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Comprehension
Dependence of spontaneity on
temperature :
For a process to be spontaneous, at constant temperature and pressure, there must be decrease in free energy of the system in the direction of the process, i.e. \( (\Delta \mathrm{G})_{P, T}0 .(\Delta G)_{P, T}=0 \) implies the equilibrium condition and \( (\Delta G)_{P, T}0 \) corresponds to nonspontaneity.
Gibbs-Helmholtz equation relates the free energy change to the enthalpy and entropy change of the process as :
\[
(\Delta \mathrm{G})_{\mathrm{P}, \mathrm{T}}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}
\]
The magnitude of \( \Delta H \) does not change much with the change in temperature but the entropy factor T \( \Delta \mathrm{S} \) changes appreciably. Thus, spontaneity of a process depends very much on temperature.
For endothermic process, both \( \Delta \mathrm{H} \) and \( \Delta \mathrm{S} \) are positive. The energy factor, the first factor of equation, opposes the spontaneity whereas entropy factor favours it. At low temperature, the favourable factor \( \mathrm{T} \Delta \mathrm{S} \) will be small and may be less than \( \Delta \mathrm{H}, \Delta \mathrm{G} \) will have positive value indicating the non-spontaneity of the process. On raising temperature, the factor \( \mathrm{T} \Delta \mathrm{S} \) increases appreciably and when it exceeds \( \Delta \mathrm{H}, \Delta \mathrm{G} \) would become negative and the process would be spontaneous.
For an exothermic process, both \( \Delta \mathrm{H} \) and \( \Delta \mathrm{S} \) would be negative. In this case, the first factor of eq. 1 favours the spontaneity whereas the second factor opposes it. At high temperature, when \( \mathrm{T} \Delta \mathrm{S}\Delta \mathrm{H} \),
\( \Delta \mathrm{G} \) will have positive value, showing thereby the non-spontaneity of the process. However, on decreasing temperature, the factor \( \mathrm{T} \Delta \mathrm{S} \) decreases rapidly and when \( \mathrm{T} \Delta \mathrm{S}\Delta \mathrm{H}, \Delta \mathrm{G} \) becomes negative and the nromescenomesnontaneously. Thus, an exothermic process
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(c) \( 20,0 \mathrm{~N} \)
temperature and non-spontaneous at
\( \mathrm{K}, 2 \mathrm{~A}+\mathrm{B} \longrightarrow \mathrm{C} \)
\( =0.050 \mathrm{kcal} \mathrm{K}^{-1} \). If \( \Delta \mathrm{H} \) and \( \Delta \mathrm{S} \) are over the temperature range, above he reaction become spontaneous?
(b) \( 1500 \mathrm{~K} \)
(d) \( 2500 \mathrm{~K} \)
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