Answer:
The system makes the transition from nonspontaneous to spontaneous at a temperature of 954.7 K.
Under 954.7 K the reaction is nonspontaneous; more than 954.7 K is the reaction spontaneous.
Explanation:
CH4(g) + 2H2O(g) ⇆ CO2(g) + 4H2(g)
CH4(g) H2O(g) CO2(g) H2(g) ΔH°f (kJ/mol): –74.87 –241.8 –393.5 0
ΔG°f (kJ/mol): –50.81 –228.6 –394.4 0
S°(J/K·mol): 186.1 188.8 213.7 130.7
ΔG<0 to be spontaneous
ΔG = ΔH- TΔS <0
ΔH = ∑nΔH(products) - ∑nΔH(reactant)
ΔH = (-393.5) - (–74.87 + 2*–241.8)
ΔH = 164.97 kJ = 164970 J
ΔS = ∑nΔS(products) - ∑nΔS(reactant)
ΔS = (213.7 + 4*130.7) - (186.1 + 2*188.8)
ΔS = 172.8 J
0 > 164970 J - T* 172.8 J
-164970 J > - T* 172.8 J
954.7< T
The system makes the transition from nonspontaneous to spontaneous at a temperature of 954.7 K.
Under 954.7 K the reaction is nonspontaneous; more than 954.7 K is the reaction spontaneous.
