From the Arrhenius to the Clausius–Clapeyron Equation
Department of Chemistry, Faculty of Science, National University of Singapore, Singapore117543, Singapore, firstname.lastname@example.org Received June 10, 2002. Accepted August 25, 2002.
Abstract: The dynamical nature of chemical equilibrium and the relationship between kinetics andthermodynamics are illustrated by the example of a pure liquid that is in equilibrium with its vapor.
Introduction The topics of chemical equilibrium and reaction rates are fundamental concepts in chemistry.The behavior of a pure liquid in equilibrium with its vapor is described by the Clausius–Clapeyron equation and the rates of chemical reactions are described by the Arrhenius equation. In this work wedraw educationally useful parallels between the two equations and also between kinetics and thermodynamics. The approach outlined uses elementary mathematics and is suitable for freshmen studyinggeneral chemistry or as a review for second-year students studying physical chemistry. Discussion The pure liquid is in equilibrium with its vapor in a closed vessel (fixed volume and temperature; thevapor behaves ideally). A(l) A(g)
The term (ln Av – ln Ac) is constant because A factors are constant (as required by the Arrhenius equation), so are their logarithms, and thus the difference betweenthe logarithms is constant as well. The (Ea,v – Ea,c) term can be expressed in term of internal energies as Ea,v = U‡ – Uv and Ea,c = U‡ – Uc, where U‡ is the internal energy for the transition statein going from the liquid to vapor or vice versa. The difference in activation energies between the phases then becomes ∆U = Uc – Uv. Also, from the definition of enthalpy we have Uc = Hc and Uv = Hv –(PV)v, so Ea,v – Ea,c = ∆U = Hc – Hv + (PV)v (4)
The first two terms in eq 4 represent the enthalpy of vaporization, that is, ∆Hvap = Hc – Hv, The third term, the work term, is constant because...