Calculate `DeltaG^(Theta)` for the following reaction at 298K:
`CO(g) +((1)/(2))O_(2)(g) rarr CO_(2)(g), DeltaH^(Theta) =- 282.84 kJ`
Given,
`S_(CO_(2))^(Theta)=213.8 J K^(-1) mol^(-1), S_(CO(g))^(Theta)= 197.9 J K^(-1) mol^(-1), S_(O_(2))^(Theta)=205.0 J K^(-1)mol^(-1)`,

Explanation

`DeltaS^(Theta) = sum S^(Theta) ("products") -sumS^(Theta) ("reactants")`
`=[S^(Theta)underset(CO_(2)).]-[S^(Theta)underset(CO).+(1)/(2)S^(Theta)underset(O_(2)).]`
`= 213.8 - [197.9 +(1)/(2)205] =- 86.6 J K^(-1)`
According to Gibbs-Helmholtz equation,
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta)`
`=- 282.84 - 298 xx (-86.6 xx 10^(-3))`
`=- 282.84 +25.87`
`=- 257.033 kJ`