Questions: For the reaction NH4Cl(s) ⇌ NH3(g) + HCl(g) ΔH° = 176 kJ·mol⁻¹ and ΔG° = 91.2 kJ·mol⁻¹ at 298 K. What is the value of ΔG at 1000 K? (A) -109 kJ·mol⁻¹ (B) -64 kJ·mol⁻¹ (C) 64 kJ·mol⁻¹ (D) 109 kJ·mol⁻¹

Solution Steps

To find the Gibbs free energy at a different temperature, I'll use the Gibbs-Helmholtz equation: \( \Delta G = \Delta H - T\Delta S \)

First, I need to find \( \Delta S° \) at 298 K using the given values: \( \Delta G° = \Delta H° - T\Delta S° \) \( 91.2 \text{ kJ·mol}^{-1} = 176 \text{ kJ·mol}^{-1} - 298 \text{ K} \times \Delta S° \) \( 298 \text{ K} \times \Delta S° = 176 - 91.2 = 84.8 \text{ kJ·mol}^{-1} \) \( \Delta S° = \frac{84.8 \text{ kJ·mol}^{-1}}{298 \text{ K}} = 0.2846 \text{ kJ·K}^{-1}·\text{mol}^{-1} \)

Assuming \( \Delta H \) and \( \Delta S \) remain constant with temperature: \( \Delta G_{1000 \text{ K}} = \Delta H° - T\Delta S° \) \( \Delta G_{1000 \text{ K}} = 176 \text{ kJ·mol}^{-1} - 1000 \text{ K} \times 0.2846 \text{ kJ·K}^{-1}·\text{mol}^{-1} \) \( \Delta G_{1000 \text{ K}} = 176 - 284.6 = -108.6 \text{ kJ·mol}^{-1} \)

Final Answer