The effect of temperature on the spontaneity of reactions are represented as: Which of the following is correct?
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The spontaneity of a reaction depends on both the enthalpy and the entropy change, and the effect of temperature can either make a reaction spontaneous or non-spontaneous.
To determine the spontaneity of a reaction based on the effect of temperature, we use the Gibbs free energy change equation:
\(\Delta G = \Delta H - T\Delta S\)
Where:
\(\Delta G\) is the change in Gibbs free energy.
\(\Delta H\) is the change in enthalpy.
\(T\) is the temperature in Kelvin.
\(\Delta S\) is the change in entropy.
The spontaneity of the reaction depends on the signs of \(\Delta H\) and \(\Delta S\):
\(\Delta H > 0\) and \(\Delta S < 0\):
Non-spontaneous at any temperature since both terms increase \(\Delta G\).
\(\Delta H > 0\) and \(\Delta S > 0\):
Spontaneous at high temperature because \(T\Delta S\) term can outweigh the positive \(\Delta H\).
\(\Delta H < 0\) and \(\Delta S < 0\):
Spontaneous at low temperature because the negative \(\Delta H\) outweighs the negative \(T\Delta S\).
\(\Delta H < 0\) and \(\Delta S > 0\):
Spontaneous at any temperature since both terms decrease \(\Delta G\).
The correct options are (B) and (C) because they correspond to scenarios 2 and 3, respectively, where reactions can be spontaneous depending on the temperature.
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Approach Solution -2
The spontaneity of a reaction is determined by the Gibbs free energy \( \Delta G = \Delta H - T \Delta S \).
- For \( \Delta H > 0 \) and \( \Delta S <0 \), the reaction is non-spontaneous at any temperature.
- For \( \Delta H > 0 \) and \( \Delta S > 0 \), the reaction is spontaneous at low temperatures.
- For \( \Delta H <0 \) and \( \Delta S <0 \), the reaction is non-spontaneous at low temperatures.
- For \( \Delta H <0 \) and \( \Delta S > 0 \), the reaction is spontaneous at any temperature.
Thus, the correct answers are (B) and (C) only.
