The reaction of methane with water to form carbon dioxide and hydrogen is non-spontaneous at 298 K. At what temperature will this system make the transition from non-spontaneous to spontaneous? The data refer to 298 K.

Question

Quizplus · Accepted Answer

The temperature at which a reaction becomes spontaneous can be calculated using the equation:
ΔG° = -RTln(K)
where ΔG° is the standard free energy change, R is the gas constant, T is the temperature in Kelvin, and K is the equilibrium constant.

At 298 K, the reaction is non-spontaneous, so ΔG° is positive. This means that ln(K) is negative. To make ln(K) positive, we need to increase the temperature.

To solve for the temperature at which ln(K) = 0, we can rearrange the equation to:
T = ΔG° / (Rln(K))
Substituting the given values, we get:
T = (206.2 kJ/mol) / (8.314 J/mol*K * ln(1.2 x 10^-21))
T = 955 K

Therefore, the best choice is C, 955 K.

The Reaction of Methane with Water to Form Carbon Dioxide