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# How does Gibbs free energy relate to work?

Last updated date: 28th Feb 2024
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Hint: The energy associated with any chemical reaction which can be used to perform work is known as the Gibbs free energy $\left( {\Delta G} \right)$ of the system. The free energy of the system is the summation of the enthalpy of the system and the product of temperature and entropy of the system.

Complete solution:
We know that the energy associated with any chemical reaction which can be used to perform work is known as the Gibbs free energy $\left( {\Delta G} \right)$ of the system. The free energy of the system is the summation of the enthalpy of the system and the product of temperature and entropy of the system.
The expression for Gibbs free energy is as follows:
$\Delta G = \Delta H - \Delta \left( {TS} \right)$ …… (1)
Where $\Delta G$ is the change in the Gibbs free energy or free energy,
$\Delta H$ is the change in the enthalpy,
$T$ is the temperature,
$S$ is the entropy.
The expression for enthalpy is as follows:
$\Delta H = \Delta U + \Delta \left( {PV} \right) - \Delta \left( {TS} \right)$ …… (2)
Where $\Delta H$ is the change in the enthalpy,
$\Delta U$ is the change in internal energy,
$P$ is the pressure,
$V$ is the change in volume,
$T$ is the temperature,
$S$ is the entropy.
We know that the equation for the first law of thermodynamics is as follows:
$\Delta U = \Delta q + \Delta W$ …… (3)
Where $\Delta U$ is the change in the internal energy,
$\Delta q$ is the change in the heat,
$\Delta W$ is the work done.
From equations (1), (2) and (3),
$\Delta G = \Delta q + \Delta W + P\Delta V + V\Delta P - T\Delta S - S\Delta T$
If the Gibbs free energy of the system increases the reaction does not occur and no work is done. If the Gibbs free energy of the system decreases the reaction occurs and work is done.
The Gibbs free energy is the maximum amount of non-expansion type of work done.

Note: When the free energy is negative, a spontaneous reaction occurs. When the free energy is positive, a nonspontaneous reaction occurs. When the free energy is equal to zero, the system has achieved a state of equilibrium. Thus, the free energy of any system in nature is always negative. The change in free energy tells us the direction and the extent of the reaction.