Abstract
Full Text
PHYSICAL CHEMISTRY
Corresponding Member of the Academy of Sciences of the USSR B. P. NIKOL’SKII, M. M. SHUL’TS, and A. A. BELYUSTIN
THE INFLUENCE OF THE NATURE OF THE SECOND GLASS-FORMING OXIDE ON THE SODIUM AND POTASSIUM ELECTRODE FUNCTIONS OF SILICATE GLASSES
Glass electrodes possessing the electrode function of an alkali metal over a wide pH range can be obtained from alkali-silicate glasses containing, in addition to SiO₂, certain other glass-forming oxides, for example Al₂O₃, B₂O₃, Ga₂O₃, Fe₂O₃ (¹–³).
In earlier works, the existence of a metallic function in glasses containing B₂O₃ and Al₂O₃ (⁴,⁵) was thermodynamically rigorously demonstrated; the influence of foreign cations on the sodium and potassium functions and the transition from one to the other were studied (⁶–⁹); and it was shown that the “simple” ion-exchange theory of the glass electrode (¹⁰) describes with high accuracy the behavior of individual glasses in the case of Na⁺—K⁺ and Na⁺—Li⁺ exchange (¹¹). In the work (¹²), devoted to an investigation of the electrode properties of sodium aluminosilicate glasses, ways were outlined for creating electrodes with increased specificity toward Na⁺ or K⁺ ions. In the present work the sodium electrode function of glasses of composition Na₂O—RₓOᵧ—SiO₂, where R = B, Al, Ga, Fe^III, Sn^IV, was investigated in order to test the applicability to them of the “simple” ion-exchange theory.
To study the electrode properties of the glasses we used the galvanic cell:
\[ \mathrm{Ag/AgCl,\ NaCl\ (0.1M)\ (glass)\ external\ solution,\ AgCl/Ag.} \tag{1} \]
The emf of cell (1) was measured at room temperature with an accuracy of ±1 mV. The composition of the external solutions and the designations of the measured emf are clear from Table 1.
Table 1
| External solution (in the order of the experiments) | Designation of emf | Name of emf |
|---|---|---|
| NaCl (0.1 M) | \(\varphi_{\mathrm{as}}\) | Asymmetry potential |
| NaCl (1—0.001 M) | \(E_{\mathrm{Na}}\) | Calibration values of emf |
| NaCl (1—0.001 M) + KCl (0.05 M) | \(E\) | Emf in mixed solutions |
| KCl (0.1 M) | \(E_{\mathrm{NaK}}\) | Biionic potential |
The procedure for melting the glasses, preparing the electrodes, and measuring the emf has been described earlier (³,¹³). For the investigation, glasses possessing a sodium function at pH 4 and above were selected (³). All measured emf values were corrected for \(\varphi_{\mathrm{as}}\); for several electrodes made from one glass, the mean value was taken, from which the emf for individual electrodes differed on average by ±6 mV. Curves \(E\)—\(\lg a_{\mathrm{NaCl}}\) were constructed, which for NaCl solutions had the form of straight lines (“calibration” of the electrodes). In the case of mixed solutions, where \(a_{\mathrm{NaCl}} = m_{\mathrm{NaCl}}\cdot m_{\mathrm{NaCl+KCl}}\gamma^{2}_{\pm\mathrm{NaCl(KCl)}}\), we assumed that the values of the activity coefficients of electrolytes in mixed solutions \(\gamma_{\pm\mathrm{NaCl(KCl)}}\)
and \(\gamma_{\pm\mathrm{KCl}(\mathrm{NaCl})}\) equal to the values of \(\gamma_{\pm\mathrm{NaCl}}\) and \(\gamma_{\pm\mathrm{KCl}}\) in pure solutions of the same ionic strength as the mixed solutions.
