Question

The standard entropy change for the reaction \(4Fe(s) + 3O_2(g) → 2Fe_2O_3(s)\) is \(–550\ J K^{–1}\) at \(298\ K\). The temperature in K at which the reaction attains equilibrium is ______. (Nearest Integer)
[Given: The standard enthalpy change for the reaction is \(–165\ kJmol^{–1}\)].

Answer 1

Correct Answer: 300

To determine the temperature at which the reaction reaches equilibrium, we need to apply the Gibbs free energy equation, \( \Delta G = \Delta H - T\Delta S \). At equilibrium, \( \Delta G = 0 \). Therefore, the equation becomes \( 0 = \Delta H - T\Delta S \).

Solve for \( T \): \( T = \frac{\Delta H}{\Delta S} \).

Given:

• \( \Delta H = -165 \text{ kJ/mol} = -165000 \text{ J/mol} \)
• \( \Delta S = -550 \text{ J K}^{-1} \)

Substitute these values:

\( T = \frac{-165000}{-550} \approx 300 \text{ K} \)

Thus, the reaction reaches equilibrium at \( \mathbf{300 \text{ K}} \), which is within the specified range [300,300].