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Compute the standard free energy of the ...

Compute the standard free energy of the reaction at `27^(@)C` for the combustion of methane using the given data.
`CH_(4)(g)+2O_(2)(g)to CO_(2)(g)+2H_(2)O(l)`
`{:("Species",CH_(4),O_(2),CO_(2),H_(2)O),(Delta_(f)H^(@)//(kJ mol^(-1)),-74.8,-,-393.5,-285.8),(S^(@)//(JK^(-1)mol^(-1)),186,205,214,70):}`

Text Solution

Verified by Experts

`DeltaH^(@) = DeltaH_(t)^(@)(CO-(2))+ 2DeltaH_(t)^(@)(H_(2)O) - DeltaH_(t)^(@)(CH_(4))`
`=-393.5 + 2 xx (-285.8) -(-74.8)`
`=-890 kJ mol^(-1)`
`DeltaS^(@) = S_(CO_(2))^(@) + 2S_(H_(2)O)^(@) - S_(CH_(4))^(@) - 2SO_(O_(2))^(@)`
`=-242 JK^(-1) "mol"^(-1)`
`DeltaG^(@) = DeltaH^(@) - T DeltaS^(@)`
`=-890 - 300 xx (-242 xx 10^(-3))`
`=817.4 jK mol^(-1)`.
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