**Free energy **(G)**:**

We have learnt that for a system, it is the total entropy change, ∆S _{total} which helps to decide the spontaneity of a process. However, most of the chemical reactions are either closed systems or open systems. Therefore, for most of the chemical reactions, there are changes in both enthalpy and the entropy. It is not possible to predict the spontaneity of a reaction on the basis of enthalpy or entropy alone. For this purpose to predict the spontaneity of a chemical reaction, a new function known as **Gibbs energy **or **free energy** is defined. Free energy of a system is **the maximum amount of energy available to a system during a process that can be converted into useful work. **It is denoted by symbol **G** and is given by

G = H – TS

Where, H = the enthalpy of the system.

S = the entropy of the system.

T = the absolute temperature.

We know,

H = E + PV

Then, G = E + PV – TS

**Free Energy Change** (∆G):

The change in free energy may be expressed as

∆G = ∆E + ∆(PV) – ∆(TS)

If the process is carried out at constant temperature and pressure, the terms ∆(PV) and ∆(TS) become

∆ (PV) = P∆V

∆ (TS) = T∆S

∆G = ∆E + P∆V – T∆S

However,

∆H = ∆E + P∆V

∆G = ∆H – T∆S

This equation is called **Gibbs Helmholtz equation** and very useful in predicting the spontaneity of a process.

**Free Energy Change For Predicting Spontaneity of a Reaction**:

As we have studied, the total entropy change (∆S _{total}) of system and surroundings determines the spontaneity of a process. The total entropy change during a process is given by-

∆S _{total }= ∆S _{sys} + ∆S _{surr}

If the reaction is carried out at constant temperature and pressure, heat involved is equal to enthalpy change i.e.

q _{system} =∆H _{system}

Now, if a reaction is conducted at constant temperature and pressure and heat (q) is given out to the surroundings reversibly, then

(q _{p}) _{surroundings} = – (q _{p}) _{system} = – ∆H _{system}

The entropy change of the surroundings is-

∆S_{ Surroundings} = (q _{p}) _{Surrounding }/ T = -∆H_{ System}/ T

Substituting the value of ∆S_{ Surroundings} in expression ∆S _{total }= ∆S _{sys} + ∆S _{surr}, we get-

∆S _{total }= ∆S _{sys} -∆H_{ System}/ T

Multiplying both sides by T, we get-

T∆S _{total }= T∆S _{system} -∆H_{ System}

-T∆S _{total }=∆H_{ System} – T∆S _{system}

– T∆S _{total }= ∆G_{ System}

We learnt that for spontaneous chemical change, ∆S _{total} is positive so that ∆G is equal to –ve for spontaneous chemical changes. Therefore, the spontaneity of a chemical change can be predicted either by-

(i) T∆S _{system} = positive or

(ii) ∆G = negative.

**Note**:

1) When energy and entropy factors are favourable, i.e. ∆H is negative and T∆S is positive, then ∆G must be negative.

∆G = (-) – (+) = – ve

Thus, **∆G is negative for a spontaneous process**.

2) If both the tendencies are oppose, i.e. ∆H is positive and T∆S is negative, then ∆G is positive.

∆G = (+) – (-) = + ve

Thus, **∆G is positive for a nonspontaneous process**.

3) If **∆G = 0 (Zero), the process is in equilibrium state**. There is no net reaction in either direction.