Question

A<->B<->C

delta G⁰ for A<->B =11.4 kJ mol^-1

delta G⁰ for B<->C = -22.8 kJ mol^-1

A. What is the deta G⁰ for the conversion of A to C?

B. Write an equation for the free energy change (delta G) of the first reaction, A to B, taking into account concentrations of reactants and products.

C. At equilibrium, what are the concetration ratios of [B]/[A], [C]/[B], and [C]/[A]?

Answer 1

A)

the overall reaction is:

A <-> B

B <-> C

A + B <-> B+ C

so

A <-> C

dGtotal = dG1 + dG2 = 11.4 - 22.8 = -11.4 kJ/mol

B)

equation for the free energy change:

dG1 = dG°1 + RT*ln(Q1)

dG1 = dG°1 + RT*ln([B]/[A])

dG2 = dG°2 + RT*ln(Q2)

dG2 = dG°2 + RT*ln([C]/[B])

dG total =  dG°1 + RT*ln([B]/[A]) + dG°2 + RT*ln([C]/[B])

dG total = (dG°1+dG°2) + RT*ln([C]/[A])

dG total = (dG°1+dG°2)  + RT*ln([C]/[A])

C)

in equilibrium, this will be true:

Q1 = [B]/[A] = 1

Q2 = [C]/[B] = 1

so

Qtotal = [C]/[A] = 1