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: Rearrange:
$0 = \Delta H - T\Delta S$, so $T\Delta S = \Delta H$.

Step 2: Substitute:
$T = \frac{40 \times 10^{3}\ \text{J}}{80\ \text{J K}^{-1}} = 500$ K.
Check: $T \Delta S = 500 \times 80 = 40000$ J, which equals $\Delta H$, so $\Delta G = 0$ as required.

Final Answer:
$T = 500$ K, option (A). \[ \boxed{500\ \text{K}} \]