Question

Suggest how the thermodynamic equilibrium constant and the equilibrium constant expressed in terms of partial pressures may respond differently to changes in temperature and pressure.

Answer 1

Basically , we know that a mixture of reactants and products in an equilibrium state is called an equilibrium mixture ,

Let's consider a general reversible reaction : A + B ----------> C + D where A , B are reactants and C , D are products in this balanced chemical reaction

Generally a chemical reaction reach a state of dynamic equilibrium , in which the rates of the forward and backward reactions are equal and there is no net change in composition of the equilibrium mixture.

Thus we can relate the concentrations in this equilibrium mixture as

Kc = [ C ].[ D ] / [ A ].[ B ] , where Kc is called the equilibrium constant .

However this is calculated from the molar concentration of reactants and products , but to calculate equilibrium constant in terms of partial pressures , we use :

Partial pressures , for calculating the pressure constant. In the above image _ we use partial pressures PA , PB , PC , PD , raised to exponents equal to their respective coefficients in the above given chemical equation.

Kp is calculated using Kc , temperature and change in moles using , following equation :

And , this particular concentration ratio has a dimensions of concentration ,

Where as the thermodynamic equilibrium constant is the internal state of a single thermodynamic system , denoted with 'K' is a dimensionless quotient. Thermodynamics tells only about the feasibility of a reaction , and it discuss the spontaneity based on equilibrium constant. And the thermodynamic equilibrium constant can be written as following ( in logarithmic form ) from Gibbs free energy ;

Where ; ln K = natural logarithm of K

T = temperature in Kelvin

∆G = standard Gibbs free energy

Here , ∆G is defined at a single standard pressure and thus is independent of the pressure used in a specific reaction

The thermodynamic equilibrium constant , is therefore independent of reaction pressure , doesn't mean that the equilibrium composition is independent of pressure ( or partial pressure )

For ex : consider a general equation : 2A(g) ----------> B(g)

Assume mole fraction of A = xA ( at equilibrium ) then , xB = 1.0 - xA and the thermodynamic equilibrium constant is given by :::

Because K doesn't change , xA must change in response to any variation in total pressure Ptotal.

Thank you !