Question

For a certain reaction \(\Delta H = -50\) kJ and \(\Delta S = -100\) J/K find the temperature so that the reaction is spontaneous.

• A. \(650\) K
• B. \(600\) K
• C. \(550\) K
• D. \(450\) K

Hint:

A reaction is spontaneous when the Gibbs energy change is negative, so write the Gibbs equation and solve for the temperature.

Answer 1

The Correct Option is D

Step 1: Set up the free energy condition.
Spontaneous means $\Delta G < 0$, where $\Delta G = \Delta H - T\Delta S$.

Step 2: Find the limiting temperature.
At equilibrium $\Delta G = 0$, so $T_{eq} = \Delta H/\Delta S$.
\[ T_{eq} = \frac{-50000\text{ J}}{-100\text{ J/K}} = 500\text{ K} \]

Step 3: Decide which side is spontaneous.
Take a test value $T = 0$ K. Then $\Delta G = \Delta H = -50$ kJ, which is negative. So the reaction is spontaneous at temperatures below 500 K and not above it.

Step 4: Match with the options.
Only 450 K lies below 500 K. The values 550 K, 600 K and 650 K give a positive $\Delta G$, so they are wrong.

Final Answer:
Option (D) is the only temperature below the 500 K limit. \[ \boxed{450\text{ K}} \]