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JEE Main levelSingle correct optionDifficulty 2 of 3td103

For $N X_{2} (g) + 3 H X_{2} (g) 2 NH X_{3} (g)$ , $Δ H^{\circ} < 0$ and $Δ S^{\circ} < 0$ . When the temperature is raised from $298 K$ to $500 K$ (assume $Δ H^{\circ}$ , $Δ S^{\circ}$ constant), which is correct?

A $K$ decreases and $Δ G^{\circ}$ becomes less negative
B $K$ increases and $Δ G^{\circ}$ becomes more negative
C $K$ decreases and $Δ G^{\circ}$ becomes more negative
D $K$ is unchanged because $Δ G^{\circ}$ does not depend on $T$

Answer: A

Δ G^{\circ} = Δ H^{\circ} - T Δ S^{\circ}

; with

Δ S^{\circ} < 0

the term

- T Δ S^{\circ}

is positive and grows with

T

, so

Δ G^{\circ}

becomes less negative. Since

Δ G^{\circ} = - RT ln K

,

K

falls. This agrees with van't Hoff:

K

decreases with

T

for an exothermic reaction.

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