The molar heat of formation of NH_4NO_ 3(s) is -367.54 ,kJ and th…

MCQ

The molar heat of formation of $NH_4NO_{3(s)}$ is $-367.54\,kJ$ and those of $N_2O_{(g)}$ and $H_2O_{(l)}$ are $+ 81.46\,kJ$ and $-285.78\,kJ$ respectively at $25\,^oC$ and $1.0$ atmospheric pressure. Calculate $\Delta U$ at $25\,^oC$ for the reaction

$NH_4NO_{3(s)} \to N_2O_{(g)} + 2H_2O_{(l)}$ .....$kJ$

A
$-122.56$
✓
$-125.04$
C
$-140.34$
D
$-112.04$

✓

Answer

Correct option: B.

$-125.04$

b
${\text{N}}{{\text{H}}_4}{\text{N}}{{\text{O}}_{3(s)}} \to {{\text{N}}_2}{{\text{O}}_{({\text{g}})}} + 2{{\text{H}}_2}{\text{O}}$

$\Delta {\text{H}} = {\left( {\Delta {{\text{H}}_{\text{f}}}} \right)_{{{\text{N}}_2}{{\text{O}}_{({\text{g}})}}}} + 2 \times {\left( {\Delta {{\text{H}}_{\text{f}}}} \right)_{{H_2}{O_{(l)}}}} - {\left( {\Delta {{\text{H}}_{\text{f}}}} \right)_{{\text{N}}{{\text{H}}_4}{\text{N}}{{\text{O}}_{3(s)}}}}$

$ = - 122.56\,{\text{kJ}}$

$\Delta {\text{H}} = \Delta {\text{U}} + \Delta {{\text{n}}_{\text{g}}}{\text{RT}}$

$\Delta {\text{U}} = \Delta {\text{H}} - \Delta {{\text{n}}_{\text{g}}}{\text{RT}}$

$ = - 125.04\,{\text{kJ}}$

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