# Gibbs Free Energy Formula

Willard Gibbs defined a function known as Gibbs energy (G), to calculate the changes in entropy and enthalpy values. The maximum work done is the amount of energy produced, given by the decrease in the thermodynamic property called Gibbs free energy.

Gibbs Free energy formula is given below.

$\Delta G=\Delta H-(T\times \Delta S)$

Î”G=Gibbs free energy

Î”H = change in enthalpy

Î”S=change in entropy

T=temperature

Gibbs free energy has extensive property and a function with a single value.

Example 1

Determine the standard Gibbs free energy change for the creation of methane from carbon and hydrogen at 298 K. Given Î”H = -74.9KJ/mol and Î”S = -80.7J/K.mol

Solution

change in enthalpy,Î”H = -74.9 KJ/mol

change in entropy,Î”S = -80.7J/Kmol

Î”S = -0.0807 KJ/Kmol (1KJ=1000J)

We have the equation

Î”G = Î”H â€“ T Î”S

Substitute the above values in this equation

Î”G =( -74.9 ) â€“ (298 ) (-0.0807)

Î”G = -50.9KJ/mole

Example 2

Determine the standard free energy change for the following reaction at 25oC.

N2 + 3H2 —> 2NH3

Given Î”H and Î”S are -91.8KJ and -198.0J/K

Solution

We have an equation

Î”G = Î”H â€“ T Î”S

change in enthalpy,Î”H = -91.8 KJ/mol

change in entropy,Î”S = -198.0J/Kmol

Î”S = -0.198 KJ/Kmol (1KJ=1000J)

Substitute the above values in this equation

Î”G = (-91.8 )â€“ (298 ) (-0.1980)

Î”G = -32.8KJ

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