On the Effect of Electrolytes with Common Ions on the Solubility and Solubility Product of AgBrO3
Abstract Generated abstract
This study examines how electrolytes with and without a common ion affect the solubility and solubility product of silver bromate at 25 degrees C. The authors measured AgBrO3 solubility in aqueous KBrO3 solutions and in mixed KBrO3 and NaNO3 solutions, comparing these results with earlier data for NaNO3 alone. Potassium bromate, which supplies a common bromate ion, regularly decreased AgBrO3 solubility, while sodium nitrate increased it more weakly, so that mixed systems reflected the superposition of these opposing effects. Despite these solubility changes, the solubility product increased substantially in all systems studied, and the authors conclude that broader generalizations require additional experimental data.
Full Text
On the Question of the Influence of Electrolytes with Common Ions on the Solubility and Solubility Product of the AgBrO₃ Precipitate
Yu. L. Lel’chuk, L. V. Surnina and V. I. Barkhatova
The present communication is the next report in a series of works carried out by us on the study of the influence of electrolytes of various types on the solubility of silver bromate precipitate. The main aim of the investigation is to reveal the general regularities in the influence of electrolytes of various types on the solubility of precipitates in the absence of obvious chemical interaction between the precipitate and the corresponding electrolytes. Investigations in this field, as follows from the resolutions of the All-Union Conference on Classical Methods of Chemical Analysis, held in Moscow in November 1951, and from the statements of leading Soviet analytical chemists, are of great theoretical and practical importance for the further development of modern analytical chemistry.
In the first three communications published by us, we considered the results of studying the influence of nitrates of the metals of the first group of the periodic system—lithium, sodium and potassium [1], nitrates of the metals of the second group of the periodic system—magnesium, calcium, strontium and barium [2], and nitrates of aluminum and thorium [3]—on the solubility of silver bromate precipitate at concentrations of the external electrolytes from 0.001 to 1 mole/l.
Analysis of the experimental data obtained for the above-mentioned ternary systems allowed us to draw definite conclusions about the relative influence of the corresponding cations on the solubility of silver bromate precipitate, depending on the valence type of the cations, the radii of the atoms of the corresponding chemical elements, and the position of the latter in D. I. Mendeleev’s periodic system of the elements.
In these investigations it was established that the solubility of the AgBrO₃ precipitate, at equal molar concentrations of external electrolytes, increases regularly with increasing atomic weight and atomic radius of the elements of the corresponding groups of the periodic system. Of all the cations of the first group studied by us, potassium gives the greatest increase in solubility and in the solubility product, and lithium the smallest. The solubility and solubility product of the precipitate change in the same direction under the influence of nitrates of the metals of the second group of the periodic system.
A comparative evaluation of the experimental data on the solubility of AgBrO₃ in the systems AgBrO₃—NaNO₃—H₂O, AgBrO₃—Mg(NO₃)₂—H₂O and AgBrO₃—Al(NO₃)₃—H₂O also made it possible to establish the relative influence of the cations Na, Mg and Al on the solubility and solubility product of the precipitate, depending on the position occupied by these elements in the third period of D. I. Mendeleev’s periodic system. The experimental data show that the increase in the solubility of the precipitate lags appreciably behind the increase in the valence of the corresponding cation of the external salt. When comparing the solubility of the precipitate in solutions of sodium, magnesium and
for aluminum of the same normality, the greatest increase in solubility is produced by sodium nitrate solutions, and the smallest by aluminum nitrate solutions.
Thus, in these systems as well, the statements of Corresponding Member of the Academy of Sciences of the USSR I. V. Tananaev [4] and other Soviet scientists are confirmed: in assessing the influence of external electrolytes on the solubility of a given precipitate, it is necessary to take into account not only the concentration and valence of the ions of the external electrolytes, but also the individual chemical characteristics of these ions and the position of the corresponding elements in D. I. Mendeleev’s periodic system of the elements.
On the basis of the experimental data obtained for the above-mentioned ternary systems, we have proposed calculating the solubility of the silver bromate precipitate in solutions of nitrates of alkali and alkaline-earth metals of any concentration in the interval from 0.001 to 1 mol/l by the formula
\[ C_{\mathrm{AgBrO_3}}=\sqrt{\frac{L_a}{\gamma^2}}, \]
where the activity product of the precipitate is \(L_a=5.50\cdot10^{-5}\), and the activity coefficient of \(\mathrm{AgBrO_3}\) (\(\gamma\)) is determined graphically with the aid of the curves proposed by us for the dependence of the mean values \(\gamma_{\mathrm{AgBrO_3}}\) on the molar concentration of nitrates of alkali and alkaline-earth metals.
