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# Gibbs Free Energy

## What is Gibbs Energy?

Generally, the total entropy change is the fundamental parameter that defines the spontaneity of any process.

Since most of the chemical reactions fall under the category of a closed system and open system; we can say there is a change in enthalpy too along with the change in entropy.

Gibbs energy is a state function and an extensive property. 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.

Knowledge of the Gibbs energy under one condition compared with another allows us to predict the direction of spontaneous change or movement: A spontaneous change in a system at constant temperature and pressure proceeds in the direction of decreasing free energy.

## Expression for Gibbs Energy Change

General expression for Gibbs energy change at constant temperature is expressed as:

$$\begin{array}{l}\triangle G_{sys}\end{array}$$
=
$$\begin{array}{l}\triangle H_{sys} – T\triangle S_{sys}\end{array}$$

Where,

$$\begin{array}{l}\triangle G_{sys}\end{array}$$
= Gibbs energy change of the system

$$\begin{array}{l}\triangle H_{sys}\end{array}$$
= enthalpy change of the system

$$\begin{array}{l}\triangle S_{sys}\end{array}$$
= entropy change of the system

$$\begin{array}{l} T \end{array}$$
= 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,

$$\begin{array}{l}\triangle S_{total}\end{array}$$
is greater than zero.

$$\begin{array}{l}\triangle S_{total}\end{array}$$
=
$$\begin{array}{l}\triangle S_{sys} + \triangle S_{surr}\end{array}$$

Where,

$$\begin{array}{l}\triangle S_{total}\end{array}$$
= total entropy change for the process

$$\begin{array}{l}\triangle S_{sys}\end{array}$$
= entropy change of the system

$$\begin{array}{l}\triangle S_{surr}\end{array}$$
= entropy change of the surrounding

In case of thermal equilibrium between system and surrounding, temperature change between system and surrounding,

$$\begin{array}{l}\triangle T\end{array}$$
=
$$\begin{array}{l}0\end{array}$$
. 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,

$$\begin{array}{l}\triangle S_{surr}\end{array}$$
=
$$\begin{array}{l}\frac{\triangle H_{surr}}{T} = – \frac{\triangle H_sys}{T}\end{array}$$

$$\begin{array}{l}\triangle S_{total}\end{array}$$
=
$$\begin{array}{l}\triangle S_{sys} + (- {\triangle H_sys}{T})\end{array}$$

$$\begin{array}{l}\triangle H_{surr}\end{array}$$
= change in enthalpy of the surrounding

$$\begin{array}{l}\triangle H_{sys}\end{array}$$
= change in enthalpy of the system

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

$$\begin{array}{l}T\triangle S_{sys} – \triangle H_{sys} >0\end{array}$$

$$\begin{array}{l}\triangle H_{sys} – T\triangle S_{sys} <0\end{array}$$

Above equation can be related to Gibbs equation as,

$$\begin{array}{l}\triangle G_{sys} < 0\end{array}$$

On the basis of above equation we can infer:

• $$\begin{array}{l}\triangle G_{sys} < 0\end{array}$$
, the process is spontaneous
• $$\begin{array}{l}\triangle G_{sys} > 0\end{array}$$
,, 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 the 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.

## Gibbs Energy in Chemistry

The energetics of processes for systems at constant temperature and pressure, the appropriate quantity is known as the Gibbs free energy. The Gibbs free energy has a very useful property; it decreases for a spontaneous process at constant temperature and pressure. Under such conditions the decrease in Gibbs free energy equals the maximum amount of energy available for work, whereas if it increases for some transition, the change in Gibbs free energy represents the minimum amount of work required.

The transformation of a system from one state to another, at constant temperature and pressure, is spontaneous if the Gibbs free energy decreases. If the Gibbs free energy is unchanged by the transformation the two states are in equilibrium. In other words the criterion for the thermodynamic equilibrium of a system at constant temperature and pressure is that the Gibbs free energy of the system be at the minimum value. The Gibbs free energy is sometimes called the thermodynamic potential at constant pressure in order to indicate its analogy with the potential energy of a mechanical system, which also has a minimum value under equilibrium conditions.

## Frequently Asked Questions – FAQs

### Why is Gibbs free energy called free energy?

The reason Gibbs Energy is referred to as free energy is that for some system the increase in Gibbs Energy is the maximum possible work that the process can generate due to constant pressure and temperature in the atmosphere.

### Why is Gibbs free energy important?

It is important to be able to measure the free energy of Gibbs because you can use it to determine the likelihood of a reaction. Negative enthalpy and positive entropy support a potential reaction

### How does Gibbs’s free energy predict spontaneity?

Spontaneity informs us of the path of the reaction, but not how rapidly it is going. Gibbs free energy is a simple formula that incorporates enthalpy, entropy, and temperature. G = H — TS. And finally, for a spontaneous reaction, the delta G sign is ALWAYS negative.

### What is the concept of entropy?

Entropy, the calculation of the thermal energy of a device per unit temperature inaccessible for useful work. The sum of entropy is also a measure of a system’s molecular disorder, or randomness since research is derived from ordered molecular motion.

### What happens when G is equal to zero?

If delta-G zero is zero, let’s write it down here, so if your standard free energy change, delta-G zero, is zero, K is zero. And that means your products and reactants are equally favoured in equilibrium.

### When Gibbs free energy is negative?

The ΔG sign will be changed from positive to negative (or vice versa) where T = ΔH / ΔS is changed. In cases where the subject is: negative, the process is spontaneous and can proceed as written in the forward direction. Positive, the process is non-spontaneous as written, but may proceed in the opposite direction spontaneously.

### What does a decrease in free energy mean?

If free energy is diminishing, the reaction can continue. If the free energy grows, the reaction can not proceed. A reaction is favored when the system’s free energy diminishes. A reaction is not preferred if the system’s free energy rises.

### How does Gibbs free energy relate to work?

Gibbs free energy measures useful work at a constant temperature and pressure obtainable from a thermodynamic system. The Gibbs free energy (G) is equal to the work exchanged by the system with its surroundings when a system changes from an initial state to a final state, minus the work of the pressure force.

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

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