Question

23

Part IV.Bonas points (10 points in total) You can choose to complete one or both of the two bous questions below Howewer, your bones points wil be calclatd hased on the particular question that yow earn the most partial credit or full credi 22. Express the equilibrium constant of a gas-phase reaction in terms of the quilibrium value of the extent of reaction, &. given the initially A and B were present in stoichiometric proportions. Find an expression for as a function of the total pressure p of the reaction misture and sketch a graph of the expression obtained 23. Use the Gibbs-Duhem equation to derive the G equation dlnf atnfa lnxa where f is the fugacity. Use the relation to show that when the fugacities are replaced by pressures, that if Raoult's law applies to one component in a misture, it must also apply to the other

Answer 1

Given data: The Gibbs-Duterm equation to desire the Gibbs Duhem mauler equation [partial ln fa/partial ln xa] p, T = [partial ln fb/partial ln xb] P, T Here f = fugacity rightarrow The Gibbs's-Duhem equation x_A partial mu_A + x_B partial mu_B = 0 Divide the 'partial x_A' above equation x_A [partial mu_A/partial x_A]_p, T + x_B [partial mu_B/partial x_A]_P, T = 0 x_A + x_B = 1: d x_B = -d x_A \r\n x_A [partial mu_A/partial x_A]_P, T - x_B [partial mu_B/partial x_B]_P, T = 0 [partial mu_A/partial mu_A/partial ln x_A]_P, T = [partial mu_b/partial ln x_B]_P, T [therefore d ln alpha = dx/x] we know mu = mu^theta + R_T ln f/p^theta [partial ln f_A/partial ln x_A]_p, T = [partial ln F_B/partial ln x_B]_P, T Gibbs Duhem-Mauguler equation Here we Replace fugacity by pressure \r\n A satisfy Raults law P_A = x_A P_A^* [partial ln P_A/partial ln x_A]_p, T = partial ln x_A/partial ln x_A + partial ln