Graphically, the following were determined:
\[ \Delta E_{\mathrm{Na}} = E - E_{\mathrm{Na}} \tag{2} \]
and \(E_{\mathrm{t}}\)—the theoretical values of the emf—were calculated from equation (3) \((^{10,8})\):
\[ E_{\mathrm{t}} = E^0 + \vartheta_{\mathrm{e}}\lg\left(a_{\mathrm{NaCl}} + K_{\mathrm{NaK}}a_{\mathrm{KCl}}\right), \tag{3} \]
where
\[ K_{\mathrm{NaK}} = \frac{a_{\mathrm{NaCl}}\cdot a_{\mathrm{K}^{+}}^{\mathrm{st}}} {a_{\mathrm{KCl}}\cdot a_{\mathrm{Na}^{+}}^{\mathrm{st}}}; \]
\(a_i^{\mathrm{st}}\) is the activity of ions in the glass; \(\vartheta_{\mathrm{e}}\) and \(E^0\) are constants determined from the calibration line;
\[ \vartheta_{\mathrm{e}} = \frac{dE_{\mathrm{Na}}}{d\lg a_{\mathrm{NaCl}}} \]
(\(\vartheta_{\mathrm{e}}\) often differed from
\[ \vartheta = \frac{RT}{F}\cdot 2.303); \]
\(E^0 = E_{\mathrm{Na}}\) at \(a_{\mathrm{NaCl}} = 1\).
Also calculated was
\[ \Delta E_{\mathrm{t}} = E - E_{\mathrm{t}}. \tag{4} \]
The calculation of \(K_{\mathrm{NaK}}\) was carried out, as a rule*, from the values of the biionic potential:
\[ \lg K_{\mathrm{NaK}} = \frac{E_{\mathrm{NaK}}}{\vartheta_{\mathrm{e}}}. \tag{5} \]
Fig. 1 clearly shows the variation of the quantities considered here, \(E_{\mathrm{t}}\), \(E_{\mathrm{Na}}\), and \(E\), as functions of \(\lg a_{\mathrm{NaCl}}\) for several glasses, from a glass with a predominantly sodium function (curve 1) to a glass with a predominantly potassium function (curve 5).
The results of measurements and calculations for all the investigated glasses are summarized in Table 2**. From the data of Table 2 it is seen that the values of \(\Delta E_{\mathrm{t}}\) nowhere exceed 5–6 mV, i.e., the limits of reproducibility of the measurements for each glass, which proves the applicability to all the glasses studied of equation (3) of the “simple” ion-exchange theory. It follows from this that the exchange constant \(K_{\mathrm{NaK}}\) can serve as a sufficiently accurate measure of the specificity of the electrode function—
![Figure 1 graph]
Fig. 1. Dependence of the calibration, theoretical, and measured emf values of the element (1) in mixed solutions on \(\lg a_{\mathrm{NaCl}}\). Glasses: \(1\)—NaAl-1313, \(K_{\mathrm{NaK}} = 0.022\); \(2\)—NaB-1914, \(K_{\mathrm{NaK}} = 0.09\); \(3\)—NaG-2214, \(K_{\mathrm{NaK}} = 0.45\); \(4\)—NaFe-2210, \(K_{\mathrm{NaK}} = 1.1\); \(5\)—NaAl-2705, \(K_{\mathrm{NaK}} = 5.0\). \(a\)—\(E_{\mathrm{Na}}\); \(b\)—\(E_{\mathrm{t}}\); \(v\)—\(E\). The numerical ordinate values refer to curve 1. Each subsequent curve is shifted along the ordinate by 40 mV relative to the preceding one.
* See note (?) to Table 2.
