The heat of formation of `C_(2)H_(5)OH(l)` is `-66Kcal//mol` . The heat of combustion of `CH_(3)OCH_(3)(g)` is `-348Kcal//mol` , `DeltaH_(f)` for `H_(2)O` and `CO_(2)` are `-68Kcal//mol` and `-94Kcal//mol` . Respectively. Then, the `DeltaH` for the isomerisation reaction `C_(2)H_(5)OH(l)rarrCH_(3)OCH_(3)(g)` , and `DeltaE` for the same are at `T=25^(@)C`

Options

A. `DeltaH=18Kcal//mol,DeltaE=17.301Kcal//mol`
B. `DeltaH=22Kcal//mol,DeltaE=21.408Kcal//mol`
C. `DeltaH=26Kcal//mol,DeltaE=25.709Kcal//mol`
D. `DeltaH=30Kcal//mol,DeltaE=25.709Kcal//mol`

Answer

A

Explanation

`DeltaH_(F^(@))C_(2)OH(l)=-66Kcal//mol`
`2C+3H_(3)+(1)/(2)O_(2)rarrC_(2)H_(3)OH` ,
`DeltaH=-66Kcal//mol" "...(1)`
`CH_(3)-O-CH_(3)+3HO_(2)rarr2CO_(3)+3H_(2)O`
`deltaH=-348Kcal//mol" "...(2)`
`[H_(2)(g)+O_(2)(g)rarrH_(2)O] DeltaH_(3)=-68Kcal//mol" "(3)`
`[C+(1)/(2)O_(2) rarr CO_(2)]`
`DeltaH_(4) =-94` Kcal/mol`" "...(4)`
Target equation `=-eq. 1-eq. 2+3eq. 3+2eq. 2`
`DeltaH+66+348-3x68-2xx94=+66+348-204-188,DeltaH=22Kcal//mol`
`DeltaH=DeltaE+Deltan_(g)RT implies 22=DeltaE+1xx2xx298xx10^(-3),DeltaE=21.4Kcal//mol`