The present investigation is devoted to the study of the influence of an electrolyte with an ion common to the precipitate on the solubility of the silver bromate precipitate. For this purpose we studied the solubility of \(\mathrm{AgBrO_3}\) in the system \(\mathrm{AgBrO_3—KBrO_3—H_2O}\). Since in systems of analytical significance, as a rule, in addition to the precipitant (the electrolyte with an ion common to the precipitate), external electrolytes without ions common to the precipitate are also present, we attempted to study the solubility of the precipitate with the simultaneous presence in solution of an electrolyte with a common ion and an electrolyte without an ion common to the precipitate. For this purpose, the solubility was studied in the four-component system \(\mathrm{AgBrO_3—KBrO_3—NaNO_3—H_2O}\) at potassium bromate concentrations of 0.001, 0.01, and 0.1 mol/l and sodium nitrate concentrations from 0.001 to 1 mol/l.
The need to accumulate experimental material on solubility in such systems is especially emphasized in the resolution of the All-Union Conference on Classical Methods of Analysis [4] and in statements by leading Soviet analytical chemists [5;6].
For a comparative evaluation of the degree of increase in the solubility of the precipitate due to an electrolyte of the 1–1 type without ions common to the precipitate, and of the degree of decrease in the solubility of the \(\mathrm{AgBrO_3}\) precipitate under the influence of an electrolyte of the 1–1 type with an ion common to the precipitate, when they are simultaneously present in solution, a comparison was made of the data obtained earlier by one of the authors of the present work for the system \(\mathrm{AgBrO_3—NaNO_3—H_2O}\) with solubility data in the systems \(\mathrm{AgBrO_3—KBrO_3—H_2O}\) and \(\mathrm{AgBrO_3—KBrO_3—NaNO_3—H_2O}\).
Starting substances and method of work
A pure preparation of potassium bromate was obtained by us from potassium hydroxide hydrate and bromine by the method of Il’in [7].
The preparation met the requirements of the OST for chemically pure \(\mathrm{KBrO_3}\) [8]. Sodium nitrate was obtained by double recrystallization of a domestic commercial preparation by the Leighty method, described by Karyakin [9]. Silver bromate was obtained from silver nitrate and potassium bromate. The method of its preparation is described in detail in our first communication on the solubility
of silver bromate in aqueous solutions of nitrates of alkaline-earth metals [2]. All sodium nitrate solutions were prepared by appropriate dilution of a one-molar solution of NaNO₃, and the potassium bromate solutions by dilution of a 0.3 molar solution of KBrO₃. Preparation and dilution of the solutions were carried out with bidistilled water stored in vessels paraffined on the inside. Experiments to determine the solubility of AgBrO₃ in the AgBrO₃—KBrO₃—H₂O system were carried out in brown-glass bottles of 400–500 ml capacity, paraffined on the inside. A bottle closed with a cork stopper, containing 1 g of silver bromate and 250 ml of a potassium bromate solution of the appropriate concentration, was placed in a water thermostat at a temperature of \(25 \pm 0.1^\circ\), where vigorous stirring by a motor was carried out for 8 hours.
The constant temperature in the thermostat was maintained by means of a mercury–toluene thermoregulator.
In studying the solubility in the AgBrO₃—KBrO₃—NaNO₃—H₂O system, the required concentrations of sodium nitrate and potassium bromate in the liquid phase were achieved by adding the necessary amount of KBrO₃ salt to a sodium nitrate solution of the corresponding concentration. Sampling of the liquid phase for analysis and determination of the silver bromate content in the liquid phase were carried out by the procedure described by us earlier in a communication on the solubility of silver bromate in aqueous solutions of alkali-metal nitrates [1].
System AgBrO₃—KBrO₃—H₂O
The experimental data obtained by us for the AgBrO₃—KBrO₃—H₂O system are given in Table 1 and Fig. 1. The first column of the table gives the molar concentrations of potassium bromate; the last gives the average values of the solubility of the silver bromate precipitate in the corresponding aqueous potassium bromate solutions.
Table 1
Solubility of AgBrO₃ in aqueous KBrO₃ solutions
| KBrO₃, mol/l | Experiment No. 1, AgBrO₃ mol/l | Experiment No. 2, AgBrO₃ mol/l | Experiment No. 3, AgBrO₃ mol/l | Average, AgBrO₃ mol/l |
|---|---|---|---|---|
| 0.000 | \(8.244 \cdot 10^{-3}\) | \(8.252 \cdot 10^{-3}\) | \(8.249 \cdot 10^{-3}\) | \(8.25 \cdot 10^{-3}\) |
| 0.001 | \(7.25 \cdot 10^{-3}\) | \(7.33 \cdot 10^{-3}\) | \(7.37 \cdot 10^{-3}\) | \(7.32 \cdot 10^{-3}\) |
| 0.003 | \(5.29 \cdot 10^{-3}\) | \(5.31 \cdot 10^{-3}\) | \(5.28 \cdot 10^{-3}\) | \(5.29 \cdot 10^{-3}\) |
| 0.010 | \(3.98 \cdot 10^{-3}\) | \(4.01 \cdot 10^{-3}\) | \(3.97 \cdot 10^{-3}\) | \(3.99 \cdot 10^{-3}\) |
| 0.030 | \(2.48 \cdot 10^{-3}\) | \(2.47 \cdot 10^{-3}\) | \(2.52 \cdot 10^{-3}\) | \(2.49 \cdot 10^{-3}\) |
| 0.100 | \(9.75 \cdot 10^{-4}\) | \(1.10 \cdot 10^{-3}\) | \(1.10 \cdot 10^{-3}\) | \(1.06 \cdot 10^{-3}\) |
| 0.300 | \(7.00 \cdot 10^{-4}\) | \(7.12 \cdot 10^{-4}\) | \(6.96 \cdot 10^{-4}\) | \(7.03 \cdot 10^{-4}\) |
As is evident from these data, the solubility of the precipitate decreases regularly with increasing concentration of the potassium bromate solution. Of all the KBrO₃ concentrations studied by us, the greatest decrease in the solubility of AgBrO₃ is attained in a 0.3 molar potassium bromate solution, where the solubility of the precipitate, instead of \(8.25 \cdot 10^{-3}\) in pure water, becomes equal to only \(7.03 \cdot 10^{-4}\), i.e., decreases by a factor of 11.8. The comparatively good agreement of the three parallel determinations of the solubility of AgBrO₃ for each point of the AgBrO₃—KBrO₃—H₂O system, and the general course of the curve in Fig. 1, indicate the low probability of formation in this system of solid solutions and, still more, of double salts. As is known, the presence of such solid solutions and the formation of a double salt of composition AgBrO₃·NaBrO₃ were established by Ricci and Aleshnikov [10] in their study of the composition of the solid
solid phase in the system AgBrO\(_3\)—NaBrO\(_3\)—H\(_2\)O at NaBrO\(_3\) concentrations in the liquid phase of 22% and higher. Richi and Aleshnik explain the impossibility of obtaining a chemically pure silver bromate preparation from concentrated solutions of sodium bromate and silver nitrate, and the large discrepancies in the literature data on the solubility of silver bromate in water, by the formation of solid solutions and the double salt AgBrO\(_3\)·NaBrO\(_3\).
Of particular interest is the course of the change in the solubility product of the precipitate in this system. As can be seen from the data of Table 2 and Fig. 7, the solubility product of the AgBrO\(_3\) precipitate in 0.001 and 0.003 molar solutions
Table 2
Change in the solubility product of AgBrO\(_3\) in the system AgBrO\(_3\)—KBrO\(_3\)—H\(_2\)O
| KBrO\(_3\), mol/l | 0.000 | 0.001 | 0.003 | 0.010 | 0.030 | 0.100 | 0.300 | \(L_i : L'_i\)\(^{1}\) | \(L'_p : L_p\)\(^{2}\) |
|---|---|---|---|---|---|---|---|---|---|
| \(L_p \cdot 10^5\) | 6.80 | 6.09 | 4.38 | 5.38 | 8.09 | 10.7 | 21.1 | 11.8 | 3.1 |
| \(\lg L_p\) | −4.17 | −4.21 | −4.36 | −4.25 | −4.09 | −3.97 | −3.68 | — | — |
\(^{1}\) \(L_i\) and \(L'_i\) are the solubility of AgBrO\(_3\), in mol/l, respectively in water and in a 0.3 molar KBrO\(_3\) solution.
\(^{2}\) \(L'_p\) and \(L_p\) are the solubility product of AgBrO\(_3\), respectively in a 0.3 molar KBrO\(_3\) solution and in water.
of potassium bromate is somewhat smaller in magnitude than in pure water. However, with a further increase in the concentration of KBrO\(_3\) in the solution, the solubility product increases regularly, reaching a value of
Fig. 1. Solubility of AgBrO\(_3\) in aqueous KBrO\(_3\) solutions
Fig. 2. Solubility of AgBrO\(_3\) in aqueous NaNO\(_3\) solutions
\(2.11 \cdot 10^{-4}\) for a 0.3 molar KBrO\(_3\) solution, i.e., it increases by a factor of 3.1 in comparison with pure water. Thus, exactly as in the ternary systems without ions common with the precipitate that we studied earlier, where, as a rule, with increasing concentration of the external electrolyte the solubility of the precipitate increases regularly, so also in the ternary system under consideration, despite the decrease in the solubility of the precipitate under the action of the common ion, with increasing concentration of the external
electrolyte, the solubility product also increases considerably.
