Compute the standard free enegry of the reaction at `27^(@)C` for the combustion fo methane using the give data:
`CH_(4)(g) +2O_(2)(g) rarr CO_(2)(g) +2H_(2)O(l)`
`{:(Species,CH_(4),O_(2),CO_(2),2H_(2)O(l)),(Delta_(f)H^(Theta)(kJmol^(-1)),-74.8,-,-393.5,-285.8),(S^(Theta)(JK^(-1)mol^(-1)),186,205,214,70):}`

Explanation

`DeltaH^(Theta) = Delta_(f)H^(Theta)underset((CO_(2))).+2Delta_(f)H^(Theta)underset((H_(2)O)).-Delta_(f)H^(Theta)underset((CH_(4)))`
`=- 393.5 +2 xx (-285.8) -(-74.8)`
`=- 890 kJ mol^(-1)`
`DeltaS^(Theta)=S^(Theta)underset((CO_(2))).+2S^(Theta)underset((H_(2)O)).-S^(Theta)underset((CH_(4))).-2S^(Theta)underset((O_(2))."sup")`
`=214 +2 xx 70 - 186 -2xx 205`
`=- 242 J K^(-1)mol^(-1)`
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta)`
`=-890 - 300 xx (-242 xx 10^(-3))`
`=- 890 + 72.6 =- 817.4 kJ mol^(-1)`