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(3.3.6) The value of lim log y cl - may not be put equal to zero, as the overall ionic strength of the solution is not equal to zero, but it may be calculated using the Bates-Guggenheim equation (1.3.35). The values of pH(RVS) obtained in this way are listed in Table 3.7.
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194 Table 3.7 Values of pH(RVS) for the reference value standard of 0.05 mol kg"1 potassium hydrogen phthalate at various temperatures
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pH(RVS) 4.000 3.998 3.997 3.998 4.001 4.005 4.011
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pH(RVS) 4.018 4.022 4.027 4.038 4.050 4.064 4.080
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pH(RVS) 4.097 4.116 4.137 4.159 4.183 4.210 4.240
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For practical measurements, six further solutions were measured as primary standards and fifteen additional solutions as operational standards (the difference between these two types of standards lies in the presence or absence of a liquid junction; they need not be distinguished for routine measurements). In practice, the pH is mostly measured with a glass electrode (see Section 6.3), connected with a calomel electrode (see Section 3.2.2). The measuring system is calibrated by using a single standard S, with a pH(S) value lying as close as possible to the pH(X) value. The pH(X) value is then calculated from (S), E(X) and pH(S) by Eq. (3.3.4). It is preferable to use two standards Si and S2, selected so that p H ^ ) is smaller and pH(S2) larger than pH(X) (both the pH(S) values should be as close to pH(X) as possible). The value of pH(X) is then calculated from the usual formula for linear interpolation: E(S2)-E(Sl)
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Analogously to water, standards are measured for a mixture of methanol and water (50 per cent by weight) as well as for heavy water, pD = -loga(D 3 O + ). An operational approach to the determination of the acidity of solutions in deuterium oxide (heavy water) was suggested by Glasoe and Long. This quantity, pD, is determined in a cell consisting of an aqueous (H2O) glass electrode and a saturated aqueous calomel reference electrode on the basis of the equation = pHpHmeter reading
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where the subscript pHmeter reading denotes the pH value indicated on the conventional pHmeter. Determination of the pH in non-aqueous solvents is discussed in Section 3.2.7.
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3.3.3 Measurement of activity coefficients Mean activity coefficients can be measured potentiometrically, mostly in a concentration cell with or without transfer. Consider, for example, the cell (with a non-aqueous electrolyte solution) Ag | AgCl(s) | KCl( mi ) | K,Hg | KCl(m2) | AgCl(s) | Ag On passing a positive charge from the left to the right in the graphical scheme of this cell, silver is oxidized to form silver chloride; potassium passes through the amalgam into the other solution. Here, silver chloride is reduced to metallic silver and chloride ions. The overall reaction is the transfer of KC1 from a region of higher concentration to a region of lower concentration, so that the EMF of the cell is given by the equation ^
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where a2 = aK+acr is the mean activity of KC1. On rearrangement we obtain 2RT 2RT \na l= \na 2 r r
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= In ra2 + In y 2 + E (3.3.10) F F The concentration of solution 1 is kept constant while E is measured for different concentrations of solution 2. The expression (2RT/F) In m2 + E is plotted against ra2. The value of the ordinate at point ra2 = 0 yields the term (2RT/F) lna >1 as In y )2 = 0 at this point. Once the value of a l is known, then Eq. (3.3.10) and the measured E values can be used to calculate the actual mean activity of the electrolyte at an arbitrary concentration. 3.3.4 Measurement of dissociation constants The dissociation constants of acids and bases are determined either exactly, by means of a suitable cell without liquid junction and without measuring the pH directly, or approximately on the basis of a pH measurement in a cell with liquid junction, the potential of which is reduced to a minimum with the help of a salt bridge. In the former case we shall use, for example, the cell Pt,H2(/ H2 = 1) I HA(m1),NaA(m2),NaCl(m3) | AgCl(s) | Ag whose EMF is given by the expression (where H 3 O + is replaced by H + for
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- in (aH+acr)