D20.5 Temperature Dependence of Gibbs Free Energy
Whether a reaction is product-favored, that is, whether the reactants are converted to products under standard-state conditions, is reflected in the arithmetic sign of its ΔrG°. This equation
shows that the sign of ΔrG° depends on the signs of ΔrH° and ΔrS°, and, in some cases, the absolute temperature (which can only have positive values). Four possibilities exist:
- Both ΔrH° and ΔrS° are positive—an endothermic process with an increase in system entropy. ΔrG° is negative if TΔrS° > ΔrH°, and positive if TΔrS° < ΔrH°. Such a process is product-favored at high temperatures and reactant-favored at low temperatures.
- Both ΔrH° and ΔrS° are negative—an exothermic process with a decrease in system entropy. ΔrG° is negative if |TΔrS°| < |ΔrH°| and positive if |TΔrS°| > |ΔrH°|. Such a process is product-favored at low temperatures and reactant-favored at high temperatures. (Remember that |TΔrS°| represents the magnitude of TΔrS°, ignoring mathematical sign.)
- ΔrH° is positive and ΔrS° is negative—an endothermic process with a decrease in system entropy. ΔrG° is positive regardless of the temperature. Such a process is reactant-favored at all temperatures.
- ΔrH° is negative and ΔrS° is positive—an exothermic process with an increase in system entropy. ΔrG° is negative regardless of the temperature. Such a process is product-favored at all temperatures.
These four scenarios are summarized in this figure:
The next figure illustrates the four scenarios graphically, where ΔrG° is plotted versus temperature:
For most reactions, neither ΔrH° nor ΔrS° change significantly as temperature changes. Thus, in the preceding figure, the plots representing ΔrG° are linear because the slope of each plot (−ΔrS°) is the same at all temperatures. The orange and green plots (representing examples of scenario 1 and 2, respectively) cross from product-favored to reactant-favored (cross ΔrG° = 0) at a temperature that is characteristic to each specific process. This temperature is represented by the x-intercept, the value of T for which ΔrG° is zero:
Hence, saying a process is product-favored at “high” or “low” temperatures is simply indicating whether the temperature is above or below TΔrG°=0 for that process. These relative terms are reaction-specific, that is, what is a “high” temperature for one reaction may very well be a “low” temperature for another reaction.
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