\mathrm{A}_s\) (A and B are assumed to be present in equal numbers of molecules), so that either compound A or compound B increases its D content.
*
Separation of this kind usually does not occur in pure form; however, already in discussing the electrolysis of water (§ 5) we pointed out that, under certain conditions, the equilibrium reaction
\[ \mathrm{H_2O} + \mathrm{HD} \rightleftharpoons \mathrm{HOD} + \mathrm{H_2} \]
can by itself cause separation of both isotopes of hydrogen. The question of how large a role this kind of separation plays in any particular reaction must be discussed separately in each case.
§ 11. Exchange reactions in a homogeneous gas space
One of the simplest exchange reactions is the reaction
\[ \mathrm{H_2} + \mathrm{D_2} \rightleftharpoons 2\mathrm{HD}. \tag{1} \]
It was investigated by A. and L. Farkas\(^{55}\), and it turned out that this reaction (in pure quartz vessels) proceeds at an appreciable rate (at pressures of several millimeters) only at temperatures above \(600^\circ\mathrm{C}\). Its heat of activation lies between 55 and 60 kg-cal; its order is between \(3/2\) and 2. The formation of HD accordingly occurs partly by atomic reactions (of order \(3/2\)):
\[ \mathrm{H} + \mathrm{D_2} \rightleftharpoons \mathrm{HD} + \mathrm{D} \tag{2} \]
\[ \mathrm{D} + \mathrm{H_2} \rightleftharpoons \mathrm{HD} + \mathrm{H}, \tag{3} \]
and partly directly by reaction (1) (of order 2). The rate constants of the separate reactions are not yet known. A comparison of the rates of (2) with the thermal conversion of parahydrogen
\[ (\mathrm{H} + \mathrm{H_2} \rightleftharpoons \mathrm{H_2} + \mathrm{H}) \]
would show to what extent the zero-point energy affects the rate of reaction in this simplest case. On the basis of the conclusions of § 10 these two constants should be in the ratio
\[ \sqrt{2} e^{-\frac{1789}{RT}}, \]
whence it follows that constant (3) and the rate constant of the “thermal conversion of ortho-para-\(\mathrm{D_2}\)”
\[ \mathrm{D} + \mathrm{D_2} \rightleftharpoons \mathrm{D_2} + \mathrm{D} \]
are in the same ratio.
The rates of the reverse reactions \(\mathrm{HD} + \mathrm{D}\) and \(\mathrm{HD} + \mathrm{H}\), on the other hand, would show to what extent in these cases the heat of activation changes upon isotopic substitution.
At room temperature a mixture of \(\mathrm{H_2} + \mathrm{D_2}\) is stable in the absence of catalysts.
The following simple exchange reaction in a homogeneous gas phase is as follows:
\[ \mathrm{H_2O}+\mathrm{D_2}\rightarrow \mathrm{D_2O}+\mathrm{H_2} \tag{4} \]
\[ \rightarrow \mathrm{HOD}+\mathrm{HD}, \tag{4a} \]
where reaction (4a) proceeds as an atomic one, and reaction (4) as a molecular exchange reaction of the type \(\mathrm{H_2}+\mathrm{J_2}\rightleftarrows 2\mathrm{HJ}^{55}\). In reaction (4) no mixed \(\mathrm{HD}\) molecules are formed; therefore the two reactions can be separated from one another, although they proceed at similar rates. The heat of activation of both reactions is about 60 kg-cal, as a result of which no exchange occurs between heavy hydrogen and water vapor or liquid water at room temperature in the absence of catalysts either.^72 Other exchange reactions in a homogeneous gas phase have not yet been studied; however, it may be said that substitutions of types (2) and (4a) between light and heavy hydrogen compounds must in any case occur when the concentration of H and D atoms becomes appreciable at the dissociation equilibrium (above \(550^\circ\mathrm{C}\)) or when these atoms capable of reaction are introduced into the reacting mass photochemically.
