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Δ G = Δ H T Δ S

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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.

These four scenarios are summarized in [link] .

A table with three columns and four rows is shown. The first column has the phrase, “Delta S greater than zero ( increase in entropy ),” in the third row and the phrase, “Delta S less than zero ( decrease in entropy),” in the fourth row. The second and third columns have the phrase, “Summary of the Four Scenarios for Enthalpy and Entropy Changes,” written above them. The second column has, “delta H greater than zero ( endothermic ),” in the second row, “delta G less than zero at high temperature, delta G greater than zero at low temperature, Process is spontaneous at high temperature,” in the third row, and “delta G greater than zero at any temperature, Process is nonspontaneous at any temperature,” in the fourth row. The third column has, “delta H less than zero ( exothermic ),” in the second row, “delta G less than zero at any temperature, Process is spontaneous at any temperature,” in the third row, and “delta G less than zero at low temperature, delta G greater than zero at high temperature, Process is spontaneous at low temperature.”
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:

2C ( s ) + O 2 ( g ) 2CO ( g )

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:

4Fe ( s ) + 3O 2 ( g ) 2Fe 2 O 3 ( s )

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.

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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:

Practice Key Terms 3

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Source:  OpenStax, Ut austin - principles of chemistry. OpenStax CNX. Mar 31, 2016 Download for free at http://legacy.cnx.org/content/col11830/1.13
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