Chemqueries: Relation between Kp, Kc, Kx and Kn

Relation 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  KP = KC (RT)∆n ...........................(eq 1)

        

        Relationship between KP and Kn

            ...........................(eq 2)                                 
            From ideal gas equation,PV=nRT
                                         =>P=n(RT/V)
            Where, n is the number of moles

            So,  PA =nA(RT/v), PB = nB(RT/V), PC =nC(RT/V) and PD =nD(RT/V)
         
            Replacing equation 2 by the above value we get that,     
                   [nC(RT/V)]c  . [nD(RT/V)]d 
       K=  -------------------------------------     
                   [nA(RT/V)]a  . [nB(RT/V)]b
                         nC. nDd
      = > Kp =  -------------- .  ( RT/V ) (c + d) – (a + b)
                         nAa. nBb  
      = >  Kp = Kn . (RT/V) ∆n

      = >  Kp = Kn . (PT/nT∆n

                                           
      Where ∆n =  (Number of gaseous moles of product ) - (Number of gaseous moles of reactant) 


      Relation between  Kand Kx
               From  above (eq 2)   
                                                             



              Partial pressure(P) = Mole fraction(x) . Total pressure(PT)
                So,   PA =  xA .  PT
                        PB =  xB .  PT
                        PC =  xC .  PT
                        PD =  xD .  PT

                Putting the values in whole equation:
                                   ( xC .  P)c . ( xD .  PT )d
                         K= ---------------------------------
                                   ( xA .  PT )a . ( xB .  PT )b

                                     xCc .  xDd
                               =  --------------   PT(c+d) - (a+b)
                                     xAa .  xBb

                    = >     KP  = Kx  (PT) ∆n


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