§ 12. Exchange reactions in a homogeneous solution
Whereas at low temperatures in the gaseous state no exchange occurs between H and D atoms in light and heavy hydrogen compounds, in solutions of various compounds in water exchange reactions take place if ionizable groups are present. Lewis^98 and Bonhoeffer and Braun^23 studied, as the first example of such exchange reactions, which proceed as a result of ionization processes, the dissolution of \(\mathrm{NH_3}\) and \(\mathrm{NH_4Cl}\) in water with a small D content. Exchange occurs here as a result of the reaction:
\[ \mathrm{NH_3}+\mathrm{HOD}\rightleftarrows \mathrm{NH_3D^+}+\mathrm{OH^-} \tag{1} \]
\[ \mathrm{NH_3}+\mathrm{D^+}\rightleftarrows \mathrm{NH_3D^+}. \tag{1a} \]
The rate of exchange is immeasurably great, as was to be expected by analogy with most ionic reactions. Bonhoeffer and co-workers^21,24 (see also^74) investigated the exchange of H and D atoms with water in a whole series of organic compounds. It turned out that H or D atoms bound to O or N exchange rapidly with water, whereas those bound to C do so only when a CO group is also bound to the given C atom. Table 9 gives some examples of exchange of hydrogen atoms between organic compounds and water.
In hydroxyl groups and in hydrogen atoms bound to N, exchange occurs by direct ionization and, apparently, rapidly when the latter is not large (for example, in sugar).
In acetone in alkaline solution the rate of exchange is determined by the rate of enolization, which proceeds according to the formula
\[
\mathrm{CH_3COCH_3 \rightleftarrows CH_3C{=}CH_2}
\]
\[
\hspace{5.2em}\mathrm{|}
\]
\[
\hspace{5.0em}\mathrm{OH}
\]
whereby the H atoms of the OH group undergo ionization.
The hydrogen atoms of other organic molecules cannot be so simply replaced by D. For this purpose one must use either intermediate reactions (for example, according to Bonhoeffer\({}^{21}\), alcohol obtained by fermentation from D-containing sugar has D in the \(\mathrm{CH_3}\) group) or catalytic reactions.*
TABLE 9*
Exchange by hydrogen atoms between organic compounds and water
| Compound | Reaction |
|---|---|
| Benzene | No exchange |
| \(\mathrm{CH_3COONa}\) | * |
| Acetic aldehyde | Slow exchange over a short time |
| \(\mathrm{CH_3COCH_3}\), neutral | Very slow exchange |
| \(\mathrm{CH_3COCH_3}\), alkaline | Rapid exchange |
| Cane sugar | Exchange by hydrogen atoms in hydroxyl groups |
| Glucose | Exchange by hydrogen atoms in hydroxyl groups |
| Cellulose | Exchange by hydrogen atoms in hydroxyl groups |
| Protein | At least bound C-atoms undergo exchange |
§ 13. Catalytic exchange reactions
Whereas \(\mathrm{H_2 + D_2}\) in a homogeneous gaseous space, as already mentioned, forms HD molecules through exchange only at high temperatures, on metallic surfaces (nickel, platinum, etc.) exchange proceeds very readily (A. and L. Farkas\({}^{55,56}\)). The mechanism of this exchange is the same as in the catalytic conversion of ortho- and parahydrogen. The \(\mathrm{H_2}\) and \(\mathrm{D_2}\) molecules, upon adsorption on the metal, split into atoms; upon desorption, \(\mathrm{H_2}\), HD, and \(\mathrm{D_2}\) molecules arise in thermal equi-
* See §§ 13 and 74. In general, one should expect that all H and D atoms in an organic compound gradually exchange with the atoms of water or another organic compound in the presence of Pt, Ni, Pd, etc.
** Acetylene in alkaline solution exchanges its H atoms with water, as should also be expected on the basis of the acidic character of these atoms.
