Determine `Delta U^(@) ` at 300K for the following reaction using the listed enthalpies of reaction :
`4CO(g)+8H_(2)(g)to3CH_(4)(g)+CO_(2)(g)+2H_(2)O(l)`
`C("graphite")+(1)/(2)O_(2)(g)to CO(g), DeltaH_(1)^(@)=-110.5KJ`
` CO(g)(1)/(2)O_(2)(g)toCO_(2)(g), DeltaH_(2)^(@)=-282.9KJ`
`H_(2)(g)+(1)/(2)O_(2)(g)to H_(2)O(l), DeltaH_(3)^(@)=-285.8KJ`
`C("graphite")+2H_(2)(g)to CH_(4)(g), DeltaH_(4)^(@)=-74.8KJ`

Options

A. `-653.5 KJ`
B. `-686.2 KJ`
C. `-747.4 KJ`
D. None of these

Answer

D

Explanation

`DeltaH^(@) =- 3DeltaH_(1)^(@)DeltaH_(2)^(@) + 2DeltaH_(3)^(@) + 3DeltaH_(4)^(@)`
`=-747.4` KJ
`DeltaH^(@) =DeltaU^(@) + Deltan_(g) RT , "where" Deltan_(g) =- 8`
`747.4 = DeltaU^(@) - (8xx8.314 xx300)/(1000)`
`DeltaU^(@)=-747.44` KJ.