** In the designation of the glasses their composition (mol. %) by synthesis is indicated. For example: NaAl-1505 is a glass containing 15 mol.% Na\(_2\)O, 5 mol.% Al\(_2\)O\(_3\), 80 mol.% SiO\(_2\); NaB-2209—22% Na\(_2\)O, 9.4% B\(_2\)O\(_3\), 68.6% SiO\(_2\); NaFe-2210—22% Na\(_2\)O, 10% Fe\(_2\)O\(_3\), 68% SiO\(_2\), etc.
i.e. The smaller its numerical value is than unity, the more specific is the sodium function of the glass; and, conversely, the greater \(K_{\mathrm{NaK}}\) is than 1, the more specific the glass is with respect to \(K^+\) ions. From the applicability of equation (3) it also follows that, if \(K_{\mathrm{NaK}}\) is known, the value of \(\Delta E_{\mathrm{Na}}\) can be calculated for any ratio of the activities (concentrations) of \(Na^+\) and \(K^+\) from the equation
\[ \Delta E_{\mathrm{Na}}=\vartheta \lg \left(1+\frac{a_{\mathrm{KCl}}}{a_{\mathrm{NaCl}}}K_{\mathrm{NaK}}\right). \tag{6} \]
It was found earlier \((^{2,13})\) that the values of \(K_{\mathrm{HNa}}\) are in a one-to-one dependence on the ratio of the molar concentrations of acidic (glass-forming) and basic (modifying) oxides in the glass. The same
Fig. 2. Dependence of \(\lg K_{\mathrm{NaK}}\) on the ratio of the concentrations of the second glass-forming oxide and the basic oxides in glasses of various systems
\[ X=[R_xO_y]/[\mathrm{M_2O}]. \]
\(1\)—LiAl-23\(_3\)10;
\(2\)—Na\(_2\)O—Al\(_2\)O\(_3\)—SiO\(_2\);
\(3\)—Na\(_2\)O—B\(_2\)O\(_3\)—SiO\(_2\);
\(4\)—Na\(_2\)O—Al\(_2\)O\(_3\)—B\(_2\)O\(_3\)—SiO\(_2\).
The data are taken from \((^{4,8,7})\), respectively, for the glasses NaAlB-110311, -150311 and -250509. In these cases
\[ X=\frac{[\mathrm{Al_2O_3}]+[\mathrm{B_2O_3}]}{[\mathrm{Na_2O}]}; \]
\(5\)—Na\(_2\)O—Ga\(_2\)O\(_3\)—SiO\(_2\);
\(6\)—Na\(_2\)O—Fe\(_2\)O\(_3\)—SiO\(_2\);
\(7\)—Na\(_2\)O—SnO\(_2\)—SiO\(_2\).
rule is also fulfilled for \(K_{\mathrm{NaK}}\), as was first shown for glasses with Al\(_2\)O\(_3\) \((^{12})\) and is evident from Fig. 2. With an increase in the ratio \(X=[R_xO_y]/[\mathrm{Na_2O}]\), the sodium function of the glasses becomes more specific. It is also evident from Fig. 2 that, at the same \(X\), different \(K_{\mathrm{NaK}}\) values are obtained depending on the nature of the glass former. Since, as \(X\) changes, the constants change from values \(K_{\mathrm{NaK}}<1\) to \(K_{\mathrm{NaK}}>1\), this means that in each system one may have glasses predominantly with a sodium function (for example, NaAl-1118, -1313) and predominantly with a potassium function (for example, NaAl-2140\(_2\), -2204, NaGa-2204). Of interest is the fact that in the regions of the limiting values of \(X\) in the investigated range of glass compositions, the nature of the second glass-forming oxide has no substantial effect on the specificity of the electrode function of the glass, whereas at intermediate values of \(X\) (\(0.4<X<0.9\)) its influence is more noticeable.
The points for the investigated NaSn glasses are located near the curve for NaAl glasses, and for NaFe near NaGa, although, apparently, \(K_{\mathrm{NaK}}\) for them does not change so strongly with composition.
As for the nature of the basic oxide, the example of LiAl-23\(_3\)10 glass shows that lithium glasses can attain a higher ability to exhibit a sodium function in the presence of potassium ions than sodium glasses. This is evidently connected with steric hindrance for potassium ions in lithium glasses.