HEAVY ISOTOPE OF HYDROGEN
...weights. The parallelism of the catalytic formation of HD and the conversion of parahydrogen was proved directly by the experiments of Bonhoeffer and Fajans²². The reaction \(H_2 + D_2 \rightleftarrows 2HD\) proceeds on the catalyst approximately 3 times more slowly than the parahydrogen conversion
\[ pH \rightleftarrows oH. \]
However, between the catalysis of the parahydrogen conversion and the reaction \(H_2 + D_2 \rightleftarrows 2HD\) on some catalysts there is a fundamental difference. The reaction \(pH_2 \rightleftarrows oH_2\) can proceed, owing to the magnetic forces of the adsorbent, as a true monomolecular reaction in the adsorbed state, with the nuclear magnets of the hydrogen molecule turning in different directions. The reaction \(H_2 + D_2 \rightleftarrows 2HD\), however, can occur only by exchange of the atoms of two molecules, for which \(H_2\) and \(D_2\) must dissociate. This difference can be demonstrated by adsorbing pure hydrogen, on the one hand, and \(H_2 + D_2\), on the other, on charcoal at \(78^\circ K\). In the first case the equilibrium \(pH_2 - oH_2\) is established in a few minutes, whereas in the second case even after several hours no appreciable formation of HD is observed (A. and L. Farkas⁵⁶).
Another simple catalytic exchange reaction occurs between \(C_2H_4\) and hydrogen on nickel, for example (A. Farkas, L. Farkas and E. Rideal⁵⁹). The exchange reaction
\[ C_2H_4 + HD \rightleftarrows C_2H_3D + H_2 \tag{1} \]
leads to equilibrium, with H and D distributed between free hydrogen and ethylene approximately equally. This exchange reaction occurs alongside the conversion of ethylene into ethane and, at temperatures above \(100^\circ C\), proceeds considerably faster than hydrogenation. At low temperature, on the contrary, the rate of hydrogenation is greater, and since an analogous exchange reaction with ethane does not take place, the final concentration of D in these cases is not determined by reaction (1). Investigation of this catalytic reaction promises to yield important results concerning the bonding of hydrogen in organic molecules, as well as concerning the adsorption state of these compounds on the catalyst.
A very important catalytic reaction is also the establishment of equilibrium between liquid water and gaseous hydrogen:
\[ (H_2O)_{\text{liquid}} + HD \rightleftarrows (HOD)_{\text{liquid}} + H_2. \tag{2} \]
It was investigated by Horiuti and Polanyi⁸⁵, ⁸⁶ and by Bonhoeffer and Rummel²¹, ²⁵. Platinum and palladium powder suspended in water cause rapid establishment of equilibrium, the final concentration of D in the water and in the hydrogen being determined by the equilibrium constant (2) (see § 3). Table 10 gives the results of an experiment by A. and L. Farkas⁵⁸—establishment of equilibrium between 26.2% \(D_2O\) and \(H_2\). The course of the experiment in time is distorted owing to diffusion effects
however, it is nevertheless clearly evident that the distribution of H and D in water and hydrogen corresponds to an equilibrium constant of about 3.3.
According to Polanyi and Horiuti^86, the exchange reaction (2) between water and hydrogen takes place on the catalyst as a result of ionization processes. The metal adsorbs hydrogen and ionizes it. The ions formed pass into the solution, while an equal number of H^+ and D^+ ions is discharged on the surface of the metal. According to these authors, ionization takes place on an “unpoisoned” platinum surface, generally speaking, so rapidly that, for the rate of the exchange reaction, the determining factor is the diffusion of hydrogen to the metal. Only in an alkaline alcoholic solution (owing to the small concentration of D^+) can the actual rate of ionization be measured. Polanyi and Horiuti^86 showed that the exchange reaction (2) proceeds proportionally to \(p^{-1/2}\) (\(p\)—hydrogen pressure), and its temperature dependence is determined by a heat of activation of 10,000 cal. Here the rate-determining moment is not the formation of H and D atoms from molecular hydrogen, but the ionization of these atoms and the discharge of H^+ and D^+ on the catalyst. These processes are retarded by a potential barrier of 10,000 cal, which lies between the metallic surface and the homogeneous solution.
