equilibrium constant, 𝐾c , for the reaction

Question

Calculate the value of the equilibrium constant, 𝐾c , for the reaction

Q(g)+X(g)↽−−⇀2M(g)+N(g)

given that

M(g)↽−−⇀Z(g) 𝐾c1=3.61

6R(g)↽−−⇀2N(g)+4Z(g) 𝐾c2=0.576

3X(g)+3Q(g)↽−−⇀9R(g) 𝐾c3=14.6

Answer 1

Hess' Law:

Rearrange the given equations in order to arrive at the target equation.

TARGET EQUATION:

Q(g) + X(g) <==> 2M(g) + N(g)

Given:

(1). M(g) <==> Z(g) ... Kc = 3.61

(2). 6R(g) <==> 2N(g) + 4Z(g) ... Kc = 0.576

(3). 3X(g) + 3Q(g) <==> 9R(g) ... Kc = 14.6

Procedure:

Copy (3)÷ 3: X(g) + Q(g) <==> 3R(g) ... Kc = cube root 14.6 = 2.44

Copy (2)÷2: 3R(g) <==> N(g) + 2Z(g) ... Kc = √0.576 = 0.759

Reverse (1)x2: 2Z(g) <==> 2M(g) ... Kc = 1/(3.61)² = 0.0767

______________________________________________________ add the three equations

X(g) + Q(g) + 3R(g) + 2Z(g) <=> 3R(g) + N(g) + 2Z(g) + 2M(g) now combine and or cancel like terms...

X(x) + Q(g) <==> N(g) + 2M(g) ... TARGET EQUATION

Kc = 2.44 * 0.759 * 0.0767 = 0.142