Question

For a certain reaction, \(\Delta \text{H}^{\circ} = 40 \text{kJ}\) and \(\Delta \text{S}^{\circ} = 80 \text{JK}^{-1}\). Find the temperature so that \(\Delta \text{G}^{\circ} = 0\)

• A. \(500 \text{K}\)
• B. \(400 \text{K}\)
• C. \(300 \text{K}\)
• D. \(600 \text{K}\)

Hint:

At equilibrium delta G is zero, so T = delta H / delta S with consistent units.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Gibbs equation is \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\). A reaction sits at the borderline between spontaneous and non-spontaneous when \(\Delta G^{\circ} = 0\).

Step 2: Key Formula or Approach:
Setting \(\Delta G^{\circ} = 0\) gives \(T = \frac{\Delta H^{\circ}}{\Delta S^{\circ}}\). Convert \(\Delta H\) to joules because \(\Delta S\) is in J/K.

Step 3: Detailed Explanation:
\(\Delta H^{\circ} = 40\ \text{kJ} = 40000\) J and \(\Delta S^{\circ} = 80\) J/K.
\[ T = \frac{40000}{80} = 500\ \text{K} \]
If the units are mixed (40 divided by 80) one gets \(0.5\), which matches none of the options. The values \(300\), \(400\) and \(600\) K would need \(\Delta H\) of \(24\), \(32\) or \(48\) kJ for this \(\Delta S\).

Final Answer:
The temperature is \(500\) K, option (A). \[ \boxed{500\ \text{K}} \]