TABLE 10
Water: 26.2% D*; catalyst—palladium black
| Time in minutes | % in hydrogen |
|---|---|
| 0 | 0 |
| 30 | 5.0 |
| 48 | 7.5 |
| 55 | 9.5 |
| 93 | 10.2 |
| 120 | 10.1 |
Just as the metals platinum and palladium can catalyze the equilibrium reaction (2), so also can certain bacteria (Bacterium coli, Lactis aerogonase, Dispar), as found by A. Farkas, L. Farkas, and I. Yudkin^61. This indicates a far-reaching parallelism between the enzymes acting here and the noble metals—a result at which Stickland and Green* recently arrived by another route, showing that the bacteria mentioned can produce a water—hydrogen ion potential.
In § 6 we have already drawn attention to the role of these exchange reac-
* In these experiments the amount of hydrogen could be neglected in comparison with the amount of water, so that, when equilibrium was established, the concentration of D in the water did not change. Since the conditions in aqueous gasometers are analogous, and catalysts influencing the establishment of equilibrium often cannot be avoided, it is not recommended to store heavy hydrogen over water (Oliphant^121), and in the case of catalysis of the equilibrium reaction the final concentration of D in the gas is practically equal to zero.
** See also the work of Kowan, Horiuti, and Polanyi^32.
* Stickland and Green, Nature, 133**, 573, (1934).
tions during the electrolysis of water; we shall see in § 15 that they also play a role in the formation of hydrogen and the dissolution of metals in water or acids.
§ 14. Some Gas Reactions of H₂, HD, and D₂ and Their Rates
The difference in the rates of reactions of heavy and light hydrogen compounds, which is due to the phenomena considered in § 10, can best be studied in gas reactions; the photochemical reaction of detonating chlorine gas, the thermal formation of hydrogen bromide, and certain experiments on the formation of water from O and hydrogen are the first examples of such investigations.
The rate of reaction of both isotopes in the photochemical formation of hydrogen chloride was investigated by Rollefson^136, and then by A. and L. Farkas^60. Rollefson finds for the ratio of rates
\[ \frac{k_{\mathrm{H}_2}}{k_{\mathrm{D}_2}} \]
at \(0^\circ\mathrm{C}\)—13.4, at \(32^\circ\mathrm{C}\)—9.75.* It follows from this that the activation energy of the reaction of \(D_2\) is greater by 1,630 cal than for \(H_2\); the number of collisions
\[ \frac{Z_{\mathrm{H}_2}}{Z_{\mathrm{D}_2}}=0.66 \]
instead of the theoretical value
\[ \frac{1}{\sqrt{2}}. \]
A. and L. Farkas investigated the change in the concentration of D in mixtures of hydrogen with \(Cl_2\) and D under illumination. Since HD and \(D_2\) react with chlorine more slowly than with \(H_2\), the concentration of D increases under illumination. When 30% heavy hydrogen is used (42% HD and 9% \(D_2\)), one obtains
\[ \frac{k_{\mathrm{H}_2}}{k_{\mathrm{D}_2}}=3.7, \]
whence it follows that, for the HD reaction, the heat of activation is greater than for the \(H_2\) reaction by 670 or 800 cal, depending on whether or not the difference in the number of collisions of HD and \(H_2\) is taken into account.
The different rates of disappearance** of \(H_2\), HD, and \(D_2\) are determined primarily by the difference in the rates of the reactions:
\[ \mathrm{Cl}+\mathrm{H}_2 \to \mathrm{HCl}+\mathrm{H} \tag{1} \]
\[ \mathrm{Cl}+\mathrm{HD} \to \mathrm{DCl}+\mathrm{H} \tag{1a}*** \]
\[ \mathrm{Cl}+\mathrm{D}_2 \to \mathrm{DCl}+\mathrm{D}; \tag{1b} \]
* This ratio of rates is given by the distribution of chlorine in \(H_2+CO\), on the one hand, and \(D_2+CO\), on the other. CO was used in these experiments because in this way readily reproducible reaction rates are obtained.
