`C(s) +H_(2)O(g) hArr CO(g) +H_(2)(g)`
the standard Gibbs enegry for the reaction at `1000K` is `-8.1 kJ mol^(-1)`. Calculate its equilibriu constant.
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We know, `K – antilog ((-DeltaG^(Theta))/(2.3030 RT)) …(i)`
Given that, `DeltaG^(Theta) =- 8.1 kJ mol^(-1)`
`R = 8.314 xx 10^(-3) k J K^(-1)mol^(-1)`
`T = 1000K`
Substituting these values in equation (i), we get
`K = antilog [(+(8.1))/(2.303 xx8.314xx 10^(-3)xx1000)]`
`K = 2.65`
`-DeltaG^(@)=2.303RTlogK_(C)`
`+8.1xx10^(3)=2.303xx8.314xx1000 logK_(C)`
`K_(C)=2.648mol litre^(-1)`
We know that:
`Delta_(r)G^(Theta) = – 2.303 RT log K`
or `logK = (-Delta_(r)G)/(2.303 RT)`
`Delta_(r)G^(Theta) =- 8.1 kJ mol^(-1), T = 1000K`,
`R = 8.314 xx 10^(-3) kJ mol^(-1)K^(-1)`
`:. Log K =- (8.1)/(2.303 xx 8.314 xx 10^(-3) xx 1000) = 0.423`
or `K = 2.64`