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Equilibrium constant for the following r...

Equilibrium constant for the following reactions at 1200 K are given :
`2H_(2)O_((g))iff2H_(2(g))+O_(2(g)),K_(1)=6.4xx10^(-8)`
`2CO_(2(g))iff2CO_((g))+O_(2(g)),K_(2)=1.6xx10^(-6)`
The equilibrium constant for the reaction
`H_(2(g))+CO_(2(g))iffCO_((g))+H_(2)O_((g))` at 1200 K will be

A

`0.05`

B

20

C

`0.2`

D

`5.0`

Text Solution

Verified by Experts

The correct Answer is:
D
Given :
`2H_(2)O_((g))iff2H_(2(g))+O_(2(g))`
`K_(1)=6.4xx10^(-8)" "...(i)`
`2CO_(2(g))iff2CO_((g))+O_(2(g))`
`K_(2)=1.6xx10^(-6)" "...(ii)`
Required equation is,
`H_(2(g))+CO_(2(g))iffCO_((g))+H_(2)O_((g)),K=?`
By reversing equation (i) and by multiplying it with 1/2, we get
`H_(2(g))+(1)/(2)O_(2(g))iffH_(2)O_((g)),K._(1)=sqrt((1)/(6.4xx10^(-8)))" "...(iii)`
And by multiplying equation (ii) with 1/2, we get
`H_(2(g))+CO_(2(g))iffCO_((g))+H_(2)O_((g)),K.=K._(1)xxK._(2)`
`K.=sqrt((1.6xx10^(-6))/(6.4xx10^(-8)))=sqrt(25)=5`
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