## Tuesday, August 12, 2008

### Criterion of Spontaneity and Free Energy

July-December Revision

The flow of heat takes from a body at high temperature to a body at low temperature through conduction, convection or radiation. Similarly a liquid at higher level flows to a lower level. In both these cases the action occurs without any additional support. But if a liquid at lower level has to go higher level additional supporting activity is required.

Similarly in chemical reactions some reactions take place if the reactants are in contact. Some reactions will not take place through contact but require additional inputs like heat, catalysts etc. Reactions that take place due to contact alone are called spontaneous reactions. The rate of reaction is not the issue here. Even if the rate of reaction is very slow, if the reaction is taking place, it is a spontaneous reaction.

What determines the spontaneity of a chemical reaction?

Is decrease in enthalpy in the reaction a criterion for spontaneity?

In exothermic reactions, enthalpy of products is less than that of reactants. Thus some persons postulated that a spontaneous chemical reaction may be due to decrease in energy of the products. It sounds reasonable. But some scientists found that some endothermic reactions are also spontaneous. Therefore it is concluded that enthalpy may be a contributory factor for spontaneity, but it is not the complete explanation.

Is entropy a criterion for spontaneity?

Entropy is a thermodynamic function. It can be interpreted as measuring disorder in the system. A gas is more disordered than a liquid and a liquid is more disordered than a solid. In a chemical reaction, if the disorder in products is more than that of reactants, entropy increases. It is found in examples like diffusion of gases etc. that in spontaneous activities disorder increases.

As heat is added to the system, solids become liquids and liquids become gases. Hence heat increases entropy. Entropy is defined as

ΔS = qrev/T for a reversible reaction.

The criterion of spontaneity is defined by the total entropy change of system and surrounding. The total entropy change (ΔStotal) for the system and surroundings of a spontaneous process is given by

ΔStotal = ΔSsystem + ΔSsurrounding > 0

Gibbs energy of Free energy

Gibbs energy or Gibbs function is a thermodynamic functions defined by

G = H-TS

For a constant temperature reaction

ΔGsys = ΔHsys -T ΔSsys

Criterion for spontaneity in terms of Gibbs energy or function is that

If ΔG is negative or< 0, the reaction will be spontaneous.

This condition comes from the condition that was given above only. That is

ΔStotal = ΔSsystem + ΔSsurrounding > 0

ΔSsurr = ΔHsurr/T = -ΔHsys/T (because what system loses surrounding gains and vice versa)

Hence
ΔStotal = ΔSsystem - ΔHsys/T

=> TΔStotal = TΔSsystem - ΔHsys
As spontaneity criterion is ΔStotal > 0

RHS must be greater than 0.
=> TΔSsystem - ΔHsys > 0
=> -( ΔHsys - TΔSsystem) > 0
=> ( ΔHsys - TΔSsystem) < 0