CK-12-Chemistry Intermediate

http://www.ck12.org Chapter 20. Entropy and Free Energy

∆H° for the reaction is +206.1 kJ/mol, while∆S° is +215 J/K•mol. Calculate∆G° for this reaction at 25°C and
determine whether it is spontaneous at that temperature.

Step 1: List the known values and plan the problem.

Known

• ∆H° = 206.1 kJ/mol


• ∆S° = 215 J/K•mol = 0.215 kJ/K•mol


• T = 25°C = 298 K

Unknown

• ∆G° =? kJ/mol

Prior to substitution into the Gibbs free energy equation, the entropy change is converted to kJ/K•mol and the
temperature to Kelvins.

Step 2: Solve.

∆G° =∆H° - T∆S° = 206.1 kJ/mol - 298 K(0.215 kJ/K•mol)

∆G° = +142.0 kJ/mol

The resulting positive value of∆G indicates that the reaction is not spontaneous at 25°C.

Step 3: Think about your result.

The unfavorable increase in enthalpy outweighed the favorable increase in entropy. The reaction will be spontaneous
only at a more elevated temperature.

Practice Problem

1. For the reaction in Sample Problem 20.1, calculate∆G at a temperature of 1200. K. Is the reaction spontaneous
   at that temperature?

Available values for enthalpy and entropy changes are generally measured at the standard conditions of 25°C and 1
atm pressure. They are slightly temperature dependent, so we must use caution when calculating specific∆G values
at temperatures other than 25°C, as in the practice problem above. However, since the values for∆H and∆S do not
change a great deal, the tabulated values can safely be used when making general predictions about the spontaneity
of a reaction at various temperatures.

Lesson Summary

• A reaction or process is considered to be spontaneous when the formation of products is favored at a given set
  of conditions.


• Spontaneous reactions release free energy, which can be used to do work.


• A mathematical combination of enthalpy change and entropy change allows the change in free energy to be
  calculated. A reaction with a negative value for∆G releases free energy and is thus spontaneous. A reaction
  with a positive∆G is nonspontaneous and will not favor the products.


• Some reactions may be spontaneous at some temperatures and nonspontaneous at other temperatures.