 Education

# Gibbs Free Energy and Entropy

Thermodynamics is a science which deals with heat and work and also the energy transfer during chemical and physical changes. The two terms come under thermodynamics.

## Gibbs Free Energy

Gibbs free energy is a thermodynamic property proposed by Josiah Willard Gibbs in 1876 to predict whether a process will occur spontaneously at constant temperature and pressure. Gibbs free energy is defined as the free energy of the system is the sum of its enthalpy plus the product of the temperature and the entropy of the system.

## Mathematical expression for Gibbs Free Energy

Gibbs Free energy is defined as,

G = H – TS

Where,

G = Gibbs free energy

H = enthalpy

T = temperature

S = entropy

The SI unit of Gibbs free energy is Kilojoule

## Free energy of a reaction (ΔG)

The free energy of a reaction is the change in enthalpy of the system minus the product of the temperature and change in the entropy of the system.

ΔG = ΔH – TΔS

This equation is called the Gibbs Helmholtz equation

## Positive and negative Free energy

Gibbs free energy can be used for determining whether the reaction proceeds spontaneously or not by its sign

Free energy = ΔG

If  ΔG is positive the reaction does not occur spontaneously and additional energy should be provided

If ΔG is negative the reaction occurs spontaneously and will be thermodynamically favorable.

## How to determine the direction and extent of a chemical change

If the free energy of the reactant (A) is greater than the product (B) the entropy will increases and reaction occurs in the same direction

If the free energy of the product exceeds that of the reactant then the reaction will tend to proceed in the reverse reaction.

ΔG>0; the reaction is non-spontaneous and reaction proceeds B → A

ΔG<0; the reaction is spontaneous and exergonic A → B

ΔG=0; the reaction is at equilibrium A and B won’t change

## Standard-state free energy of reaction (∆G°)

The difference between the free energy of a substance and the free energy of its element in their most thermodynamically stable states at the standard-state condition

∆G°=∆H°-T∆S°

## Entropy

Clausius introduced the concept of entropy by expressing in the second law of thermodynamics.

The second law of thermodynamics states that spontaneous change for an irreversible process in an isolated system ( that does not exchange heat or work with its surroundings) always proceeds in the direction of increasing entropy.

By the Clausius definition, if an amount of heat Q flows into a large heat reservoir at temperature T above absolute zero, then the entropy increase is

ΔS = Q/T.

Where,

ΔS represents the change in entropy,

Q represents the heat,

T is the temperature in the Kelvin scale.

## Properties of Entropy

• For harder and brittle substances entropy seems to be lower whereas greater for malleable solids
• Entropy decreases when gas is dissolved in water whereas it increases when liquid or solid is dissolved in water.
• As chemical complexity increases, the entropy also increases.
• As mass increases entropy increases.

## The relationship between Enthalpy, Entropy, and Gibbs Free Energy

• When ΔHreaction is negative and ΔSreaction is positive, ΔGreaction will be negative overall temperatures.
• When ΔHreaction is negative and ΔSreaction is negative, ΔGreaction will be negative at high temperatures.
• When ΔHreaction is positive and ΔSreaction is negative, ΔGreaction will not be negative at any temperature.
• When ΔHreaction is positive and ΔSreaction is positive, ΔGreaction will be negative at low temperatures.

## Isentropic process

It is the process of the system where entropy remains constant. During the isentropic process, the value of entropy of the system at initial and final state remains constant. Hence during the isentropic process, ΔS will be 0. The isentropic process can be reversible or irreversible. The process which is always reversible and adiabatic is always an isentropic process

## Why the Entropy of the system increases?

The entropy of the system can be increased mainly due to two reasons

1. The external reaction: The mass will remain constant in a closed system but it can exchange heat with surroundings thus any change in the heat content will disturb the system and increases the entropy
1. Internal changes in the system: The movement of molecules in the system may cause disturbance and irreversibility and thus tends to increase the entropy

## Summary

• Gibbs free energy is defined as the free energy of the system is the sum of its enthalpy plus the product of the temperature and the entropy of the system.

G = H – TS

• The second law of thermodynamics says that the entropy of the universe always increases for a spontaneous process
• When ΔG is negative , a process will proceed spontaneously If  ΔG is positive the reaction does not occur spontaneously
• Depending on signs of ΔH and ΔS, the spontaneity of a process changes
• Isentropic is the process of the system where entropy remains constant