# Spontaneity of Chemical Reaction: Gibbs Energy and Spontaneity (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Gibbs Energy and Spontaneity

We use this equation

At constant temperature and pressure if is the heat given out by the system to the surroundings, is the heat gained by the surroundings we can write

It is defined as Gibbs energy and given by the equation

For a change in Gibbs energy, we write

At constant temperature

Therefore,

H, T and S are state functions, so G is also a state function.

The Gibbs energy can be useful in defining that a process is spontaneous or non-spontaneous.

If a process occurring at constant temperature and pressure, then

- (negative) , the process is spontaneous
- (positive) , the process is non-spontaneous.
- (zero) , the process is at equilibrium

**The Spontaneity of chemical reaction is depend upon two factor**:

- The energy factor
- The entropy factor

**Based on the signs of (∆ H) and (∆ S) , there are four possibilities**:

These possibilities are outlined in table

**Example**:

For the reaction

Calculate at when enthalpy and entropy changes are respectively and

**Solution**:

Given

Substituting the values in

## Standard Gibbs Energy Change and Equilibrium Constant (K)

The standard Gibbs energy change is defined as the change in Gibbs energy for the process in which the reactants in their standard states are converted into the products in their standard states.

It is denoted by the symbol .

The value of can be found from the standard Gibbs energy of formation of substance.

The standard Gibbs energy of formation of a compound is defined as the change in Gibbs energy when 1 mole of the compound is formed from its constituent elements in their standard states.

The standard Gibbs energy of formation of an element in its standard state is taken as zero . Thus, for the reaction

The standard Gibbs energy change is related to the equilibrium constant of the reaction by the expression

**Example**:

The equilibrium constant of the reaction

is at . Calculate the value of .

**Solution**:

Given

**Example**:

Calculate the standard Gibbs energy change for the reaction

at . The standard Gibbs energies of formation of and at are and respectively.

**Solution**: