Consider the following two equilibrium reactions at a constant temperature:

(i) $CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)$ ; Equilibrium constant $= K_1$
(ii) $3CH_3OH(g) \rightleftharpoons 3CO(g) + 6H_2(g)$ ; Equilibrium constant $= K_2$

Which of the following correctly expresses the relationship between $K_1$ and $K_2$ ?

Question

Consider the following two equilibrium reactions at a constant temperature:

(i)

CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)

; Equilibrium constant

= K_1

(ii)

3CH_3OH(g) \rightleftharpoons 3CO(g) + 6H_2(g)

; Equilibrium constant

= K_2

Which of the following correctly expresses the relationship between

K_1

and

K_2

?

Quantrex Academy · Accepted Answer

Correct answer: C. K_2 = (1)/(K_1^3)

For the first reaction: CO(g) + 2H_2(g) leftharpoons CH_3OH(g) The equilibrium constant is given by: K_1 = ([CH_3OH])/([CO][H_2]^2) For the second reaction: 3CH_3OH(g) leftharpoons 3CO(g) + 6H_2(g) The equilibrium constant is given by: K_2 = ([CO]^3[H_2]^6)/([CH_3OH]^3) Rearranging the expression for K_2 in terms of K_1 : K_2 = ( ([CO][H_2]^2)/([CH_3OH]) )^3 K_2 = ( (1)/(K_1) )^3 = (1)/(K_1^3) Answer: K_2 = (1)/(K_1^3)

Consider the following two equilibrium reactions at a constant...

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