IONIZATION THERMODYNAMICS OF SURFACES WITH FIXED DISSOCIABLE GROUPS

For solids that do not dissolve in the contacting solution and whose s urfaces contain fixed dissociable groups a rigorous thermodynamic trea tment shows that when m(i) much greater than m(H)+ or m(OH)-, the expr ession (partial derivative ln m(H)+/partial derivative T)(p,mi,Gamma p ) = -Delta h(p)/RT(2) describes the temperature dependence of potentio metric titration curves both at and away from the zero point of charge (ZPC), where m(H)+, m(OH)-, and mi respectively are bulk concentratio ns of hydrogen ions, hydroxyl ions, and supporting electrolyte ions, F Gamma(p) is the primary surface charge density, and Delta h(p), the p artial molar enthalpy of surface group protonation, is well defined ph ysically and accessible via calorimetry. Consequently the necessary an d sufficient condition for temperature congruence of potentiometric ti tration curves is that Delta h(p), does not depend on Gamma(p) at cons tant T, p, and m(i). An expression for the enthalpy of forming a diffu se double layer is forwarded that differs from the so-called field ene rgy by a factor of (1 + partial derivative ln epsilon/partial derivati ve ln T), where epsilon is the dielectric constant of water. It follow s therefrom that any contribution to Delta h(p) from the diffuse layer is insignificant. When the method of congruence plots is applied to t itration data on hematite and rutile it is found in common with other systems that the BET area per gram is about half the electrochemical s urface area. The resultant inner region capacitances at 20 degrees C a re 58 and 88 mu F cm(-2), respectively.