K,Q,G Relationship And Le Chatelier'S Principle

The change in the Gibbs free energy of a chemical reaction can be defined as the difference in the Gibbs free energy of the products and that of the reactants. This can be represented as

ΔG = G_(products) - G_(reactants)

When ∆G =0, (that means G_(reactants) = G _(products)

At this stage, the system is said to have achieved equilibrium.

∆G > 0, the process is non - spontaneous

The change in the Gibbs energy for a reaction in which all the reactants and products are in the standard state is known as standard Gibbs energy change

(∆G°)

The relationship between Gibbs energy changeand standard Gibbs energy changeis given as
   ∆G = ∆G° + RTlnQ

where,

R is universal gas constant

T is absolute temperature

Q is reaction quotient

For a reaction A + B $\rightleftharpoons$C + D

'.' Q = $\frac{\text{[C][D]}}{\text{[A]}\text{[B]}}$

ΔG = ΔG° + RTln$\frac{\text{[C][D]}}{\text{[A]}\text{[B]}}$

At equilibrium, when ΔG = 0 and Q = K_c, the equation

ΔG = ΔG° + RTln$\frac{\text{[C][D]}}{\text{[A]}\text{[B]}}$

Becomes ΔG = ΔG° + RTlnK_c = 0

ΔG° = - RTlnK_c

lnK_c = $\frac{\text{-}∆\text{G}⁰}{\text{RT}}$$\frac{}{}$

Taking antilog on both sides,

K = e ^{$$ - ∆ G ⁰ RT}  

If ΔG° < 0, then $\frac{\text{-}∆\text{G}⁰}{\text{RT}}$$\frac{}{}$ becomes positive and e^{$$ - ∆ G ⁰/ RT} >1

If k > 1 It is a spontaneous reaction.

If ΔG° > 0, then $\frac{\text{-}∆\text{G}⁰}{\text{RT}}$$\frac{}{}$ becomes positive and e^{$$ - ∆ G ⁰/ RT} <1

If k < 1 It is a non-spontaneous reaction.

According to Le Chatelier's principle: "If a system at equilibrium is subjected to a change in the temperature, pressure or concentration of the reactants or the products that govern the equilibrium, then the equilibrium position shifts in the direction in which this change is reduced or nullified."