Question

True or false? Show work and explain.

The Gibbs Helmholtz equation predicts that the equilibrium constant for calcium carbonate decomposition does not exceed 1.0 at 1000 K

Answer 1

H° =177.8 kJ/mol = 177.8*10³ J/mol

S° =160.5 J/K·mol

the reaction is

           CaCO₃(s) CaO(s)+ CO₂(g)

(a)   temperature , T= 1000 K

we have the relation between gibbs free energy(ΔG) andequilibrium constant (K_P)

        ΔG⁰ = - RT ln K_P

where R = 8.314 J/mol K

we know that ,  ΔG⁰ =H° -TS° =177.8*10³ - (1000*160.5) = 17,300J/mol

substituting in

                     ΔG⁰ = - RT ln K_P

                17,300 = -(8.314*1000)*ln  K_P

              ln  K_P = - 2.080

∴K_P = exp( - 2.080) = 0.124

So the answer is less than 1 hence it is TRUE