# Gibbs’ Free Energy Function

- All
**spontaneous processes**tend to achieve a state of**minimum energy**and**maximum entropy.** **For a system**, generally it is not possible to achieve both, the minimum energy and maximum entropy simultaneously.- There are cases where either of the two factors is favourable.
**For example**, many endothermic reactions are spontaneous because the favourable entropy factor (**ΔS**is highly positive) outweighs the unfavourable entropy factor (**ΔH**is positive).- On the other hand in some reactions the unfavourable entropy factor (
**ΔS**i.e.,_{sys}< 0**ΔS**is negative) is outweighed by the favourable enthalpy factor (_{sys}**ΔH**is negative). - From these observations, it becomes clear that
**ΔH**(or,**ΔE**), nor**ΔS**alone can predict whether a reaction is spontaneous or not._{sys } - However, the quantity,
**ΔS**can be used in predicting the_{total }= ΔS_{sys}+ ΔS_{surr}**spontaneity**of a process. - For a spontaneous process,
**ΔS**should be positive._{total} - For chemical systems, however, it is not always possible to determine
**ΔS**._{surr} - Under these conditions,
**it was felt that**a new**thermodynamic function**is needed to predict the direction of spontaneity.

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**Gibbs’ free energy**function was introduced by**J. Willard Gibbs**to predict the direction of spontaneity.- This function is denoted by the symbol
**G.** - The Gibbs’ free energy function (
**G)**accounts for the enthalpy and entropy changes in a system and is defined by

**G = H – TS**…………………………………..(i)

Where,** H** is the enthalpy of the system; **S** is the entropy of the system; **T** is the temperature of the system in Kelvin scale.

Since, **H, T, S** are state functions, hence, **G** is also **a state function**.

- The
**Gibbs’ free energy i**s defined as the**amount of energy**available for doing useful work under constant temperature and pressure conditions. - The free energy function (G) as such is not very useful. Instead, the change in free energy function
**ΔG**is very useful in predicting the state of any system. - The
**ΔG**is generally termed as the**free energy change**.

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Suppose a system is in its initial state, say **state 1**.

Let it be changed to another state, **say state 2**, under constant temperature and pressure conditions. Then, we can write,

State 1: **G1 = H1 – TS1 ** State 2: **G2 = H2 – TS2**

The change in free energy **ΔG** is then given by

**ΔG = G2 – G1** = (H2 – TS2) – (H1 – TS1) = (H2 – H1) – T (S2 – S1)

Or, **ΔG = ΔH – T ΔS**

This equation is known as **Gibbs’ – Helmholtz equation.**

**Gibbs’ Free Energy Change and Spontaneity of a Process**

For a system which is not isolated, the direction of spontaneity can be predicted by the total energy entropy **(ΔS _{total})**.

**ΔS**is given by,

_{total}**ΔS _{total} = ΔS_{sys }+ ΔS_{surr}**………………………………..(ii)

If a reaction is carried out at **constant temperature and pressur**e, and heat equal to** ΔH** is given out to the surrounding, then,

**ΔS _{surr} = qrev/T = – ΔH_{sys}/T**…………………………….(iii)

Substituting equation (iii) in equation (ii), we get,

**ΔS _{total }= ΔS_{sys} – (ΔH_{sys}/T)**

Since, all the terms on the right refer to the system, hence the subscript **sys** is dropped. The above equation than can be written as

**T ΔS _{total }= TΔS – ΔH**

Or, -T ΔS_{total }= ΔH – TΔS………………………………..(iv)

**We know that,**

G = H – TS

Or,** ΔG = ΔH – TΔS – SΔT**

For a change conducted at c**onstant temperature** and pressure, since **ΔT = 0**, hence

**ΔG = ΔH – TΔS**…………………………………………….(v)

Comparing equation (v) and (iv) one gets,

**ΔG = – TΔS**_{total}…………………………………………..(vi)

Thus, from above equation we can say that **ΔG** can also be used for** predicting the direction** of spontaneity.

**References: **

i) https://goldbook.iupac.org/terms/index/A

ii) https://link.springer.com/article/10.1557/mrs.2019.162