Equilibrium constant in terms of partial pressure.

 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 ,

            Equilibrium Constant

  • 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

                 ……………………. (eq1)
                                                                                                                                                           
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,
            P=(n/V)RT
            P=CRT
  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


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