Temperature for Spontaneous Reaction

At what temperatures is this reaction spontaneous?

Based on the given data, which temperature range makes the reaction spontaneous?

A. At no temperature

B. T< 50 K

C. T>617 K

D. T<617 K

Answer: C. T>617 K

Explanation:

We are given that ΔH = 176 kJ/mol and ΔS = 0.285 kJ/(K•mol). In order to determine the temperature at which the reaction is spontaneous, we need to consider the Gibbs free energy equation.

When ΔH > 0 and ΔS > 0, the reaction is spontaneous at certain temperatures.

The Gibbs free energy equation is given by ΔG = ΔH - TΔS. If ΔG is negative, then the reaction is spontaneous.

For T>617 K:

Suppose T=618 K:

ΔG = 176 - 0.285 * 618 = -0.13 < 0

Therefore, ΔG is negative, and the reaction is spontaneous. Hence, option C is correct.