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For the following three reactions (i), (...

For the following three reactions (i), (ii) and (iii), equilibrium constants are given
(i) `CO_(g)+H_(2)O_(g) Leftrightarrow CO_(2(g)) +H_(2(g)) , _(1)`
`(ii) CH_(4(g)) +H_(2)O_(g) Leftrightarrow CO_(g)+3H_(2(g)) , K_2`
`(iii) CH_(4(g))+2H_(2)O_(g) Leftrightarrow CO_(2(g))+4H_(2(g)), K_3`
Which of the following relations is correct?

A

`K_(3) K_(2)^(3)=K_(1)^(2)`

B

`K_(1) sqrt(K_(2))=K_(3)`

C

`K_(2)K_(3)=K_1`

D

`K_(3)=K_(1)K_(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`CO_(g) +H_(2)O_(g) Leftrightarrow CO_(2(g)) +H_(2(g))`
`K_(1)=([CO_(2)] [H_(2)])/([CO] [H_(2)O]) ………….(i)`
`CH_(4(g)) +H_(2)O_(g)) Leftrightarrow CO_(g)+3H_(2(g))`
`K_(2)=([CO] [H_(2)]^3)/([CH_(4)] [H_(2)O]) …………….(ii)`
`CH_(4(g)) +2H_(2)O_(g) Leftrightarrow CO_(2(g)) +4H_(2(g))`
`K_(3)=([CO_(2)] [H_(2)]^4)/([CH_(4)] [H_(2)O])^2 ...........(iii)`
From equations (i), (ii) and (iii) , `K_(3)=K_(1) xx K_(2)`
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