** With this method of determining the difference in the rates of the two isotopes, the experiment proceeds independently of interference from inhibitors and from the irreproducibility of the reaction rate, since in one and the same experiment the rates of light and heavy hydrogen are compared.
*** For simplicity we do not take into account here the reaction
\[ \mathrm{Cl}+\mathrm{HD}\to \mathrm{HCl}+\mathrm{D}. \]
the observed differences in the heats of activation are in satisfactory agreement with the differences of the zero-point energies \((\varepsilon_{\mathrm{H}_2} - \varepsilon_{\mathrm{HD}} = 817\ \text{cal},\ \varepsilon_{\mathrm{H}_2} - \varepsilon_{\mathrm{D}_2} = 1789\ \text{cal},\) see § 3), which, as shown in § 10, give rise to the same differences in activation energies. However, the kinetics of the chlorine detonating-gas reaction is in reality more complicated, since there are also differences in the second member of the chain:
\[ \mathrm{H} + \mathrm{Cl}_2 \to \mathrm{HCl} + \mathrm{Cl} \tag{2} \]
\[ \mathrm{D} + \mathrm{Cl}_2 \to \mathrm{DCl} + \mathrm{Cl} \tag{2a} \]
(the yields of these collisions are in the ratio \(1 : 0.72\)); the reverse reactions also play a role \((\mathrm{H} + \mathrm{HCl} \to \mathrm{H}_2 + \mathrm{Cl},\ \mathrm{D} + \mathrm{DCl} \to \mathrm{D}_2 + \mathrm{Cl}\), etc.). It may be hoped that a study of the chlorine detonating-gas reaction in the presence of D will give important indications concerning the ratio of the rates of (1) to (2) and concerning the reverse reactions.
The thermal formation of hydrogen bromide from \(\mathrm{Br}_2 + \mathrm{D}_2\) proceeds at \(578^\circ\mathrm{K}\), according to Bonhoeffer and Bachu \(^{21, 22}\), 5 times more slowly than the formation of HBr from \(\mathrm{H}_2 + \mathrm{Br}_2\). This is caused by the heat of activation of \(\mathrm{Br}_2 + \mathrm{D}_2 \to \mathrm{DBr} + \mathrm{Br}\), which is 2000 cal higher than for the reaction \(\mathrm{Br}_2 + \mathrm{H}_2 \to \mathrm{HBr} + \mathrm{Br}\), in very good agreement with the theory.
The formation of water in the reaction of hydrogen with oxygen, sensitized by mercury, proceeds, according to Melville \(^{118}\), at room temperatures and low pressures equally rapidly for both isotopes. The rate-determining reaction is the combination of H or D with \(\mathrm{O}_2\) during a triple collision; although the number of collisions of D with \(\mathrm{O}_2\) is then smaller than that of H with \(\mathrm{O}_2\) by a factor of \(\sqrt{2}\), the concentration, owing to the slower diffusion of these atoms to the walls, increases by the same factor, so that in the given pressure range the two effects compensate one another.
At high temperatures, where the formation of water proceeds as a chain reaction, the HD- or D-reactions proceed more slowly than the \(\mathrm{H}_2\)-reaction. The differences in heats of activation are given by the differences in zero-point energies, and from the observed difference in reaction rates of the two isotopes it follows that in this case the chain must contain such a rate-determining reaction in which molecular hydrogen takes part (see also \(^{67}\) and \(^{82}\)).
§ 15. Preparation of Both Hydrogen Isotopes from Aqueous Solutions
In § 6, in speaking of the electrolysis of water, we discussed various processes that may cause different rates of formation of the two isotopes from water. It might have been expected that, also when metals dissolve in water or acids, separation of the isotopes occurs, so that the hydrogen evolved has a different concentration of D than the water. This was indeed shown by A. and L. Farkas \(^{54}\) in the dissolution of sodium, calcium, aluminum in water and of zinc in dilute sulfuric
acid and confirmed by other authors* (Davis and Johnston^40, Horiuti and Sabo^87). The separation of isotopes during such processes was studied in greatest detail by Urey, Ingold, and Wilson^88,89.
