The equilibrium constant is given for one of the reactions below.Determine the value of the missing equilibrium constant.
N₂O₄(g) ⇌ 2 NO₂(g) K_c = 1.46
3 N₂O₄(g) ⇌ 6 NO₂(g) K_c = ?

Question

The equilibrium constant is given for one of the reactions below.Determine the value of the missing equilibrium constant. N₂O₄(g)⇌ 2 NO₂(g)K_c = 1.46 3 N₂O₄(g)⇌ 6 NO₂(g)K_c = ?

Quizplus · Accepted Answer

The equilibrium constant expression for the second reaction is: 
(Kc)second = ([NO]^2*[N2O]^3)/[N2O5]^3 
Since the first reaction is happening in the reverse direction of the second reaction, we can use the inverse of its equilibrium constant: 
(Kc)first = 1/1.46 = 0.6849… 
Multiplying the equilibrium constant expressions for the two reactions gives us the expression for the third reaction: 
(Kc)third = (Kc)second*(Kc)first^2 
(Kc)third = ([NO]^2*[N2O]^3)/[N2O5]^3*(0.6849…)^2 
(Kc)third = 3.11 
Therefore, the missing equilibrium constant for the third reaction is 3.11.

The Equilibrium Constant Is Given for One of the Reactions