## What is Gibbs Energy?

Generally, total entropy change is the fundamental parameter which defines the spontaneity of any process. Since, most of the chemical reactions fall under the category of closed system and open system; we can say there is a change in enthalpy too along with the change in entropy. Since, change in enthalpy too increases or decreases the randomness by affecting the molecular motions, entropy change alone cannot account for the spontaneity of such process. Therefore we use the Gibbs energy change for explaining the spontaneity of a process. Gibbs energy is a state function and an extensive property. General expression for Gibbs energy change at constant temperature is expressed as:

\(\triangle G_{sys}\) = \(\triangle H_{sys} – T\triangle S_{sys}\)

Where,

\(\triangle G_{sys}\) = Gibbs energy change of the system

\(\triangle H_{sys}\) = enthalpy change of the system

\(\triangle S_{sys}\) = entropy change of the system

\( T \) = Temperature of the system

Above equation is popularly known as Gibbs equation. Gibbs equation relates enthalpy and entropy of the system. We know that for a spontaneous process, the total entropy change, \(\triangle S_{total}\) is greater than zero.

\(\triangle S_{total}\) = \(\triangle S_{sys} + \triangle S_{surr}\)

Where,

\(\triangle S_{total}\) = total entropy change for the process

\(\triangle S_{sys}\) = entropy change of the system

\(\triangle S_{surr}\) = entropy change of the surrounding

In case of thermal equilibrium between system and surrounding, temperature change between system and surrounding, \(\triangle T\) = \(0\). Hence, we can say that enthalpy lost by the system is gained by the surrounding. Hence, the entropy change of the surrounding is given as,

\(\triangle S_{surr}\) = \(\frac{\triangle H_{surr}}{T} = – \frac{\triangle H_sys}{T}\)

\(\triangle S_{total}\) = \(\triangle S_{sys} + (- {\triangle H_sys}{T})\)

\(\triangle H_{surr}\) = change in enthalpy of the surrounding

\(\triangle H_{sys}\) = change in enthalpy of the system

As discussed earlier, for the spontaneity of a process, ΔStotal > 0. Above equation becomes,

\(T\triangle S_{sys} – \triangle H_{sys} >0\)

\(\triangle H_{sys} – T\triangle S_{sys} <0\)

Above equation can be related to Gibbs equation as,

\(\triangle G_{sys} < 0\)

On the basis of above equation we can infer:

- \(\triangle G_{sys} < 0\), the process is spontaneous
- \(\triangle G_{sys} > 0\),, the process is non-spontaneous

## The Spontaneity of A Process

Gibbs equation helps us to predict the spontaneity of reaction on the basis of enthalpy and entropy values directly. When the reaction is exothermic, enthalpy of the system is negative making Gibbs free energy negative. Hence we can say that all exothermic reactions are spontaneous.

In case of endothermic reactions, when enthalpy of the system is positive, the process is spontaneous under two conditions:

- Temperature is very high to make the Gibbs energy value negative
- Entropy change is very high to make the Gibbs free energy negative.

Spontaneity can only indicate if a reaction can occur not necessarily if a reaction will occur. For example, the conversion of diamond to graphite is a spontaneous process at Standard Temperature and Pressure (STP) but it is a slow process. It will take years for the transformation to occur.

For detailed discussions on the spontaneity of a process on the basis of Gibbs free energy change, check out Byju’s-The Learning App.