Topic: Gibbs energy change and equilibrium constant· Chemical Thermodynamics

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

1. T > 425 K

2. all temperatures

3. T > 298 K

4. T < 425 K

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Answer: 1. T > 425 K

Key idea: a reaction is spontaneous when \(\Delta G = \Delta H - T\Delta S < 0\).

For \(\Delta G<0\): \(T > \dfrac{\Delta H}{\Delta S}\).

\(T > \dfrac{35.5\times10^{3}\ \mathrm{J\,mol^{-1}}}{83.6\ \mathrm{J\,K^{-1}mol^{-1}}} \approx 424.6\ \mathrm{K} \approx 425\ \mathrm{K}\).

Since both \(\Delta H\) and \(\Delta S\) are positive, the reaction is spontaneous only at high temperature, above about 425 K. So \(T<425\) K and \"all temperatures\" are wrong. \(T>298\) K is too loose, because at 300 K the reaction is not yet spontaneous.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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

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