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

Answer

C

Explanation

We can notice that Eq. (C ) can be obtained by adding Eqs. (A) and (B):
`CO(g)+H_(2)(g)hArrCO_(2)(g)+H_(2)(g)`
`(CH_(4)(g)+H_(2)O(g)hArr CO(g)+3H_(2)(g))/(CH_(4)(g)+2H_(2)O(g)hArrCO_(2)+4H_(2)(g))`
Whenever we add two or more equations to create another equation, the equilibrium constants are multiplied: `K_(3)=K_(1)K_(2)`