Activity coefficient determination from cell potentials

THE DETERMINATION OF ACTIVITIES AND ACTIVITY COEFFICIENTS FROM CELL POTENTIALS... 

In this table, P represents anions of protein and organic phosphate. The membrane is permeable to the group represented by P. The mean values of the charge on P are -6.7 and -1.08 for the interior and the exterior of the cell, respectively. An electrical potential difference of At// = i/t, t// = 90 mV is measured, i and o denote the intracellular and extracellular, respectively. The activity coefficients of components inside and outside the cell are assumed to be the same, and pressure and temperature are 1 atm and 310 K. Assume that the diffusion flows in from the surroundings are positive and the diffusion flows out are negative. Using tracers, the unidirectional flows are determined as follows ... 

The standard potential of the silver-silver bromide electrode has been determined from emf measurements of cells with hydrogen electrodes and silver-silver bromide electrodes in solutions of hydrogen bromide in mixtures of water and N-methylacetamide (NMA). The mole fractions of NMA in the mixed solvents were 0.06, 0.15, 0.25, and 0.50, and the dielectric constants varied from 87 to 110 at 25°C. The molality of HBr covered the range 0.01-0.1 mol kg 1. Data for the mixed solvents were obtained at nine temperatures from 5° to 45°C. The results were used to derive the standard emf of the cell as well as the mean ionic activity coefficients and standard thermodynamic constants for HBr. The information obtained sheds some light on the nature of ion-ion and ion-solvent interactions in this system of high dielectric constant. 

The activity coefficients of sulfuric acid have been determined independendy by measuring three types of physical phenomena cell potentials, vapor pressure, and freezing point. A consistent set of activity coefficients has been reported from 0.1 to 8 m at 25°C (14), from 0.1 to 4 m and 5 to 55°C (18), and from 0.001 to 0.02 m at 25°C (19). These values are all based on cell potential measurements. The activity coefficients based on vapor pressure measurements (20) agree with those from potential measurements when they are corrected to the same reference activity coefficient. 

Electromotive force (emf) measurements are frequently used to determine activity coefficients of electrolyte solutions. Equation (136a) relates the emf to the activities of the reacting cell components. From concentration-dependent measurements the standard potential E° of the cell reaction and the activity coefficients can be obtained. As an example, according to Eq. (136a), the emf of the Galvanic cell... 

The standard potential is determined according to Eq. (5.1.5) using cell 11. The Hamed ceU is fiUed with hydrochloric acid of known molality (/mhci = 0.01 mol kg ). The mean activity coefficient of HCl, y hci> various temperatures is taken from the literature [13]. 

In routine blood analysis of electrolytes, where ion-selective electrodes are used nearly universally, very small concentration changes are sometimes determined with direct potentiometry. This requires potential stabilities and reproducibihties on the order of 10-100 pV, which is achieved in temperature controlled flow-through cells and with frequent, automated recalibrations between measurements/ In batch mode benchtop analyses with ISEs and in environmental monitoring applications, such a high precision is often not achieved. Precision and accuracy is mainly limited by variations in the liquid junction potential between the calibration and sample phases and by interferences from other sample ions, temperature fluctuations, and, if concentrations rather than activities are desired, variations in activity coefficients. 

Determination of the Activity Coefficient from Measured Cell Potential... 

If the electrolyte has large ionic disorder and since the blocked ionic current i,o is zero. Equations (9.5) and (9.6) indicate that no gradient can exist in the electrostatic potential within the sample. Then the steady-state transport of electrons and holes occurs only due to diffusion nnder the influence of gradients in their concentrations. These gradients must be uniform if the diffusion coefficient does not depend markedly on the concentration. From Equations (9.2) and (9.3) and the ionization equilibrium, the cell voltage determines the ratio of the activities of the electronic species at both sides of the electrolyte ... 

---