The solubility product of AgBrO\(_3\) for all the studied points of the AgBrO\(_3\)—KBrO\(_3\)—H\(_2\)O system was determined by the formula:
\[ L_{p\mathrm{AgBrO}_3} = [\mathrm{Ag}]\left([\mathrm{BrO}'_3]_{\mathrm{AgBrO}_3} + [\mathrm{BrO}'_3]_{\mathrm{KBrO}_3}\right), \]
where \([\mathrm{Ag}]\) is the concentration of silver ions in grams per liter in the liquid phase, \([\mathrm{BrO}'_3]_{\mathrm{AgBrO}_3}\) is the concentration of bromate ion due to silver bromate in the liquid phase, and \([\mathrm{BrO}'_3]_{\mathrm{KBrO}_3}\) is the concentration of bromate ion due to dissolved potassium bromate.
Attempts to apply the Debye and Hückel formulas and the calculation scheme developed by I. V. Tananaev, which we successfully used in studying solubility in ternary systems without ions common with the precipitate, did not give positive results in the ternary system considered here and in the four-component systems considered below.
System AgBrO\(_3\)—NaNO\(_3\)—H\(_2\)O
The data obtained for the AgBrO\(_3\)—NaNO\(_3\)—H\(_2\)O system are given in Table 3 and are represented graphically in Fig. 2. These data were considered in detail in our published communication on the solubility of silver bromate in aqueous solutions of alkali-metal nitrates [1]. In the above-mentioned communication the experimental data for this system were interpreted
Table 3
System AgBrO\(_3\)—NaNO\(_3\)—H\(_2\)O
| NaNO\(_3\), mol/l | AgBrO\(_3\), mol/l | \(\mu\) | \(f\) | \(L_p\) | \(L_a\) |
|---|---|---|---|---|---|
| 0.001 | \(8.22 \cdot 10^{-3}\) | 0.0092 | 0.901 | \(6.76 \cdot 10^{-5}\) | \(6.08 \cdot 10^{-5}\) |
| 0.003 | \(8.31 \cdot 10^{-3}\) | 0.0113 | 0.891 | \(6.91 \cdot 10^{-5}\) | \(5.49 \cdot 10^{-5}\) |
| 0.010 | \(8.50 \cdot 10^{-3}\) | 0.0185 | 0.865 | \(7.23 \cdot 10^{-5}\) | \(5.41 \cdot 10^{-5}\) |
| 0.030 | \(9.27 \cdot 10^{-3}\) | 0.0393 | 0.817 | \(8.59 \cdot 10^{-5}\) | \(5.72 \cdot 10^{-5}\) |
| 0.100 | \(1.008 \cdot 10^{-2}\) | 0.1101 | 0.731 | \(1.02 \cdot 10^{-4}\) | \(5.44 \cdot 10^{-5}\) |
| 0.300 | \(1.138 \cdot 10^{-2}\) | 0.3114 | 0.626 | \(1.30 \cdot 10^{-4}\) | \(5.09 \cdot 10^{-5}\) |
| 1.000 | \(1.48 \cdot 10^{-2}\) | 1.0148 | 0.501 | \(2.19 \cdot 10^{-4}\) | \(5.50 \cdot 10^{-5}\) |
from the standpoint of the relative influence of external electrolytes on the solubility of the precipitate as a function of the position of the alkali metal in the first group of D. I. Mendeleev’s periodic system. For analysis of the solubility data of AgBrO\(_3\) in the four-component system AgBrO\(_3\)—KBrO\(_3\)—NaNO\(_3\)—H\(_2\)O, the following conclusions for the AgBrO\(_3\)—NaNO\(_3\)—H\(_2\)O system are of greatest interest:
-
The solubility of AgBrO\(_3\) in this system increases regularly with increasing concentration of NaNO\(_3\) in the liquid phase, reaching in a one-molar NaNO\(_3\) solution a value of \(1.48 \cdot 10^{-2}\), i.e., increasing 1.8-fold in comparison with its solubility in water. Thus, sodium nitrate affects the solubility of the precipitate to a significantly lesser extent than potassium bromate, which decreases the solubility of AgBrO\(_3\) in a 0.3 molar solution by 11.8 times.
-
The solubility product of AgBrO\(_3\) in this system, as in the system considered earlier, increases considerably with increasing concentration of sodium nitrate, reaching a value of \(2.19 \cdot 10^{-4}\), i.e., increasing by more than 3.22 times in comparison with the solubility product of the precipitate in water.