It should be noted that the numerical values of \(K_{\mathrm{NaK}}\) calculated by us differ by several times from those found in \((^{12})\) for the same glasses. This discrepancy can probably be explained partly by the difference in procedure, and mainly by the influence of the hydrogen ion, which in these glasses should be more noticeable for the potassium function. More accurate and consistent data can be obtained by using an equation that takes into account the exchange of three
Table 2
| Glass | $\vartheta_{\mathrm{E}}$ | $E^\circ$ | $K$ | \multicolumn{3}{c}{$\mathrm{Na}^+:\mathrm{K}^+=20:1$; $a_{\mathrm{NaCl}}=4.56\cdot10^{-1}$; $a_{\mathrm{KCl}}=1.93\cdot10^{-2}$} | \multicolumn{3}{c}{$10:1$; $1.25\cdot10^{-1}$; $1.14\cdot10^{-2}$} | \multicolumn{3}{c}{$5:1$; $3.77\cdot10^{-2}$; $7.08\cdot10^{-3}$} | \multicolumn{3}{c}{$2:1$; $8.47\cdot10^{-3}$; $4.09\cdot10^{-3}$} | \multicolumn{3}{c}{$1:1$; $3.04\cdot10^{-3}$; $2.95\cdot10^{-3}$} | \multicolumn{3}{c}{$1:2$; $1.19\cdot10^{-3}$; $2.35\cdot10^{-3}$} | \multicolumn{3}{c}{$1:5$; $3.94\cdot10^{-4}$; $1.96\cdot10^{-3}$} | \multicolumn{3}{c}{$1:10$; $2.0\cdot10^{-4}$; $1.8\cdot10^{-3}$} | \multicolumn{3}{c}{$1:50$; $3.8\cdot10^{-5}$; $1.7\cdot10^{-3}$} |
|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| | | | | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ | $E$ | $\Delta E_{\mathrm{Na}}$ | $\Delta E_{\mathrm{K}}$ |
| NaAl—1118¹ | 56 | +126 | 0.017 | +105 | 0 | −2 | +75 | 0 | 0 | +46 | 0 | 0 | +9 | 0 | −1 | −17 | 0 | −2 | −39 | 0 | −2 | −64 | +1 | −1 | −80 | +1 | −2 | −113 | +7 | −5 |
| —1313 | 57 | +125 | 0.022 | +104 | 0 | −2 | +74 | 0 | 0 | +44 | 0 | 0 | +6 | 0 | −1 | −18 | 0 | −2 | −42 | 0 | 0 | −67 | 0 | −2 | −83 | 0 | −4 | −109 | +15 | −1 |
| —1515 | 55 | +123 | 0.048 | +104 | 0 | 0 | +75 | 0 | +2 | +45 | 0 | 0 | +8 | 0 | −2 | −16 | −1 | −2 | −38 | −2 | −2 | −61 | 0 | −2 | −75 | +2 | −3 | −98 | +18 | −5 |
| —1510 | 55 | +124 | (0.05)² | +105 | 0 | 0 | +75 | 0 | +1 | +44 | 0 | −2 | +9 | +2 | −2 | −16 | +1 | −3 | −38 | −2 | −4 | −64 | 0 | −6 | −73 | +6 | −2 | −90 | +29 | +1 |
| —1505 | 57 | +128 | 0.64 | +109 | 0 | 0 | +78 | +1 | 0 | +48 | 0 | −2 | +16 | +6 | −1 | −2 | +13 | +1 | −22 | +15 | −4 | −32 | +32 | −1 | −36 | +44 | 0 | −40 | +80 | 0 |
| —1717 | 56 | +122 | 0.032 | +103 | 0 | 0 | +72 | 0 | 0 | +42 | −2 | 0 | +8 | 0 | +2 | −16 | 0 | −2 | −39 | 0 | +1 | −64 | 0 | +1 | −79 | 0 | 0 | −104 | +141 | −1 |