Some results are given in Tables 11 and 12.
TABLE 11
| Metal | Li | Na | K | Mg | Ca | Al |
|---|---|---|---|---|---|---|
| Separation coefficient . . . | 1.5 | 2.8 | 1.9 | 2.2 | 1.6 | 4.3 |
TABLE 12
| Metal | Cr | Mn | Fe | Co | Zn—Cu pair | Zn—Au pair |
|---|---|---|---|---|---|---|
| Separation coefficient | 4.5 | 5.1 | 4.3 | 4.1 | 8.0 | 4.5 |
It is interesting to note that those metals which react directly with water generally give smaller separation coefficients, whereas the heavy metals give larger ones; here it is natural to admit two processes as factors determining the reaction rate. If the hydrogen evolved as a result of catalysis on the metallic surface were to undergo the exchange reaction sufficiently rapidly,
\[ \mathrm{H_2O + HD \rightleftharpoons HOD + H_2,} \tag{1} \]
then at \(20^\circ\mathrm{C}\) one could expect, for all metals, a separation coefficient of approximately 3.8, which corresponds to the equilibrium constant of the indicated reaction. If one takes into account that the observed separation coefficients for the metallic groups mentioned lie on opposite sides of the equilibrium value, then, apparently, it may be assumed that for metals dissolving in water, on the one hand, and for heavy metals, on the other, the separation is caused by different factors.
In the first group, the following reactions probably play a role:
\[ \mathrm{Me + HOH \to Me^{+} + H + OH^{-}} \tag{2a} \]
\[ \mathrm{Me + HOH \to Me^{+} + D + OH^{-};} \tag{2б} \]
for heavy metals—discharge:
\[ \mathrm{Me + H^{+} \to Me^{+} + H} \tag{3a} \]
\[ \mathrm{Me + D^{+} \to Me^{+} + D.} \tag{3б} \]
* The separation coefficient 1.2 for sodium indicated in work^54 refers to the reaction of the metal with steam.
It is difficult to say to what extent the observed separation coefficients determine the rates of reactions (2a) and (2b) or (3a) and (3b); just as in electrolysis (see § 6), it must be assumed that the exchange reaction (1) always takes place to some extent, especially because the activity of the metallic surface during the evolution of hydrogen is undoubtedly increased owing to the mechanical removal of catalytic poisons (for example, an oxide layer). In the first case the exchange reaction (1) tends to increase the separation, and in the second case to decrease it, so that the initial ratio of the rates in (2a) and (2b) is in fact smaller, and in (3a) and (3b) larger, than follows from the observed separation coefficients.* It is to be expected that, in the direct reaction of a metal with water according to (2a) and (2b), the difference in rate is smaller than in recharging, since reactions (3a) and (3b), by virtue of their nonmechanical occurrence, must have very different rates.
Whereas, in the formation of hydrogen by metals, the isotopic content of the gas does not correspond to equilibrium, in processes in which the exchange reaction is especially well catalyzed this is to be expected. We have already mentioned the electrolysis of water on activated platinum electrodes; other examples of reactions in which both isotopes of hydrogen are formed from water in the normal ratio are: the decomposition of sodium formate by palladium or by coli bacteria, the reaction
\[ \mathrm{K_4Co(CN)_6 + H_2O \to K_3Co(CN)_6 + \frac{1}{2}H_2 + KOH,} \]
the decomposition of water vapor at high temperatures up to the equilibrium point by iron, and the water—gas equilibrium.\(^{62}\) The oxidation of \(\mathrm{K_4Co(CN)_6}\) is of interest because this reaction proceeds in a homogeneous solution and the exchange equilibrium is evidently established in this case by the H and D atoms formed within it. The decomposition of water vapors at high temperatures by iron (as well as the water—gas equilibrium) are examples of the separation at equilibrium considered in § 10.
