Chemical Equilibrium

 

Phase Equilibrium

Partition/ Distribution coefficient 

Relation between   K_c  and   K_p

At constant temperature, In isolated system, Total pressure exerted on the stage is the sum of partial pressure of all teams.

P_total = P₁+ P₂+ P_3........

when all participants in a reaction vessel are in gaseous state, their concentration is determined by their partial pressure.

From Ideal gas equation we know that:

     

            PV= nRT

               P= nRT/V

          P= cRT

               P = [concentration of gas] RT

At constant temperature we can say that pressure of gas is proportional to its concentration:

P is proportional to c

Let’s take a reaction as example:

H_2(g) + I_2(g) ↔ 2HI_(g)          

For this reaction equilibrium constant will be:

                                                   K_c = [HI]² / [H] [I]

Or, if we write in terms of partial pressure, then K_c will become K_p

K_p = (P_HI)² / (P_H) (P_I)

Since P = cRT we can write:

K_p = (P_HI)² / (P_H) (P_I) = [HI]² (RT)² / [H]RT [I]RT

K_p = K_c

Here you have seen that K_p = K_c  but, it doesn't happen always. 

Here  number of moles of reactants 2 and number of moles of gaseous product is 2, that’s why for this reaction K_p= K_c.

a A + b B ↔ c C + d D

K_c  = [C]^c [D]^d / [A]^a [B]^b

K_p = (P_C) (P_D) / (P_A) (P_B)

K_p = (P_C) (P_D) / (P_A) (P_B) = [C]^c (RT)^c [D]^d(RT)^d / [A]^a (RT)^a [B]^b (RT)^b

K_p = K_c (RT)^(c+d)-(a+b)

K_p = K_c (RT)^Δn

Let’s check this relation for another reaction:

N_2(g) + H_2(g) ↔ 2NH_3(g)

t is not a balanced equation since number of H isn’t equal on both sides of arrow. First we write the balanced equation:

N_2(g) + 3H_2(g) ↔ 2NH_3(g)         

This reaction has total 4 moles of reactants and 2 moles of product, thus we get

Δn = 2-4 = -2

If the above relation is correct, we would get:

K_p = K_c (RT)^-2

Let’s try to find out:

K_c = [NH₃]² / [N] [H]³

And

K_p = (P_NH3)² / (P_N) (P_H)³

K_p = (P_NH3)² / (P_N) (P_H)³ = [NH₃]² (RT)² / [N]RT [H]³ (RT)³

K_p = K_c (RT)^-2

Yes, we have successfully proved it.