Use the reactions below and their equilibrium constants to predict the equilibrium constant for the reaction,?

This problem is solved in a similar way to problems using Hess's Law with 2 big differences. So the first reaction has A in the reactants which is what we want but we need 2A, so we square k1. Then for the third reaction we have 3D which is what we want, but we want it as a product and it is in the reactants so we will flip that equation which then makes K2 negative. The rest should cancel out which makes me wonder if the coefficient of 12 is a misprint. Anyway, once you have your new K values and the equation you want you just multiply the 2 so we would have .00334^2*(-2.35)
And we get -.0000262=Kc

As component A is solid, its effective concentration is constant and it thus should not appear in the equilibrium expressions.

Given : A(s) ⇌ (1/2)B(g) + C(g) …. K₁ = 0.0334
Then, [B]⁰·⁵ [C] = 0.0334
Square the both sides : [B] [C]² = 0.0334² …… {1}

Given : 3D(g)⇌B(g) + 2C(g) …. K₂ = 2.35
Then, [B] [C]² / [D]³ = 2.35 …… {2}

2A(s)⇌3D(g) …… K
Equilibrium constant, K = [D]^3
Then, K = ([B] [C]²) / ([B] [C]² / [D]³) …… {3}

Substitute {1} and {2} into {3} :
K = 0.0334² / 2.35
K = 0.0142

A (s) ⇌ 1/2 B(g) + C(g)
Kc = [B]^(1/2) [C] = 0.0334 -------(1)

3D(g) ⇌ B(g) + 2C (g)
Kc' = [B][C]^2 / [D]^3 = 2.35 -----(2)

Use equations (1) & (2) and find out [D]
2A(s) ⇌ 3D(g)
K = [D]^3
Units of this constant will be mol^3 / L^3

A(s)⇌1/2B(g)+ C(g) K1=0.0334

K1 = ([B]^1/2 * [C])/([A])

[A] = ([B]^1/2 * [C])/0.0334



3D(g)⇌B(g) 2C(g) K2=2.35

K2 = ([B][C]^2/([D]^3)

[D]^3 = = ([B][C]^2)/2.35



2A(s)⇌3D(g).

Kc = ([D]^3/[A]^2).

Kc = 0.0334*0.0334/2.35

Kc = 0.0004 = 4*10^-3.