§ 16. Comparison of the catalytic reactions of both hydrogen isotopes
The use of both hydrogen isotopes has also proved fruitful in various problems of catalysis, and there is no doubt that,
* Experiments on the formation of methane from aluminum carbide and water show that exchange reactions mask the difference in the rates of the primary reactions. According to Yure and Price,\(^{156}\) the formation of \(\mathrm{CD_4}\) from \(\mathrm{D_2O}\) occurs 23 times more slowly than the formation of \(\mathrm{CH_4}\) from \(\mathrm{H_2O}\) and \(\mathrm{Al_4C_3}\). Ingold and co-workers\(^{89}\), however, find that water containing D, together with \(\mathrm{Al_4C_3}\), gives methane containing D only 1.2 times less than the water used, which is evidently caused by secondary exchange reactions.
that with the aid of this method one can arrive at an understanding of the mechanism of many catalytic reactions.
The diffusion of hydrogen through palladium is a simple example of its catalytic reaction. The diffusion of hydrogen through palladium requires, just like an ordinary reaction, a heat of activation: in order to deliver H₂ or D₂ to the surface of palladium and there split them into atoms capable of diffusing, it is necessary to overcome a potential barrier of 16,000 cal. If, as a first approximation, it is assumed that the diffusion rate of both hydrogen isotopes is determined by this process, then one should expect that the temperature dependence of the ratio of the diffusion rates of H and D is expressed as
\[ e^{-\frac{1}{2}(\varepsilon_{\mathrm{H}_2}-\varepsilon_{\mathrm{D}_2})/RT} \]
(see § 10); namely, H diffuses faster, since H₂, owing to its higher zero-point energy, requires less additional energy for transition to the activated state on palladium than D.* Experience has in fact shown that D diffuses more slowly than H (see Harris, Jost, and Peers, and A. and L. Farkas⁵⁶), and the difference in activation energies for H and D is found to be 830 cal, in excellent agreement with the theoretical value of 890 cal.
Melville¹¹⁸ investigated the catalytic hydrogenation of O₂ and N₂O on nickel with both hydrogen isotopes. It turned out that heavy hydrogen reacts more slowly than light hydrogen, and in this case the explanation may be the difference in the heats of activation of the reactions of H and D due to zero-point energy. The ratios of the rates of the pure reactions of H₂ and D₂ (extrapolated from measurements of the rates of mixtures) with O₂ and N₂O are approximately equal and, in the temperature interval 160–250°, have values 2.4–1.8, whence the difference in activation energies is found to be 0.7–0.9 kg-cal. If it is assumed that the rate-determining step of the reaction is the replacement of NiH or NiD in the adsorbing layer by O₂ or N₂O, then the above-mentioned difference in activation energies arises as a consequence of the difference in the zero-point energies of these compounds.
In the hydrogenation of ethylene at 20°C, the separation of both isotopes was measured by determining the D content in the hydrogen in a direct experiment by A. and L. Farkas and E. K. Rideal⁵⁹. It was found that both isotopes react with C₂H₄ at almost the same rate; the following may be said about the mechanism of hydrogenation: activation of hydrogen is not needed for hydrogenation; at low temperature the catalyst is almost completely covered with C₂H₄, and hydrogenation occurs in such a way that hydrogen molecules enter accidentally arising gaps in the adsorption layer of C₂H₄ and, before desorbing, react with C₂H₄ and are converted into ethane.
* The factor 1/2 in the exponent enters because we assume an atomic mechanism of diffusion, and the atoms on the metal are in equilibrium with H₂, HD, and D₂.
§ 17. Reactions in Solutions, the Rate of Enzymatic Processes
In this section we shall consider certain reactions which proceed in the presence of heavy water at a rate different from that in ordinary water. The best investigated is the mutarotation of glucose, studied by Bonhoeffer and Melvin-Hughes[^21], and later by Pacsu[^124],[^126]. The monomolecular rate constants are related as
\[ \frac{k_{\mathrm{D_2O}}}{k_{\mathrm{H_2O}}}\sim 0.32; \]
this ratio does not depend on temperature. The reaction may be catalyzed by hydrogen ions; in this case the rate of the reaction catalyzed by \(\mathrm{D}^+\) ions is less (by a factor of 0.5–0.7) than that of mutarotation catalyzed by \(\mathrm{H}^+\) ions.
