20.3 Free Energy and Equilibrium
20.3 Free Energy and Equilibrium
Lesson Objectives
- Determine the temperature at which a reversible reaction will achieve equilibrium by using the Gibbs free
energy equation. - Describe the relationship between standard free energy change (∆G°) and the equilibrium constant (Keq) for
reversible reactions. - Convert between Keqand∆G° for a reaction at a given temperature.
Check Your Understanding
Recalling Prior Knowledge
- What is the equation that relates enthalpy change, entropy change, and free energy change?
- How is the value of the equilibrium constant for a reaction related to the equilibrium position?
A system is at equilibrium when the rates of the forward and reverse reactions are equal. In this case, neither reaction
is spontaneous. In this lesson, you will learn about the relationship of free energy to equilibrium and the equilibrium
constant.
Temperature and Free Energy
In the last lesson, you learned how to calculate the free energy change (∆G) for a reaction when the enthalpy
change (∆H) and the entropy change (∆S) are known. Consider the reversible reaction in which calcium carbonate
decomposes into calcium oxide and carbon dioxide gas. The production of CaO (called quicklime) has been an
important reaction for centuries, as shown by the lime kiln below (Figure20.5).
CaCO 3 (s)⇀↽CaO(s)+CO 2 (g)The∆H° value for this reaction is 177.8 kJ/mol, and the∆S° value is 160.5 J/K•mol. The reaction is endothermic
with an increase in entropy due to the production of a gas. We can first calculate the∆G° at 25°C in order to
determine if the reaction is spontaneous at room temperature.
∆G° =∆H° - T∆S°
∆G° = 177.8 kJ/mol - 298 K(0.1605 kJ/K•mol) = 130.0 kJ/molSince∆G° is a large positive quantity, the reaction strongly favors the reactants, and very little products would be
formed. In order to determine a temperature at which∆G° will become negative, we can first solve the equation for
the temperature when∆G° is equal to zero.