Question

The values of \( \Delta H \) and \( \Delta S \) for the reaction, \[ \text{C(graphite)} + \text{CO}_2(g) \rightarrow 2\text{CO}(g), \] are 170 kJ and 170 J/K, respectively. This reaction will be spontaneous at:

• A. 910 K
• B. 1110 K
• C. 510 K
• D. 710 K

Hint:

A reaction becomes spontaneous when \( \Delta G \) is negative. Use the relation \( \Delta G = \Delta H - T \Delta S \) to calculate the temperature for spontaneity.

Answer 1

The Correct Option is D

Step 1: The spontaneity of the reaction depends on the Gibbs free energy, \( \Delta G = \Delta H - T \Delta S \).
Step 2: For spontaneity, \( \Delta G \) must be negative. Using \( \Delta G = 0 \), we find that the reaction becomes spontaneous at 710 K.

Final Answer: \[ \boxed{710 \, \text{K}} \]