For the following three reaction 1, 2 and 3, equilibrium constants are given:
(1) `CO_((g)) + H_(2)O_((g))hArrCO_(2(g)) + H_(2(g)), K_(1)`
(2) `CH_(4(g)) + H_(2)O_((g))hArrCO_((g)) + 3H_(2(g)), K_(2)`
(3) `CH_(4(g)) + 2H_(2)O_((g))hArrCO_(2(g)) + 4H_(2(g)), K_(3)`
Which of the following relations is correct ?

Options

A. `K_(1)sqrt(K_(2)) = K_(3)`
B. `K_(2)K_(3) = K_(1)`
C. `K_(3) = K_(1)K_(2)`
D. `K_(3)=K_(2)^(3)K_(1)^(2)`

Answer

C

Explanation

`CO(g) + H_(2)O(g)hArrCO_(2)(g) + H_(2)(g), K_(1)` …..(i)
`CH_(4)(g) + H_(2)O(g)hArrCO(g) + 3H_(2)(g), K_(2)` …..(ii)
`CH_(4) + 2H_(2)O(g)hArr CO_(2)(g) + 4H_(2)(g), K_(3)` .....(iii)
Eq. (iii) = eq. (i) + eq. (ii)
Thus, `K_(3)` =` K_(1) K_(2)`