JEE MAIN - Chemistry (2024 - 6th April Evening Shift - No. 21)
Explanation
To determine the temperature above which the reaction $$2A+B \rightarrow C$$ becomes spontaneous, we can use the Gibbs free energy equation:
$$\Delta G = \Delta H - T\Delta S$$
The reaction becomes spontaneous when $$\Delta G$$ is negative. Therefore, we need to find the temperature at which $$\Delta G$$ changes from positive to negative. We set $$\Delta G$$ to zero to find the threshold temperature:
$$0 = \Delta H - T\Delta S$$
Substituting the given values of $$\Delta H = 400 \, \text{kJ mol}^{-1} = 400,000 \, \text{J mol}^{-1}$$ (since 1 kJ = 1000 J) and $$\Delta S = 0.2 \, \text{kJ mol}^{-1} K^{-1} = 200 \, \text{J mol}^{-1} K^{-1}$$, we get:
$$0 = 400,000 \, \text{J mol}^{-1} - T(200 \, \text{J mol}^{-1} K^{-1})$$
Solving for $$T$$, we have:
$$T = \frac{400,000 \, \text{J mol}^{-1}}{200 \, \text{J mol}^{-1} K^{-1}}$$
$$T = 2000 \, \text{K}$$
Therefore, the reaction will become spontaneous above $$2000 \, \text{K}$$. This means that at temperatures higher than 2000 K, the reaction tends towards product formation without the need for external energy to drive the process.
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