| —2020 | 57 | +127 | 0.026 | +107 | −2 | −3 | +75 | 0 | 0 | +46 | 0 | +1 | +8 | 0 | −1 | −16 | 0 | 0 | −35 | +4 | +3 | −58 | +9 | +6 | −73 | +10 | +6 | −105 | +18 | +1 |
| —2010 | 55 | +124 | 0.20 | +105 | 0 | 0 | +75 | 0 | 0 | +47 | 0 | 0 | +10 | 0 | −2 | −11 | +3 | +1 | −32 | +3 | −3 | −50 | +11 | −3 | −57 | +20 | −2 | −68 | +48 | −3 |
| —2005 | 57 | +124 | (1.1) | +105 | 0 | −1 | +75 | +2 | 0 | +51 | +6 | +3 | +20 | +14 | +4 | 0 | +18 | +1 | −12 | +28 | +2 | −22 | +45 | +2 | −25 | +57 | +5 | −30 | +90 | +2 |
| —2217 | 56 | +130 | (0.028) | +110 | 0 | −1 | +79 | 0 | 0 | +49 | 0 | 0 | +13 | 0 | −4 | −13 | 0 | −3 | −35 | 0 | −2 | −59 | +2 | −1 | −72 | +4 | 0 | −98 | +16 | 0 |
| —2207 | 58 | +128 | (1.3) | +108 | 0 | −1 | +78 | +4 | −1 | +51 | +8 | 0 | +22 | +16 | +2 | +6 | +25 | +3 | −10 | +31 | +4 | −14 | +53 | +5 | −16 | +68 | +6 | −20 | +107 | +6 |
| —2204 | 57 | +124 | 3.1 | +106 | +2 | −2 | +79 | +6 | 0 | +54 | +12 | 0 | +28 | +23 | 0 | +15 | +34 | 0 | −5 | +47 | −1 | 0 | +67 | +1 | −4 | +82 | 0 | −6 | +120 | 0 |
| —2102₂ | 56 | +125 | (6.8) | +108 | +3 | −5 | +83 | +3 | +2 | +64 | +18 | −2 | +40 | +32 | −4 | +29 | +45 | −4 | +22 | +60 | −4 | −20 | +85 | −1 | −20 | +100 | +3 | +18 | +140 | +1 |
| —2515 | 57 | +126 | 0.065 | +106 | 0 | −1 | +75 | 0 | 0 | +46 | 0 | 0 | +10 | 0 | −3 | −16 | 0 | −3 | −38 | 0 | −4 | −61 | +4 | 0 | −74 | +6 | 0 | −95 | +25 | −3 |
| —2510 | 56 | +125 | 0.56 | +105 | 0 | −2 | +75 | 0 | −1 | +45 | +2 | −3 | +14 | +6 | −1 | −6 | +11 | −1 | −21 | +18 | 0 | −32 | +38 | +1 | −38 | +44 | 0 | −42 | +80 | +1 |
| —2705 | 57 | +123 | 5.0 | +105 | +3 | −3 | +81 | +10 | 0 | +58 | +17 | 0 | +35 | +31 | 0 | +21 | +41 | −1 | −15 | +58 | 0 | +10 | +81 | +1 | +9 | +97 | +4 | +8 | +127 | +3 |
| LiAl—23310¹ | 56 | +123 | 0.018 | +103 | 0 | −1 | +73 | 0 | +1 | +45 | 0 | +2 | +7 | 0 | 0 | −18 | 0 | 0 | −40 | 0 | −1 | −62 | +4 | +3 | −78 | +3 | +2 | −112 | +9 | −2 |
| NaB—1614 | 58 | +127 | 0.065 | +108 | 0 | 0 | +76 | 0 | +1 | +46 | 0 | −1 | +10 | +2 | −4 | −15 | +3 | −3 | −36 | +5 | −3 | −68 | −10 | +5 | −78 | −16 | +4 | −98 | −36 | +4 |
| —1610 | 55 | +122 | 0.24 | +100 | 0 | −3 | +70 | +2 | −3 | +45 | +2 | 0 | +13 | +6 | +2 | −8 | +9 | +3 | −27 | +12 | +2 | −45 | +20 | +2 | −99 | +31 | +3 | −63 | +58 | 0 |
