# PH / ISE - Meter (Orion 920A)

## Measurement of the mean activity coefficients of ions (ϒ ± ) by determination of the electromotive force (EMF)

For the prediction of solid-liquid equilibria (SLE) of aqueous salt solutions the solubility product Ksp for the reaction and the mean ionic activity coefficient ( ) has to be known. Ksp can be calculated from tabulated thermodynamic data can be measured by determination of the electromotive force (EMF). Once the standard potential of the cell is known, the activities of the ions can be determined simply by measuring the electromotive force (EMF) of the cell at the salt concentration of interest. The potential difference between the two ion sensitive electrodes is measured with the help of an ion meter (model ORION 920A). Fig.1 EMF Apparatus

In contrast to other work the measurements are not performed by determination of the potential difference between a standard reference electrode and an ion selective electrode. To prevent an extensive calibration the potential difference is directly measured between the cation and the anion selective electrode. 90 cm3 of sample solution are filled into the cell and with the help of a thermostat the contents is kept at constant temperature. The temperature is measured by an mercury thermometer (0.1 K).
After determining the standard potential (E0) of the cell by a graphical method the activity coefficient of the ions ( ) can be calculated by the Nernst equation. Starting from the Nernst equation for 1,1-electrolytes it can be written (1)

E potential difference of the cell
E0 standard potential of the cell
R universal gas constant
T absolute temperature
m molality [mol salt/1000g solvent]
ϒ± mean activity coefficient of ion

Replacing ln(g±) in equation (1) with the Debye-Hückel limiting law (2)

with A = Debye-Hückel parameter and I = ionic strength) the expression rearranges for concentrations smaller than 0.1 mol× kg-1 (3)

The expression on the left hand side of eq. (3) [E-2RT/F*ln m] is evaluated at a range of molalities, plotted against , and extrapolated to m=0. The intercept at =0 is the value of E0 (figure 1). Once the standard potential of the cell is known, the mean activity coefficient of the ions can be calculated from equation 1.
Until now the binary systems NaCl/water and KCl/water in the temperature range between 25 and 60 °C and at different salt concentrations have been measured to verify the apparatus. Fig. 2 shows that the observed results at 25 °C are in good agreement with published data. Fig 2. Linear Extrapolation to determine E0
NaCl KCl Figure 3. Mean activity coefficients of NaCl and KCl in water at 25 °C

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