The reaction of methane with water to form carbon dioxide and hydrogen is nonspontaneous at 298 K. At what temperature will this system make the transition from nonspontaneous to spontaneous? The data refer to 298 K. CH4 (g) + 2H2O (g) CO2 (g) + 4H2 (g) Substance: 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

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.