Chapter 8, Problem 8.120CHP

For a process to be spontaneous, the total entropy of the system and its surroundings must increase; that is

$\Delta S_{\text{total}}=\Delta S_{\text{system}}+\Delta S_{\text{surr}}>0\text{For}\text{a}\text{spontaneous}\text{process}$

Furthermore, the entropy change in the surroundings, ΔS_surr^, is related to the enthalpy change for the process by the equation ΔS_surr = −ΔH/T.

1. (a) Since both ΔG and ΔS_total offer criteria for spontaneity, they must be related. Derive a relationship between them.
2. (b) What is the value of ΔS_surr for the photosynthesis of glucose from CO₂ at 298 K?

$\begin{array}{l}6{\text{CO}}_2(g)+6{\text{H}}_2\text{O}(l)\stackrel{}{\to }{\text{C}}_6{\text{H}}_{12}{\text{O}}_6(s)+6{\text{O}}_2(g)\Delta G°=+2879\text{kJ}\hfill \\ \Delta S°=-262\text{J/K}\hfill \end{array}$