Consider the following two equilibrium reactions at a constant temperature: (i) CO(g) + 2H₂(g) CH₃OH(g) ; Equilibrium constant = K₁ (ii) 3CH₃OH(g) 3CO(g) + 6H₂(g) ; Equilibrium constant = K₂ Which of the following correctly expresses the relationship between K₁ and K₂ ?

Step-by-step solution

For the first reaction: CO(g) + 2H₂(g) CH₃OH(g) The equilibrium constant is given by: K₁ = [CH₃OH] [CO][H₂]^2 For the second reaction: 3CH₃OH(g) 3CO(g) + 6H₂(g) The equilibrium constant is given by: K₂ = [CO]^3[H₂]^6 [CH₃OH]^3 Rearranging the expression for K₂ in terms of K₁ : K₂ = ( [CO][H₂]^2 [CH₃OH] )^3 K₂ = ( 1 K₁ )^3 = 1 K₁^3 Answer: K₂ = 1 K₁^3