Question

For the following three reactions a, b and c, equilibrium
constants are given:
(i) CO(g) H₂O(g)⇋CO₂(g) H₂(g);K₁
(ii) CH₄ (g) H₂O(g)⇋CO(g) 3H₂(g);K₂
(iii) CH₄(g) + 2H₂O(g)⇋CO₂(g) + 4H₂(g);K₃
(a) K₁ √K₂ = K₃ (b) K₂K₃ = K₁
(c) K₃ = K₁ K₂ (d) K₃.K₂³ = K₁²

Answer 1

The correct relation between the three equilibrium constants is (c)K₃ = K₁ K₂.

1. First, we write the equations of the equilibrium constants

K₁=[CO₂] [H₂]/[H₂O] [CO]

K₂=[CO] [H₂]^3/[CH₄] [H₂O]

K₃=[CO₂] [H₂]^4\[CH₄][H₂O]^2

2. Then we try out all the options by putting the values of the three constants

3. We see that,

K₁ *K₂ =[CO₂] [H₂]/[H₂O] [CO] * [CO] [H₂]^3/[CH₄] [H₂O]

= [CO₂] [H₂]^4\[CH₄][H₂O]^2.

= K₃

4. Thus we see that K₃ = K₁K₂ and hence (c) is the correct answer

Answer 2

K₃ = K₁ K₂ is the correct option.

Explanation:

• In the reaction B, we see that CH₄ (g) H₂O(g)⇋CO(g) 3H₂(g).

• The rate constant is K2.

• In the reaction A, we can see that CO(g) H₂O(g)⇋CO₂(g) H₂(g).

• The rate constant is K1.

• In the reaction C, we can see that CH₄(g) + 2H₂O(g)⇋CO₂(g) + 4H₂(g).

• The rate constant is K3.

• We can see that adding the reaction B and A, we can get reaction C.

• Reaction constant of reaction A is K2.

• Reaction constant of reaction B is K1.

• Reaction constant of reaction C is K3.

• K₁=[CO₂] [H₂]/[H₂O] [CO]
• K₂=[CO] [H₂]^3/[CH₄] [H₂O]
• K₃=[CO₂] [H₂]^4\[CH₄][H₂O]^2

• So Adding these reaction constants we get

• K₁K₂ =[CO₂] [H₂]/[H₂O] [CO] [CO] [H₂]^3/[CH₄] [H₂O]  = [CO₂] [H₂]^4\[CH₄][H₂O]^2.  = K₃
• K3 = K1K2.

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