| —1607 | 56 | +125 | (0.6) | +102 | 0 | −4 | +76 | +3 | −2 | +48 | +7 | 0 | +18 | +12 | +3 | −2 | +16 | +3 | −18 | +22 | +2 | −32 | +35 | 0 | −37 | +47 | 0 | −42 | +80 | 0 |
| —1604 | 57 | +126 | 1.6 | — | — | — | — | — | — | +46 | +20 | −5 | +22 | +15 | 0 | +4 | +21 | −2 | −5 | +34 | 0 | −15 | +52 | −1 | −37 | +66 | −1 | −21 | +82 | +1 |
| —1914 | 58 | +122 | 0.09 | +106 | 0 | −2 | +75 | [[unclear]] | 0 | +45 | +1 | 0 | +9 | +2 | +1 | −15 | +4 | +2 | −37 | +5 | 0 | −59 | +10 | +2 | −70 | +17 | +3 | −90 | +37 | −1 |
| —1910 | 57 | +124 | (0.38) | +105 | 0 | 0 | +70 | +1 | +8 | +47 | +4 | +4 | +15 | +8 | +5 | −6 | +12 | +6 | −24 | +16 | +6 | −42 | +25 | +2 | −48 | +33 | +2 | −59 | +62 | −3 |
| —1907 | 54 | +120 | (0.54) | +101 | 0 | −1 | +70 | 0 | +2 | +43 | +2 | −2 | +15 | +9 | +1 | −4 | +13 | +2 | −18 | +20 | +3 | −30 | +35 | +3 | −36 | +46 | +2 | −44 | +76 | −1 |
| —2209₄ | 58 | +124 | (1.1) | +104 | +2 | −1 | +73 | +4 | −1 | +49 | +8 | +3 | +18 | +14 | +3 | 0 | +21 | +3 | −13 | +30 | +3 | −25 | +45 | +1 | −30 | +56 | 0 | −34 | +90 | −1 |
| —2507 | 57 | +125 | 1.7 | +105 | 0 | −2 | +77 | −2 | 0 | +51 | +2 | 0 | +22 | +10 | 0 | +7 | +20 | −1 | −5 | +30 | +3 | −14 | +48 | −1 | −18 | +62 | −2 | −20 | +99 | −1 |
| NaGa—1717 | 57 | +127 | 0.06 | +105 | +2 | −3 | +35 | +2 | 0 | +47 | +4 | −2 | +13 | +5 | +3 | −12 | +5 | +3 | −33 | +6 | +3 | −56 | +18 | +5 | −70 | +12 | +1 | −94 | +29 | [[unclear]] |
| —1708 | 57 | +123 | (0.34) | +103 | −1 | 0 | +75 | +3 | +3 | +47 | +6 | −5 | +13 | +9 | +4 | −10 | +12 | +4 | −26 | +18 | +6 | −43 | +30 | +3 | −51 | +37 | +2 | −60 | +68 | 0 |
| —2214 | 54 | +121 | (0.45) | +104 | −2 | +1 | +75 | 0 | +2 | +45 | +2 | −1 | +13 | +8 | 0 | −7 | +13 | −2 | −25 | +17 | −3 | −37 | +34 | −1 | −40 | +48 | +1 | −46 | +83 | 0 |
| —2210 | 58 | +125 | 1.5 | +108 | −6 | −2 | +79 | +3 | 0 | +51 | +5 | −1 | +23 | +14 | +1 | +3 | +15 | −2 | −7 | +31 | 0 | −17 | +49 | −1 | −20 | +63 | −1 | −21 | +105 | +1 |
| —2207 | 58 | +129 | 2.2 | +110 | +1 | −2 | +79 | +2 | −2 | +53 | +7 | −2 | +26 | +17 | −1 | +12 | +17 | 0 | +3 | +43 | +1 | −7 | +60 | 0 | −10 | +74 | −1 | −13 | +111 | −2 |
| —2204 | 58 | +125 | 4.9 | +107 | −3 | −3 | +81 | +7 | −1 | +58 | +15 | −1 | +34 | +30 | −1 | +22 | +41 | −1 | +14 | +56 | −1 | +8 | +76 | −1 | +6 | +92 | −1 | +3 | +128 | −1 |
| NaFe—2214 | 55 | +121 | 0.81 | +100 | +1 | −3 | +72 | 0 | −1 | +45 | +2 | −1 | +17 | +9 | +2 | −1 | +15 | +3 | −15 | +22 | +2 | −24 | +25 | +4 | −27 | +52 | +6 | −32 | +84 | +4 |
