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

Step 1: Understanding the Concept:
The spontaneity of a reaction is determined by the Gibbs-Helmholtz equation.
: Key Formula or Approach:
Equation: \( \Delta\text{G} = \Delta\text{H} - T\Delta\text{S} \).
Rearranging for Temperature: \( T = \frac{\Delta\text{H} - \Delta\text{G}}{\Delta\text{S}} \).
Step 2: Detailed Explanation:
Convert all units to the same scale (Joules):
\( \Delta\text{G} = -5.2 \text{ kJ} = -5200 \text{ J} \).
\( \Delta\text{H} = 145.6 \text{ kJ} = 145600 \text{ J} \).
\( \Delta\text{S} = 216 \text{ J/K} \).
Plug in the values:
\[ T = \frac{145600 - (-5200)}{216} \]
\[ T = \frac{145600 + 5200}{216} \]
\[ T = \frac{150800}{216} \]
\[ T \approx 698.148 \text{ K} \].
Step 3: Final Answer:
The required temperature is \( 698.1\text{ K} \).