Chapter 18. Chemical Thermodynamics

# Gibbs Free Energy

Jessie A. Key

Learning Objectives

- To gain an understanding of Gibbs free energy.
- To understand the relationship between the sign of Gibbs free energy change and the spontaneity of a process.
- To be able to determine Gibbs free energy using standard free energies of formation.

J. Willard Gibbs (1839–1903) proposed a single state function to determine spontaneity:

where *H* is the enthalpy of the system, *S* is the entropy of the system, and *G* is **Gibbs free energy**.

The change in Gibbs free energy, Δ*G*, is the maximum amount of free energy available to do useful work. For an isothermal process, it can be expressed as:

or at standard conditions:

This single term, Gibbs free energy (*G*), allows us to avoid calculating the entropy of the surroundings. It is really just a simplification of our previous method of estimating spontaneity:

Multiply both sides of the equation by −*T*:

Therefore, .

As a result of this relationship, the sign of Gibbs free energy provides information on the spontaneity of a given reaction:

The significance of the sign of a change in Gibbs free energy parallels the relationship of terms from the equilibrium chapter: the reaction quotient, *Q*, and the equilibrium constant, *K*.

Example 18.4

Calculate Δ*G*° for a reaction where Δ*H*° is equal to 36.2 kJ and Δ*S*° is equal to 123 J/K at 298 K. Is this a spontaneous reaction?

*Solution*

Therefore the reaction is spontaneous because Δ*G*° is negative.

# Determining Δ*G*° from Standard Free Energy of Formation

The standard Gibbs free energy change, Δ*G*°, for a reaction can be calculated from the standard free energies of formation, Δ*G*°* _{f} *.

where *n* and *m* are the coefficients in the balanced chemical equation of the reaction.

Standard free energies of formation values are listed in the appendix, “Standard Thermodynamic Quantities for Chemical Substances at 25°C.”

Example 18.5

Calculate the standard free energy change for the following reaction, using standard free energies of formation:

5C(s) + 2SO_{2}(g) → CS_{2}(g) + 4CO(g)

Is this a spontaneous reaction?

*Solution*

Δ*G*° has a positive value, so this is not a spontaneous process.

Key Takeaways

- The change in Gibbs free energy (Δ
*G*) is the maximum amount of free energy available to do useful work. - If Δ
*G*> 0, the reaction is nonspontaneous in the direction written. If Δ*G*= 0, the reaction is in a state of equilibrium. If Δ*G*< 0, the reaction is spontaneous in the direction written. - The standard Gibbs free energy change,
*G*°, for a reaction can be calculated from the standard free energies of formation, Δ*G*°._{f}

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