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MASS-SPECTROMETRIC DETERMINATION OF THE MOLECULAR WEIGHT OF COMPONENTS OF ANALYZED MIXTURES*
At the present time, qualitative analysis of various mixtures by means of a mass spectrometer can be carried out only in the case where the mass spectra of each of the components entering into the mixture are known in advance.
The authors of the paper under review proposed a method of qualitative analysis free from this limitation. This method is based on determining the molecular weight from the rate of effusion of the gas, measured with a mass spectrometer.
In the instrument used by the authors, the volume containing the vapors of the mixture of substances under investigation, or the gas mixture under investigation (the so-called inlet-system part), communicated with the ion source of the mass spectrometer through an orifice of very small diameter (0.043 mm).
The intensity of the peak \(H_{ik}\), corresponding to a given ratio \(m/e = k\) and due in origin to molecules of only one definite (\(i\)-th) substance, depends on the partial pressure of this substance \(p_i\):
\[ H_{ik}=s_{ik}\cdot p_i, \tag{1} \]
where \(s_{ik}\) is a proportionality coefficient.
If molecules of different substances take part in producing the peak under consideration, its height \(H_k\) is determined by the equation
\[ H_k=H_{1k}+H_{2k}+\cdots+H_{nk}=s_{1k}p_1+s_{2k}p_2+\cdots+s_{nk}p_n. \tag{2} \]
As a result of the effusion of the investigated mixture of vapors or gases through the orifice, the partial pressure of the components entering into the mixture and contained in the volume decreases with time according to the equation
\[ dp_i/dt=c_i(p_i-p_\infty), \tag{3} \]
where \(c_i\) is the effusion constant and \(p_\infty\) is the pressure in the source.
The pressure in the source, usually not exceeding \(3\cdot10^{-6}\) mm Hg, is negligibly small in comparison with \(p_i\) (the pressure of the investigated mixture in the volume was 40 \(\mu\) Hg). If \(p_\infty=0\) is assumed, then
\[ \frac{dp_i}{dt}=c_i p_i \tag{4} \]
and
\[ \ln \frac{p_i^0}{p_i}=c_i(t-t_0), \tag{5} \]
where \(p_i^0\) is the partial pressure of the \(i\)-th component at the moment of time \(t_0\).
* M. Eden, B. E. Burr and A. W. Pratt, Anal. Chem. 23, 1735 (1951).
From equations (1) and (5) it follows that
\[ \ln \frac{H^{0}_{ik}}{H_{ik}}=c_i(t-t_0), \tag{6} \]
i.e. \(\ln \dfrac{H^{0}_{ik}}{H_{ik}}\) varies linearly with time.
From observations of the change in the intensity of the peak \(H_{ik}\) with time, the effusion constant \(c_i\) can be determined by means of equation (6). It should be noted that such a determination can be made from observations of the change in the intensity of a peak which owes its origin to any one of the fragment ions of molecules of the given substance.
It is clear that a peak whose origin is due to molecules of different substances cannot be used to determine \(c_i\). This peak is distinguished by the fact that, according to equations (2) and (6), a linear dependence of
\[ \ln \frac{H^{0}_{k}}{H_k} \]
on time is not observed.
It is known that the effusion of gases through orifices of small diameter obeys Graham’s law, according to which the effusion rates are inversely proportional to the square root of the molecular weight \(M\):
\[ c_a M_a^{1/2}=c_x M_x^{1/2}. \tag{7} \]
In order, knowing the effusion constant, to be able to calculate the corresponding molecular weights from equation (7), it is necessary to calibrate the instrument.
The instrument constant \(c_a M_a^{1/2}\) can be obtained from effusion data for a substance of known molecular weight. However, to increase accuracy it is expedient in each experiment to introduce, as a standard, a compound of known molecular weight.
The authors found that the molecular weight of the chosen standard should not differ by more than a factor of two from the probable molecular weight of any of the substances entering into the mixture, since the relative error decreases as
\[ \frac{M_a}{M_x} \]
approaches unity. For analysis of an air mixture, oxygen \((M=32)\) is expediently used as the standard; for organic compounds with molecular weights from 30 to 168, benzene \((M=78)\) is the most convenient.
The method developed by the authors was checked by analyzing various mixtures of known composition.
The calculation of the molecular weights of the principal atmospheric gases from the measurements performed was carried out with an error of 1%, as is seen from Table I.
Table I
| Gas | Concentration, % | Mass number | Calculated molecular weight |
|---|---|---|---|
| O\(_2\) | 22.00 | 32 | 32.0 |
| N\(_2\) | 76.65 | 28 | 28.2 |
| CO\(_2\) | 0.45 | 44 | 44.3 |
| Ar | 0.90 | 40 | 39.9 |
In these measurements oxygen was used as the standard.
The results of the analysis of a mixture of four organic compounds are given in Table II.
Table II
| Substance | Concentration, % | Mass number | Chemical molecular weight | Calculated molecular weight |
|---|---|---|---|---|
| Benzene | 97.00 | 39 52 78 |
78.11 | 77.2 78.5 78.0 |
| Cyclopentanone | 1.00 | 41 55 84 |
84.11 | 84.1 84.7 87.5 |
| Acetone | 1.00 | 43 58 |
58.08 | 58.1 58.4 |
| s-Tetrachloroethane | 1.00 | 83 85 |
167.41 169.03 |
175.3 177 |
The benzene peak with mass number 78 was used as the standard.
Graph labels: ordinate: \(\lg \dfrac{H_i^0}{H_k}\); abscissa: time in minutes. Legend: designation—○, △, ●, □; mass number—85, 84, 78, 58.
The figure shows curves (one for each substance), from which, on the basis of equation (6), the effusion constant was determined.
Most of the results agree to within 0.5%. However, in some cases, for example for s-tetrachloroethane, the error reaches 4%. This may be explained by the superposition of the background from the cyclopentanone peak
with mass number 84 to peaks with mass numbers 83 and 85. Confirmation of this assumption is provided by the results of analysis of pure substances and by the deviation from linearity of the curve corresponding to mass 85 (see figure). In addition, in the case of s-tetrachloroethane, the molecular weights of components with mass numbers 83 and 85 differ from one another because of the different contents of chlorine isotopes.
Some limitations on the application of the proposed method may be anticipated. Thus, for example, the results of measuring molecular weight may be affected by the formation of associations of molecules of the given substance or by mutual reaction of the components during the experiment. In addition, this method is not applicable for determining the molecular weights of substances strongly absorbed by the walls of the instrument.
Nevertheless, the described method considerably broadens the possibilities for using the mass spectrometer for qualitative analysis of mixtures of unknown composition.
L. L.