Question

For a reaction \(\Delta H = -30\ \text{kJ}\) and \(\Delta S = -45\ \text{J K}^{-1}\), at what temperature does the reaction change from spontaneous to non-spontaneous?

• A. 777.0 K
• B. 675.0 K
• C. 666.6 K
• D. 375.0 K

Hint:

When both \(\Delta H\) and \(\Delta S\) are negative, reactions are spontaneous only at low temperatures.

Answer 1

The Correct Option is C

Step 1: Use Gibbs free energy relation.
The condition for spontaneity is given by: \[ \Delta G = \Delta H - T\Delta S \] At the temperature where the reaction changes behaviour, \(\Delta G = 0\).

Step 2: Substitute the given values.
\[ 0 = (-30\,000) - T(-45) \]

Step 3: Solve for temperature.
\[ T = \frac{30\,000}{45} = 666.6\ \text{K} \]

Step 4: Conclusion.
At 666.6 K, the reaction changes from spontaneous to non-spontaneous.