Question

Ammonia is synthesized in the Haber process in the following reaction.
$𝑁_2 (𝑔) + 3𝐻_2 (𝑔) → 2𝑁𝐻_3(𝑔)$ 
The temperature above which the reaction becomes spontaneous is __________ 𝐾 (rounded off to one decimal place). 
($\bigtriangleup 𝐻^0 = −92.2 𝑘𝐽, \bigtriangleup 𝑆^0 = −199 𝐽𝐾^{ −1}$ )

Answer 1

Correct Answer: 463

The temperature for spontaneity can be found using the Gibbs free energy equation:

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

For spontaneity, \(\Delta G = 0\). Substituting the given values \(\Delta H = -92.2\) kJ/mol and \(\Delta S = -199\) J/K:

\( 0 = -92.2 \times 10^3 - T \times (-199) \)

Solving for \(T\):

\( T = \frac{92.2 \times 10^3}{199} = 463.0 \text{ K}. \)