System AgBrO₃—KBrO₃—NaNO₃—H₂O
The experimental data obtained by us for the four-component system AgBrO₃—KBrO₃—NaNO₃—H₂O are given in Tables 4, 5, 6, 7 and in Figs. 3, 4, 5, and 6. At all studied concentrations of potassium bromate, the solubility of the silver bromate precipitate increases with increasing sodium nitrate concentration. At a potassium bromate concentration of 0.001 mol/l, the decrease in the solubility of the precipitate due to the ion common with the precipitate is completely compensated by the corresponding increase in the solubility of the precipitate
Table 4
Solubility of AgBrO₃ in the system AgBrO₃—KBrO₃—NaNO₃—H₂O
| NaNO₃, mol/l | KBrO₃, mol/l | Experiment No. 1, AgBrO₃ mol/l | Experiment No. 2, AgBrO₃ mol/l | Experiment No. 3, AgBrO₃ mol/l | Average, AgBrO₃ mol/l |
|---|---|---|---|---|---|
| 0.000 | 0.001 | 7.25 · 10⁻³ | 7.39 · 10⁻³ | 7.37 · 10⁻³ | 7.32 · 10⁻³ |
| 0.001 | 0.001 | 7.50 · 10⁻³ | 7.58 · 10⁻³ | 7.55 · 10⁻³ | 7.54 · 10⁻³ |
| 0.003 | 0.001 | 7.92 · 10⁻³ | 7.88 · 10⁻³ | 7.90 · 10⁻³ | 7.90 · 10⁻³ |
| 0.010 | 0.001 | 8.29 · 10⁻³ | 8.16 · 10⁻³ | 8.22 · 10⁻³ | 8.22 · 10⁻³ |
| 0.030 | 0.001 | 8.88 · 10⁻³ | 8.82 · 10⁻³ | 8.85 · 10⁻³ | 8.85 · 10⁻³ |
| 0.100 | 0.001 | 9.68 · 10⁻³ | 9.68 · 10⁻³ | 9.66 · 10⁻³ | 9.67 · 10⁻³ |
| 0.300 | 0.001 | 1.12 · 10⁻² | 1.12 · 10⁻² | 1.13 · 10⁻² | 1.12 · 10⁻² |
| 1.000 | 0.001 | 1.35 · 10⁻² | 1.36 · 10⁻² | 1.35 · 10⁻² | 1.35 · 10⁻² |
Table 5
Solubility of AgBrO₃ in the system AgBrO₃—KBrO₃—NaNO₃—H₂O
| NaNO₃, mol/l | KBrO₃, mol/l | Experiment No. 1, AgBrO₃ mol/l | Experiment No. 2, AgBrO₃ mol/l | Experiment No. 3, AgBrO₃ mol/l | Average, AgBrO₃ mol/l |
|---|---|---|---|---|---|
| 0.000 | 0.010 | 3.98 · 10⁻³ | 4.01 · 10⁻³ | 3.97 · 10⁻³ | 3.99 · 10⁻³ |
| 0.001 | 0.010 | 4.75 · 10⁻³ | 4.83 · 10⁻³ | 4.87 · 10⁻³ | 4.82 · 10⁻³ |
| 0.003 | 0.010 | 4.94 · 10⁻³ | 4.90 · 10⁻³ | — | 4.92 · 10⁻³ |
| 0.010 | 0.010 | 5.03 · 10⁻³ | 5.06 · 10⁻³ | 5.16 · 10⁻³ | 5.08 · 10⁻³ |
| 0.030 | 0.010 | 5.43 · 10⁻³ | 5.54 · 10⁻³ | 5.50 · 10⁻³ | 5.49 · 10⁻³ |
| 0.100 | 0.010 | 6.39 · 10⁻³ | 6.35 · 10⁻³ | 6.37 · 10⁻³ | 6.37 · 10⁻³ |
| 0.300 | 0.010 | 7.54 · 10⁻³ | 7.54 · 10⁻³ | 7.58 · 10⁻³ | 7.55 · 10⁻³ |
| 1.000 | 0.010 | 1.12 · 10⁻² | 1.11 · 10⁻² | 1.13 · 10⁻² | 1.12 · 10⁻² |
Table 6
Solubility of AgBrO₃ in the system AgBrO₃—KBrO₃—NaNO₃—H₂O
| NaNO₃, mol/l | KBrO₃, mol/l | Experiment No. 1, AgBrO₃ mol/l | Experiment No. 2, AgBrO₃ mol/l | Experiment No. 3, AgBrO₃ mol/l | Average, AgBrO₃ mol/l |
|---|---|---|---|---|---|
| 0.000 | 0.100 | 9.75 · 10⁻⁴ | 1.10 · 10⁻³ | 1.10 · 10⁻³ | 1.06 · 10⁻³ |
| 0.001 | 0.100 | 1.09 · 10⁻³ | 1.05 · 10⁻³ | 1.08 · 10⁻³ | 1.07 · 10⁻³ |
| 0.003 | 0.100 | 1.12 · 10⁻³ | 1.13 · 10⁻³ | 1.14 · 10⁻³ | 1.13 · 10⁻³ |
| 0.010 | 0.100 | 1.18 · 10⁻³ | 1.21 · 10⁻³ | 1.20 · 10⁻³ | 1.20 · 10⁻³ |
| 0.030 | 0.100 | 1.24 · 10⁻³ | 1.23 · 10⁻³ | 1.26 · 10⁻³ | 1.24 · 10⁻³ |
| 0.100 | 0.100 | 1.33 · 10⁻³ | 1.33 · 10⁻³ | 1.36 · 10⁻³ | 1.34 · 10⁻³ |
