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. ${ΔH}_{f}$ for $H_{2} O (l)$ and ${CO}_{2}$ $(g)$ are -68 kcal/mole and-94 kcal/mole respectively. Then the $ΔH$ for the isomerisation reaction,
$C_{2} H_{5} OH (l) ⟶ {CH}_{3} {OCH}_{3} (g)$ and $ΔE$ for the same are : (Take : $T_{surr} = 298 K$ )

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$ΔH = 22 kcal / mole, ΔE = 21 .404 kcal / mole$

$ΔH = 18 kcal / mole, ΔE = 17 .301 kcal / mole$

$ΔH = 26 kcal / mole, ΔE = 25 .709 kcal / mole$

$ΔH = 30 kcal / mole, ΔE = 28 .522 kcal / mole$

answer is B.

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Detailed Solution

$\begin{array}{l} {CH}_{3} {OCH}_{3} (g) + 3 O_{2} (g) ⟶ 2 {CO}_{2} (g) + 3 H_{2} O (l) \\ - 348 = - 68 \times 3 - 94 \times 2 - {ΔH}_{f} \\ \Rightarrow {ΔH}_{f} = - 44 \end{array}$

$\begin{array}{l} C_{2} H_{5} OH (l) ⟶ {CH}_{3} {OCH}_{3} (g) \\ {ΔH}_{{Rx}^{n}} = - 44 + 66 = + 22 kcal / mole \\ ΔE = ΔH - {Δn}_{g} RT = 22 - \frac{1 \times 2 \times 298}{1000} \\ = 21.404 kcal / mol \end{array}$