Question

Calculate the temperature at which \( \Delta G = -5.2 \, \text{kJ mol}^{-1} \), \( \Delta H = 145.6 \, \text{kJ mol}^{-1} \) and \( \Delta S = 216 \, \text{J K}^{-1} \text{mol}^{-1} \) for a chemical reaction:

• A. 698.1°C
• B. 698.1 K
• C. 130 K
• D. 130°C

Hint:

Always match units: convert \(\Delta G\) and \(\Delta H\) to J, keep \(\Delta S\) in J/K — temperature will be in Kelvin.

Answer 1

The Correct Option is B

Concept: \[ \Delta G = \Delta H - T\Delta S \]

Step 1: Convert units to Joules. \[ \Delta G = -5.2 \times 10^3 \, \text{J}, \quad \Delta H = 145.6 \times 10^3 \, \text{J} \] \[ \Delta S = 216 \, \text{J K}^{-1} \]

Step 2: Substitute into formula. \[ -5200 = 145600 - T(216) \]

Step 3: Solve for \(T\). \[ T(216) = 145600 + 5200 \] \[ T = \frac{150800}{216} = 698.1 \, \text{K} \]