| 0.300 | 0.100 | 1.52 · 10⁻³ | 1.50 · 10⁻³ | 1.53 · 10⁻³ | 1.52 · 10⁻³ |
| 1.000 | 0.100 | 2.62 · 10⁻³ | 2.78 · 10⁻³ | 2.68 · 10⁻³ | 2.69 · 10⁻³ |
Fig. 3. Solubility of \( \mathrm{AgBrO_3} \) in the system
\( \mathrm{AgBrO_3—KBrO_3—NaNO_3—H_2O} \) at \( C_{\mathrm{KBrO_3}} = 1 \cdot 10^{-3} \).
Fig. 4. Solubility of \( \mathrm{AgBrO_3} \) in the system
\( \mathrm{AgBrO_3—KBrO_3—NaNO_3—H_2O} \) at \( C_{\mathrm{KBrO_3}} = 1 \cdot 10^{-2} \).
Table 7
System \( \mathrm{AgBrO_3—KBrO_3—NaNO_3—H_2O} \)
| \( \mathrm{NaNO_3} \), mol/l | \(\mu\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-3}\) | \(\gamma\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-3}\) | \(L_p\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-3}\) | \(L_1:L_1^0\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-3}\) | \(L_p:L_p^0\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-3}\) | \(\mu\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-2}\) | \(\gamma\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-2}\) | \(L_p\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-2}\) | \(L_1:L_1^0\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-2}\) | \(L_p:L_p^0\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-2}\) | \(\mu\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-1}\) | \(\gamma\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-1}\) | \(L_p\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-1}\) | \(L_1:L_1^0\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-1}\) | \(L_p:L_p^0\) at \(C_{\mathrm{KBrO_3}}=1\cdot10^{-1}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.001 | 0.0055 | 0.924 | \(6.44\cdot10^{-5}\) | 2.88 | 1.636 | 0.0158 | 0.878 | \(7.14\cdot10^{-5}\) | 3.48 | 1.36 | 0.1021 | 0.714 | \(1.08\cdot10^{-4}\) | 4.06 | 0.326 |
| 0.003 | 0.0089 | 0.888 | \(7.03\cdot10^{-5}\) | 2.88 | 1.636 | 0.0179 | 0.866 | \(7.34\cdot10^{-5}\) | 3.48 | 1.36 | 0.1041 | 0.695 | \(1.14\cdot10^{-4}\) | 4.06 | 0.326 |
| 0.010 | 0.0192 | 0.852 | \(7.58\cdot10^{-5}\) | 2.88 | 1.636 | 0.0251 | 0.846 | \(7.66\cdot10^{-5}\) | 3.48 | 1.36 | 0.1112 | 0.674 | \(1.21\cdot10^{-4}\) | 4.06 | 0.326 |
| 0.030 | 0.0398 | 0.794 | \(8.72\cdot10^{-5}\) | 2.88 | 1.636 | 0.0455 | 0.804 | \(8.50\cdot10^{-5}\) | 3.48 | 1.36 | 0.1312 | 0.654 | \(1.25\cdot10^{-4}\) | 4.06 | 0.326 |
| 0.100 | 0.1107 | 0.731 | \(1.03\cdot10^{-4}\) | 2.88 | 1.636 | 0.1164 | 0.727 | \(1.04\cdot10^{-4}\) | 3.48 | 1.36 | 0.2013 | 0.636 | \(1.36\cdot10^{-4}\) | 4.06 | 0.326 |
| 0.300 | 0.3122 | 0.634 | \(1.37\cdot10^{-4}\) | 2.88 | 1.636 | 0.3175 | 0.646 | \(1.32\cdot10^{-4}\) | 3.48 | 1.36 | 0.4015 | 0.508 | \(1.54\cdot10^{-4}\) | 4.06 | 0.326 |
| 1.000 | 1.0145 | 0.530 | \(1.96\cdot10^{-4}\) | 2.88 | 1.636 | 1.0242 | 0.482 | \(2.37\cdot10^{-4}\) | 3.48 | 1.36 | 1.1027 | 0.446 | \(2.76\cdot10^{-4}\) | 4.06 | 0.326 |
\(^{1)}\) \(L_1\) and \(L_p\) are the solubilities of \( \mathrm{AgBrO_3} \), respectively, in 1 m sodium nitrate solution and in water.