The hydrolysis of cane sugar (cleavage into d-glucose and d-fructose), however, proceeds under the catalytic action of \(\mathrm{D}^+\) ions 1.4–1.8 times faster than under the action of \(\mathrm{H}^+\) ions (Bonhoeffer and Melvin-Hughes[^119])—the only example so far of an increase in reaction rate as a consequence of replacing H by D.
Of the enzymatic reactions in the presence of heavy water, those so far investigated are the fermentation of cane sugar under the influence of yeast (Pacsu[^125], Rydill and Judkin—in press), the “respiration” of yeast during fermentation, and the enzymatic decomposition of sodium formate by coli bacteria (A. and L. Farkas and I. Judkin[^61]). It is found that the fermentation reaction in \(\mathrm{D_2O}\) proceeds 8 times more slowly than in water, and that the “respiration” of yeast is also somewhat slowed.
In the decomposition of sodium formate by the enzyme of coli bacteria, what were compared were not the rates of hydrogen formation in \(\mathrm{H_2O}\), but the ratio of the two isotopes in the gas formed. It was found that the hydrogen formed (with respect to its D content) was always in equilibrium with the solution, its D content at \(40^\circ\mathrm{C}\) corresponding to an equilibrium constant of 3.0 for the equilibrium reaction (§ 3, Eq. 7). Since this latter reaction is itself catalyzed by the bacterium (§ 13), this was to be expected; in any case, the experiment shows that on the surface of the enzyme both the formic acid molecule and molecular hydrogen ionize or decompose into radicals.
§ 18. Biological Experiments with Heavy Water
Although the applications of heavy water as an auxiliary means of investigation in biological chemistry and biology are very promising, only a few attempts have so far been made in this direction. Here too heavy water can be used in part to trace the path of some co-
...compounds in the organism, partly for influencing biological processes.
Hevesy and Hofer ^81 gave an example of the first kind of application: the rate of exchange between the fluid of a living fish and the environment, the aquarium containing heavy water. The exchange between the water of the fish (80% of the weight of its body) and the water in the aquarium causes a decrease in the concentration of D of the latter, and the decrease ceases if the water is distributed uniformly between the fish and the aquarium. The exchange is completed in approximately 4.5 hours.
In studying biological processes in the presence of heavy water, the chief question is: is the life of organisms possible when H is replaced by D. Lewis ^99, 100 first expressed the idea that replacement of all H atoms by D atoms in living organisms may prove fatal: the organism may prove unadapted to the altered equilibrium between heavy hydrogen compounds, to the different viscosity and permeability of heavy water.
The first experiments in this direction did indeed reveal the lethal action of heavy water. Lewis ^49 found that tobacco seeds in heavy water do not sprout; in 50% heavy water the process is greatly slowed. Taylor and co-workers ^146 report the lethal influence of pure D₂O on tadpoles, goldfish, worms, etc. Although, as can be seen, these experiments undoubtedly show the killing action of D₂O, all these experiments, especially the latter, nevertheless require verification.
Apparently it has been proved that growth in the presence of heavy water, at least at high concentrations, is retarded; alongside the already mentioned experiments of Lewis with tobacco seeds, one should note the experiments of Bonhoeffer and Zickler ^21 with yeast and Bombardier [?], which in 90% heavy water grow approximately 4 times more slowly than in ordinary water. In more dilute water as well, several germination experiments were carried out which showed that D enters the organism (Bonhoeffer ^21, Ussing and Smith ^162, ^163). In 0.2% heavy water, striking results were at first obtained: a mold fungus multiplies in such water faster than in ordinary water ^117. * However, according to R. Klar, ** this action should be attributed to organic impurities in commercial heavy water. Thoroughly purified water with 0.2% D behaves normally.
* See also works 7, 8, 9, 133.
* Nature* 134, 104, 1934.
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