Question

For a given reaction, △H = 35.5 kJ mol^–1 and △S = 83.6 JK–1 mol^–1. The reaction is spontaneous at  :
(Assume that△H and △S do not vary with temperature)

• A. T < 425 K
• B. T > 425 K
• C. All temperatures
• D. T > 298 K

Answer 1

The Correct Option is B

To determine at which temperature the given reaction is spontaneous, we need to use the Gibbs free energy equation: 

\(\Delta G = \Delta H - T \Delta S\)

For a reaction to be spontaneous, the Gibbs free energy change should be negative, i.e., \(\Delta G < 0\).

Given:

• \(\Delta H = 35.5 \, \text{kJ mol}^{-1}\)
• \(\Delta S = 83.6 \, \text{J K}^{-1} \text{mol}^{-1}\)

 

First, convert \(\Delta S\) to kJ by dividing by 1000: \(\Delta S = 0.0836 \, \text{kJ K}^{-1} \text{mol}^{-1}\)

The condition for spontaneity, \(\Delta G < 0\), can be rewritten as:

\(35.5 \, \text{kJ mol}^{-1} - T \times 0.0836 \, \text{kJ K}^{-1} \text{mol}^{-1} < 0\)

Solving for \(T\) gives:

\(T > \frac{35.5}{0.0836}\)

Calculate the temperature:

\(T > 425 \, \text{K}\)

Thus, the reaction will be spontaneous when the temperature is greater than 425 K.

Let's evaluate the options:

• T < 425 K: Incorrect, as T must be greater than 425 K for spontaneity.
• T > 425 K: Correct, because the reaction is spontaneous above this temperature.
• All temperatures: Incorrect, since spontaneity only occurs above 425 K.
• T > 298 K: Incorrect, not all temperatures above 298 K will make the reaction spontaneous. It must be above 425 K.

 

Therefore, the correct answer is: T > 425 K