\(^{2)}\) \(L_1^0\) and \(L_p^0\) are the solubility products of \( \mathrm{AgBrO_3} \), respectively, in 1 m sodium nitrate solution and in water.
at the expense of sodium nitrate already at \(0.01\ \mathrm{mol/l}\) NaNO\(_3\). A still greater increase in the concentration of sodium nitrate is accompanied by a further regular increase in the solubility of the precipitate. In a one-molar solution of NaNO\(_3\), the solubility of silver bromate reaches \(1.35\cdot 10^{-2}\), i.e.,
Fig. 5. Solubility of AgBrO\(_3\) in the system AgBrO\(_3\)—KBrO\(_3\)—NaNO\(_3\)—H\(_2\)O at \(C_{\mathrm{KBrO}_3}=1\cdot10^{-1}\)
Fig. 6. Solubility of AgBrO\(_3\) in the system AgBrO\(_3\)—KBrO\(_3\)—NaNO\(_3\)—H\(_2\)O; I—at \(C_{\mathrm{KBrO}_3}=1\cdot10^{-3}\); II—at \(C_{\mathrm{KBrO}_3}=1\cdot10^{-2}\); III—at \(C_{\mathrm{KBrO}_3}=1\cdot10^{-1}\)
increases by more than a factor of 1.6 in comparison with the solubility in water. At a potassium bromate concentration of \(0.01\ \mathrm{mol/l}\), the decrease in the solubility of the precipitate due to the bromate ion is completely compensated by the corresponding increase in solubility due to sodium nitrate only at a concentration of \(0.5\ \mathrm{mol/l}\). In a one-molar sodium nitrate solution the solubility
Fig. 7. Change in the solubility product of AgBrO\(_3\) in the system AgBrO\(_3\)—KBrO\(_3\)—H\(_2\)O
Fig. 8. Change in the solubility product of AgBrO\(_3\) in the system AgBrO\(_3\)—KBrO\(_3\)—NaNO\(_3\)—H\(_2\)O
by the corresponding increase in solubility due to sodium nitrate only at a concentration of \(0.5\ \mathrm{mol/l}\). In a one-molar sodium nitrate solution the ra-
the solubility of the precipitate becomes equal to \(1.12 \cdot 10^{-2}\), i.e., 1.36 times greater than its solubility in water. At a potassium bromate concentration of \(0.1\ \mathrm{mol/l}\), even a molar concentration of sodium nitrate makes it possible to increase the solubility of the precipitate only to \(2.69 \cdot 10^{-3}\ \mathrm{mol/l}\), i.e., under these conditions the solubility of the precipitate remains more than 3 times less than its solubility in water.
In accordance with the change in solubility, a change occurs in the solubility product of the precipitate. As can be seen from Figs. 8, 9, and 10, at all potassium bromate concentrations studied by us, an increase in the concentration of sodium nitrate in the system is accompanied by an invariable increase in the solubility product. At a \( \mathrm{KBrO_3} \) concentration of \(0.001\ \mathrm{mol/l}\) this increase reaches a value of \(1.96 \cdot 10^{-4}\); at a \( \mathrm{KBrO_3} \) concentration of \(0.01\ \mathrm{mol/l}\), \(2.37 \cdot 10^{-4}\); and at a \( \mathrm{KBrO_3} \) concentration of \(0.1\ \mathrm{mol/l}\), \(2.76 \cdot 10^{-4}\ \mathrm{mol/l}\). Thus, the greatest increase in the solubility product occurs in a decimolar solution of potassium bromate, where the solubility product of the precipitate increases by a factor of 4.06 in comparison with the solubility product in an aqueous solution of silver bromate. The smallest increase in the solubility product of the precipitate occurs in a \(0.001\)-molar \( \mathrm{KBrO_3} \) solution. However, even under these conditions it is 2.88 times greater than in water.
