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# Gibbs Free Energy Formula

In order to account for changes in both entropy and enthalpy J.Willard Gibbs defined a new function, which is called Gibbs free energy (Gibbs potential) G. The maximum useful work is the amount of energy produced, is given by the decrease in another thermodynamic property known as the Gibbs free energy.

Gibbs Free Energy Formula is independent of pressure and temperature and can be stated as

Gibbs free energy is a single valued function and is an extensive property. Since by definition H = U + PV.

Gibbs Free Energy Formula can be written as

Change in Gibbs free energy for a finite system is expressed as

At constant temperature and pressure the equation becomes

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## Gibbs Free Energy Problems

Solved problems based on Gibbs free energy are given below.

### Solved Examples

Question 1: What is the standard free energy change $\Delta$G for the following reaction at 25oC?
N2 + 3H2 $\rightarrow$ 2NH3
The values for $\Delta$H ang S is -91.8KJ and -198.0J/K
Solution:

We can use the equation

Substitute the values in the above equation
$\Delta$G = -91.8KJ - (298K)(-0.1980KJ/K)
$\Delta$G = -32.8KJ

Question 2: Calculate the standard Gibbs free energy change for the formation of methane from carbon and hydrogen at 298K.
Given the $\Delta$H value is -74.9KJ/mol $\Delta$S = -80.7J/K.mol
Solution:

Given
$\Delta$H = -74.9KJ/mole
$\Delta$S = -80.7J/K.mol

Now use the equation

$\Delta$G = $\Delta$H - T$\Delta$S

Substitute the values in the above equation

$\Delta$G = -74.9KJ/mole - (298K)(-80.7J/K.mol)(1KJ/1000J)

$\Delta$G = -50.9KJ/mole

 More topics in Gibbs Free Energy Formula Lattice Energy Formula Internal Energy Formula
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