Chapter 9, Problem 9.142CP

For a process to be spontaneous, the total entropy of the system and its surroundings must increase; that is $\Delta S_{total}=\Delta S_{system}+\Delta S_{surr}>0$ For a spontaneous process Furthermore, the entropy change in the surroundings, $\Delta S_{surr}$ , is related to the enthalpy change for the process by the equation $\Delta S_{surr}=-\Delta H/T$ .

(a) Since both $\Delta G$ and $\Delta S_{total}$ offer criteria for spontaneity, they must be related. Derive a relationship between them.

(b) What is the value of $\Delta S_{surr}$ for the photosynthesis of glucose from CO₂at 298 K?

${\text{6CO}}_{\text{2}}\text{(g)}+6H_{2}O(l)\to O{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\text{(s)}+6O_2(g)$

$\Delta G°$ = 2879 kJ

$\Delta S°$ = -262 J/K