Relationship between Kp ,Kc, Kx and Kn

• Kp=Equilibrium constant in terms of partial pressure.
• Kc=Equilibrium constant in terms of concentration.
• Kx=Equilibrium constant in terms of  mole fraction.
• Kn=Equilibrium constant in terms of  number of moles.
•  Kp and Kc are related as  K_P = K_C (RT)^∆n ………………………(eq 1)

        Relationship between K_P and K_n

            ………………………(eq 2)                                 

             [n_C(RT/V)]^c  . [n_D(RT/V)]^d 
 K_p =  ————————————-     
             [n_A(RT/V)]^a  . [n_B(RT/V)]^b
                   n_C^c . n_D^d
= > K_p =  ————– .  ( RT/V ) ^{(c + d) – (a + b)}
                   n_A^a. n_B^b  
= >  K_p = K_n . (RT/V) ^∆n

= >  K_p = K_n . (P_T/n_T) ^∆n                                   

         ∆n=number of gaseous moles of product – number of gaseous moles of reactant

Relation between  Kp and Kx

           From  above (eq 2)   

                                                         

          Partial pressure(P) = Mole fraction(x) . Total pressure(P_T)

          So,   P_{A =}  x_{A .}  P_T