Fig. 9. Change in the solubility product of \( \mathrm{AgBrO_3} \) in the system
\( \mathrm{AgBrO_3-KBrO_3-NaNO_3-H_2O} \)
Fig. 10. Change in the solubility product of \( \mathrm{AgBrO_3} \) in the system
\( \mathrm{AgBrO_3-KBrO_3-NaNO_3-H_2O} \)
The activity coefficient of silver bromate in this system also varies within wide limits. The activity coefficient was determined at all studied points of the system by the formula
\[ \gamma_{\mathrm{AgBrO_3}}=\sqrt{\frac{L_a}{L_p}}, \]
where \(\gamma_{\mathrm{AgBrO_3}}\) is the activity coefficient of silver bromate, \(L_a\) is the activity product of the precipitate, found by us to be \(5.50 \cdot 10^{-5}\), and \(L_p\) is the solubility product of the precipitate.
At all studied points of the system, an increase in the ionic strength of the solution is invariably accompanied by a decrease in the activity coefficient of silver bromate.
In one-molar solutions of NaNO₃, when the concentration of KBrO₃ is 0.001 mol/l, the activity coefficient of silver bromate becomes equal to 0.530; when the concentration of KBrO₃ is 0.01 mol/l, it becomes equal to 0.482; and when the concentration of KBrO₃ is 0.1 mol/l, it becomes equal to 0.446. Thus, the activity coefficient has its smallest value in a one-molar solution of NaNO₃ and a decimolar solution of KBrO₃.
Conclusions
The solubility of the silver bromate precipitate was studied in the three-component system AgBrO₃—KBrO₃—H₂O at KBrO₃ concentrations from 0.001 to 0.3 mol/l, and in the four-component system AgBrO₃—KBrO₃—NaNO₃—H₂O at KBrO₃ concentrations of 0.001, 0.01, and 0.1 mol/l and NaNO₃ concentrations from 0.001 to 1 mol/l at 25°.
It was established that in the system AgBrO₃—KBrO₃—H₂O the solubility of the AgBrO₃ precipitate decreases regularly with increasing potassium bromate concentration. At the highest KBrO₃ concentration in our experiments, 0.3 mol/l, the solubility of the precipitate decreases by a factor of 11.8 in comparison with its solubility in water.
In the system AgBrO₃—NaNO₃—H₂O, under the influence of the external electrolyte, as the NaNO₃ concentration increases, there is a regular increase in the solubility of the precipitate. However, sodium nitrate, as an electrolyte that has no ion in common with the precipitate, affects the solubility of the precipitate to a considerably lesser degree than potassium bromate. Even in a one-molar NaNO₃ solution, the solubility of AgBrO₃ increases only by a factor of 1.8 in comparison with its solubility in water.
In the system AgBrO₃—KBrO₃—NaNO₃—H₂O, the change in solubility of the precipitate is the result of the summation of two mutually superposed effects acting in opposite directions: a decrease in the solubility of the precipitate under the influence of potassium bromate, and an increase in the solubility of the precipitate under the influence of sodium nitrate.
It was established that in all the systems studied the solubility product of the precipitate varies over wide limits: in the system AgBrO₃—KBrO₃—H₂O it increases by a factor of 3.1; in the system AgBrO₃—NaNO₃—H₂O, by a factor of 3.22; in the system AgBrO₃—KBrO₃—NaNO₃—H₂O, at a KBrO₃ concentration of 0.001 mol/l, by a factor of 2.88; at a KBrO₃ concentration of 0.01 mol/l, by a factor of 3.48; and at a KBrO₃ concentration of 0.1 mol/l, by a factor of 4.06.
For broader conclusions concerning the influence of electrolytes with common ions and without common ions in three- and four-component systems on the solubility of precipitates, further accumulation of experimental data is necessary.
LITERATURE
- Lelchuk Yu. L., Sasonko S. M. Izv. TPI, vol. 71, 52, 1952.
- Tananaev I. V., Lelchuk Yu. L., Petrovitskaya B. Kh. ZhOKh, 19, issue 7, 1949.
- Lelchuk Yu. L. Izv. TPI, vol. 77, 1953.
- Proceedings of the Conference on Classical Methods of Analysis, 1951.
- Tananaev I. V., Mizetskaya I. B. Zhurn. an. khim., 6, issue 6, 342, 1951.
- Babko A. K. Zhurn. an. khim., 7, issue 1, 1952.
- Karyakin Yu. V. Pure Chemical Reagents, 169, 1947.
- OST 17383—39.
- Karyakin Yu. V. Pure Chemical Reagents, 1947.
- Ricci, Aleshnik, J. Amer. Chem. Soc., 66, 980, 1944.