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)`

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)),(bar(CH_(4)+2H_(2)O_((g))hArrCO_(2(g))+4H_(2(g)),K_(3)......(iii))):}`
Eq. (`iii`) `=` eq. (`i`) `+` eq. (`ii`)
Thus, `K_(3)=K_(1)*K_(2)`