Question

A reaction at \(23^{\circ} \mathrm{C}\) has \(\Delta G=1 \mathrm{kJ} \mathrm{mol}^{-1}\). Why might this reaction become spontaneous at \(37^{\circ} \mathrm{C}\)

Short answer

The reaction becomes spontaneous at \(37^{\circ} \mathrm{C}\) because increased temperature can make \(\Delta G\) negative if \(\Delta S\) is positive.

Step-by-step solution

Understand Gibbs Free Energy

Gibbs Free Energy (\(\Delta G\)) determines if a reaction is spontaneous. If \(\Delta G < 0\), the reaction is spontaneous; if \(\Delta G > 0\), the reaction is non-spontaneous.

Analyze Initial Condition

Given: At \(23^{\circ} \mathrm{C} (296 \mathrm{K})\), \(\Delta G = 1 \mathrm{kJ} \mathrm{mol}^{-1}\). This positive \(\Delta G\) indicates the reaction is non-spontaneous at this temperature.

Use Gibbs Free Energy Equation

The equation is \(\Delta G = \Delta H - T \Delta S\), where \(\Delta H\) is enthalpy change, \(T\) is temperature in Kelvin, and \(\Delta S\) is entropy change. Analyze how \(\Delta G\) changes with temperature.

Consider Temperature Change

Temperature increase from \(23^{\circ} \mathrm{C}\) to \(37^{\circ} \mathrm{C} (310 \mathrm{K})\). Higher temperature amplifies the entropy term \(T\Delta S\), potentially changing the sign of \(\Delta G\) to negative.

Conclusion

If \(\Delta S\) is positive (increase in system randomness), then \(T\Delta S\) becomes significant at higher temperature. This can make \(\Delta G\) negative, making the reaction spontaneous.

Key concepts

Spontaneity of Reactions

In chemistry, the spontaneity of a reaction is determined by Gibbs Free Energy (\(\backslash \backslash Delta G\)). If \(\backslash \backslash Delta G \)< 0, the reaction is considered spontaneous, meaning it can occur naturally without needing additional energy input. Conversely, if \(\backslash \backslash Delta G\)> 0, the reaction is non-spontaneous and requires external energy to proceed. It's important to remember that spontaneity doesn't reflect the speed of the reaction; even a highly spontaneous reaction can proceed slowly if it has a high activation energy.
If you're trying to predict if a reaction will be spontaneous at a different temperature, delta G is your go-to tool. This value can change with temperature, and sometimes, what was non-spontaneous at one temperature can become spontaneous as temperature changes. To analyze this further, let’s move to the concept of enthalpy change.

Enthalpy Change

Enthalpy change (\( \Delta H \)) reflects the heat absorbed or released during a reaction at constant pressure. It helps us understand whether the reaction releases energy (exothermic, \( \Delta H < 0 \)) or absorbs energy (endothermic, \( \Delta H > 0 \)).
In the \(\backslash \backslash Delta G = \Delta H - T \Delta S\) formula, \(\backslash \backslash Delta H\) is a significant factor. If \(\backslash \backslash Delta H\) is negative and large enough to overpower \(\backslash \backslash T \Delta S \) term, the reaction might be spontaneous even at lower temperatures. When studying how temperature changes affect spontaneity, always consider the signs and sizes of both \(\backslash \backslash Delta H\) and \(\backslash \backslash Delta S\).

Entropy Change

Entropy (\(\Delta S\)) measures the disorder or randomness of a system. An increase in entropy (\(\Delta S > 0\)) indicates that the system's randomness is increasing, while a decrease (\(\Delta S < 0\)) means the system is becoming more ordered. This change in disorder is an essential factor in determining Gibbs Free Energy.
In the Gibbs Free Energy equation, the term \(\backslash \backslash T \Delta S \) represents the impact of entropy change on the system. A positive \(\backslash \backslash Delta S\) can, at higher temperatures, contribute substantially to making \(\backslash \backslash Delta G\) negative, thus driving the reaction to become spontaneous. Understanding this interaction is crucial when predicting how a reaction might behave under different conditions.

Temperature Effect on Gibbs Free Energy

Temperature is a critical variable affecting Gibbs Free Energy. The term \(\backslash \backslash T \Delta S\) highlights why. As temperature rises, the contribution of the entropy term (\