Q28 / 90 · JEE Main 2016 (09 Apr Online) · Chemistry

For the reaction,

$A (g) + B (g) \to C (g) + D (g), ∆ H^{o}$ and $∆ S^{o}$ are, respectively, $- 29.8 k J m o l^{- 1}$ and $- 0.100 k J K^{- 1} m o l^{- 1}$ at 298 K. The equilibrium constant for the reaction at 298 k is:

A
$1.0 \times 10^{- 10}$
B
$10$
Correct answer
C
$1$
D
$1.0 \times 10^{10}$

Solution

∆ G ° = ∆ H ° - T ∆ S °

∆ G ° = - 29 .8 {kJmol}^{- 1} + 0 .1 \times 298 {kJmol}^{- 1} = 0

∆ G = ∆ G ° + R T l n Q a t E q u i l i b r i u m ∆ G = 0 & Q = k

∆ G ° = - R T l n(k)

i f l n(k) = 0, k = e

⁰

∴ K = 1

Hence, the correct answer is option: 'C'.

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