The spontaneity of a process, as reflected in the arithmetic sign of its free energy change, is then determined by the signs of the enthalpy and entropy changes and, in some cases, the absolute temperature. Since
T is the absolute (kelvin) temperature, it can only have positive values. Four possibilities therefore exist with regard to the signs of the enthalpy and entropy changes:
Both Δ
H and Δ
S are positive. This condition describes an endothermic process that involves an increase in system entropy. In this case, Δ
G will be negative if the magnitude of the
T Δ
S term is greater than Δ
H . If the
T Δ
S term is less than Δ
H , the free energy change will be positive. Such a process is
spontaneous at high temperatures and nonspontaneous at low temperatures.
Both Δ
H and Δ
S are negative. This condition describes an exothermic process that involves a decrease in system entropy. In this case, Δ
G will be negative if the magnitude of the
T Δ
S term is less than Δ
H . If the
T Δ
S term’s magnitude is greater than Δ
H , the free energy change will be positive. Such a process is
spontaneous at low temperatures and nonspontaneous at high temperatures.
Δ
H is positive and Δ
S is negative. This condition describes an endothermic process that involves a decrease in system entropy. In this case, Δ
G will be positive regardless of the temperature. Such a process is
nonspontaneous at all temperatures.
Δ
H is negative and Δ
S is positive. This condition describes an exothermic process that involves an increase in system entropy. In this case, Δ
G will be negative regardless of the temperature. Such a process is
spontaneous at all temperatures.
There are four possibilities regarding the signs of enthalpy and entropy changes.
Predicting the temperature dependence of spontaneity
The incomplete combustion of carbon is described by the following equation:
How does the spontaneity of this process depend upon temperature?
Solution
Combustion processes are exothermic (Δ
H <0). This particular reaction involves an increase in entropy due to the accompanying increase in the amount of gaseous species (net gain of one mole of gas, Δ
S >0). The reaction is therefore spontaneous (Δ
G <0) at all temperatures.
Check your learning
Popular chemical hand warmers generate heat by the air-oxidation of iron:
How does the spontaneity of this process depend upon temperature?
Answer:
Δ
H and Δ
S are negative; the reaction is spontaneous at low temperatures.
When considering the conclusions drawn regarding the temperature dependence of spontaneity, it is important to keep in mind what the terms “high” and “low” mean. Since these terms are adjectives, the temperatures in question are deemed high or low relative to some reference temperature. A process that is nonspontaneous at one temperature but spontaneous at another will necessarily undergo a change in “spontaneity” (as reflected by its Δ
G ) as temperature varies. This is clearly illustrated by a graphical presentation of the free energy change equation, in which Δ
G is plotted on the
y axis versus
T on the
x axis:
