A Thermodynamic Dilemma? Some of your readers may be interested in being challenged to detect the fallacy in the following argument which leade to conflicting statements: In a. homogeneous chemical equilibrium involving ideal gases one writes far the standard free energy change AGPo/T = R In K , and AGc0/T = - R in KO,depending on whether concentrations are in partial pressures or moles per liter, respectively. Differentiating each with respect to temperature a t constant pressure gives, by the Gibhs-Helmholtz relation, AH,'/RT~ = ( b In K P / O T ) ~ s nAHcD/RTZ d = ( 3 l n K . / b T ) ~where , AH,' and AH.* are the enthalpy changes when the gases me at unit partial pressure and one mole per liter, respectively. Since hoth K , and K. are independent of pressure, the partial notation may be dropped. Furthermore AH," = AH." = AH, since, for ideal gases, enthalpy is independent of pressure. We thus have AH/RTP = d in K,/dT and AHIRT* = d In KJdT. It follows that d ln K,/dT = d In KJdT. This last statement must he false if, as is often stated, d i n K,/dT = AH/RT2 and d ln K./dT = AE/RT2, for AH is not, in general, equal to AE. Resolution: The statement d in K,/dT = d in &/dT is indeed false in general. This erroneous conclusion ari~esfrom attempting to differentiate AGe0/T with respect to temperature at constant pressure. One cannot change the temperature of a. gas while keeping its pressure constant and still maintain its concentration a t one mole per liter. NORMAN 0. S m m FORDHAM UNIVERSITY NEWYORECITY
Volume 42, Number
6, June 1965
/
301
