The heat of formation of `C_(2)H_(5)OH(l)` is `-66 kcal//"mole"`. The heat of combustion of `CH_(3)OCH_(3) (g)` is -348 kcal/mole. `DeltaH_(f)` for `H_(2)O` and `CO_(2)` are -68 kcal/mole respectively. Then, the `Delta H` for the isomerisation reaction `C_(2)H_(5)OH(l)rarrCH_(3)OCH_(3)(g)`,and `Delta E` for the same are at `T=25^(@)C`

Options

A. `Delta H=18` kcal/mole,`Delta E= 17.301`kcal/mole
B. `Delta H=22` kcal/mole,`Delta E=21.408` kcal/mole
C. `DeltaH=26` kcal/mole, `Delta E=25.709` kcal/mole
D. `Delta H=30` kcal/mole, `Delta E= 28.522` kcal/mole

Answer

B

Explanation

`DeltaH_(F)^(o)C_(2)OH_(5)(l)= -66` Kcal/mole
`2C+3H_(2)+(1)/(2)O_(2)rarrC_(2)H_(5)OH " " DeltaH= -66 kcal//"mole"`.....(1)
`CH_(3)-O-CH_(3)+3O_(2)rarr2CO_(2)+3H_(2)O " "Delta H= -348 kcal//"mole"`.....(2)
`[H_(2)(g)+(1)/(2)O_(2)(g)rarrH_(2)O " " DeltaH_(3)-68 kcal//"mole"`.....(3)
`[C+O_(2)rarrCO" "Delta H_(4)= -94 kcal//"mole"`......(4)
Target equation `= - eq-eq2+3eq3+2 eq 2`
`DeltaH=+66 + 348 -3xx68-2xx94=+66+348-204-108 " "implies DeltaH=22 K `cal/mole
`DeltaH=DeltaE+DeltangRT" "22=DeltaE+1xx 2xx298 xx 10^(-3) " " implies DeltaE=21.4` Kcal/mole