| —2210 | 57 | +128 | 1.1 | +114 | +4 | +4 | +77 | 0 | −2 | +50 | +4 | −2 | +22 | +13 | +1 | +5 | +21 | +2 | −6 | +32 | +4 | −16 | +50 | +4 | −18 | +64 | +6 | −22 | +102 | +6 |
| —2207 | 57 | +127 | 1.7 | +107 | 0 | −2 | +77 | +1 | −2 | +52 | +5 | −1 | +26 | +18 | +2 | +12 | +28 | +2 | 0 | +39 | +3 | −6 | +60 | +5 | −10 | +73 | +4 | −12 | +110 | +5 |
| NaSn—2210 | 54 | +118 | (0.4) | +100 | +1 | 0 | +71 | +2 | +1 | +43 | +3 | 0 | +14 | +8 | +4 | −3 | +10 | 0 | −23 | +17 | +2 | −40 | +26 | 0 | −42 | +40 | +2 | −55 | +68 | +6 |
| —2207 | 51 | +117 | (0.7) | +100 | 0 | −2 | +72 | 0 | +1 | +44 | 0 | −3 | +17 | +7 | 0 | −2 | +11 | −2 | −11 | +23 | −2 | −23 | +39 | −1 | −24 | +50 | +4 | −30 | +82 | +1 |
| —2204 | 55 | +116 | (0.8) | +97 | 0 | −1 | +68 | 0 | 0 | +43 | +5 | +2 | +16 | +12 | +6 | −5 | +15 | +4 | −18 | +23 | +3 | −31 | +36 | +2 | −35 | +48 | +3 | −42 | +80 | −1 |
¹ These glasses were proposed by Eisenman (¹²).
² The values of $K_{\mathrm{NaK}}$ shown in parentheses were calculated not from $E_{\mathrm{NaK}}$, but directly from equation (3), applied to a solution of $0.001\,N$ NaCl $+0.05\,M$ KCl.
ions \(H^+\), \(Na^+\), and \(K^+\):
\[ E = E^0 + \vartheta \lg (a_{\mathrm{HCl}} + K_{\mathrm{HNa}} a_{\mathrm{NaCl}} + K_{\mathrm{HK}} a_{\mathrm{KCl}}), \tag{7} \]
or by creating conditions under which the quantity \(a_{\mathrm{HCl}}\) may be neglected in comparison with the others.
The satisfactory agreement with equation (3), in which the values of \(K_{\mathrm{NaK}}\) found by us were used, is explained by the fact that the measurements of the biionic potentials \(E_{\mathrm{NaK}}\), from which they were calculated, and the experiments in mixed solutions described by equation (3), were carried out under practically identical pH conditions. Thus, for a large number of different glasses we have shown the satisfactory applicability of the “simple” ion-exchange theory for describing their electrode behavior with respect to sodium and potassium ions. This facilitates the selection of glasses and the processing of measurement results in various fields of application of glass electrodes with sodium and potassium functions.
Leningrad State University
named after A. A. Zhdanov
Received
9 III 1962
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