MHT CET · Chemistry · Thermodynamics (C)

Equilibrium constant for a reaction is \(20 .\) What is the value of \(\Delta \mathrm{G}^{\circ}\) at \(300 \mathrm{~K} ?\left(\mathrm{R}=8 \times 10^{-3} \mathrm{~kJ}\right)\)

A \(-5 \cdot 527 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
B \(-1 \cdot 663 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
C \(16 \cdot 63 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
D \(-2 \cdot 763 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(-1 \cdot 663 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-step Solution

Detailed explanation

(A)
\(\mathrm{K}=20, \mathrm{~T}=300 \mathrm{~K}, \mathrm{R}=8 \times 10^{-3} \mathrm{~kJ} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) \(\Delta G^{0}=-2.303 \mathrm{RT} \log _{10} \mathrm{~K}\)
\(\begin{aligned} &=-2.303 \times 8 \times 10^{-3} \times 300 \times \log _{10}(20) \end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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