By Augustus Bailey
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0 moles of an alcohol (R¢OH) were mixed and allowed to attain equilibrium at 25°C. The amount of the ester at equilibrium if DG° for the reaction calculated : R—COOH + R¢OH ® R—COOR¢ + H2O is 440 cal. 35. Using the Gibbs-Helmholtz equation obtained Clapeyron equation for the equilibrium solid liquid. Clapeyron equation deals with the change in the equilibrium pressure with a change in the equilibrium temperature. Suppose T and P are temperature and pressure at equilibrium. At equilibrium, free energies of the two phases are equal.
1) where fi is the fugacity of the constituent i in the mixture. Similarly, in a non-ideal solution the chemical potential of any component; is given by Chemistry : Basic Elements mi = m0i + RT In ai ... (2) where ai is the activity of component i in the solution. , f = Y × P ... (3) where Y is called the activity coefficient of the gas. From equation (3), we have Y = f/P ... (4) Hence activity coefficient of a gas may be defined as the ratio of the fugacity of the gas to the pressure of the gas in the same state.
Let us consider the simplest case consisting of only two phases A and B. , C3) are distributed between them. (See Figure) Further suppose that at constant pressure and temperature a small amount dn1 of component 1 is transferred from phase A tophase B. If (m1)A and (m2)B represent the chemical potentials of component 1 in phases A and B respectively, we have Decrease in the free energy of component 1 in phase A = (m1)A dn1 Increase in the free energy of component 1 in phase B = (m1)B dn1 Since the system is a closed one, (DG)T, P = 0 \ _ (m1)A dn1 + (m1)B dn1 = 0 (minus sign to represent the decrease) or (m1)A = (m1)B It means for a system consisting of two phases in equilibrium, the chemical potential of any given component is same in both the phases.
Chemistry Basic Elements by Augustus Bailey