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

For the following three reaction (i), (ii) and (iii), equilibrium constants are given
(i) `CO_((g))+H_(2)O_((g))iffCO_(2(g))+H_(2(g)),K_(1)`
(ii) `CH_(4(g))+H_(2)O_((g))iffCO_((g))+3H_(2(g)),K_(2)`
(iii) `CH_(4(g))+2H_(2)O_((g))iffCO_(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))iffCO_(2(g))+H_(2(g))`
`K_(1)=([CO_(2)][H_(2)])/([CO][H_(2)O])" "...(i)`
`CH_(4(g))+H_(2)O_((g))iffCO_((g))+3H_(2(g))`
`K_(2)=([CO][H_(2)]^(3))/([CH_(4)][H_(2)O])" "...(ii)`
`CH_(4(g))+2H_(2)O_((g))iffCO_(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)xxK_(2)`
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