Both KP and Kc are equilibrium constants,but Kc is defined by molar concentration
but KP is defined by partial pressure.
Derivation of KP :
- Consider the following reversible reaction
aA(g) + bB(g) ⇔ cC(g) + dD(g)
- If equilibrium constant for the reaction is expressed in terms of the molar concentration ,
- If the equilibrium involves gaseous species, then concentration may be expressed in terms of partial pressure of the reactants and products and it is represented as
PA , PB , PC and PD are the partial pressure of A,B,C and D respectively.
Relationship between KP and Kc :We know that ,for a ideal gas pressure is directly proportional to the concentration assuming volume and temperature constant.
So, PV = nRT
Divide both sides by V,
Where,C is concentration
n is the number of moles
V is the volume
R is ideal gas constant,and
n/V is the molar concentration.
Thus the partial pressures of individual gases A, B, C and D are:
PA = [A]RT; PB = [B]RT; PC = [C]RT; PD = [D]RT
Substituting these value in equilibrium constant expression equation 1, we have
KP = KC (RT)(c+d)-(a+b)
KP = KC (RT)∆n
where ∆n = (c+d) – (a+b)
=number or gaseous moles of the product-number of gaseous moles of the reactant