Question

One gm sample of $N{H}_{4}N{O}_3\left(s\right)$ is decomposed in a bomb calorimeter (constant volume). The temperature of the calorimeter system falls by $6K$. If the heat capacity of system is $1.25kJ/K$, what is the molar enthalpy of decomposition of $N{H}_{4}N{O}_3\left(s\right)$ at $300K$?$[R=8.3J{K}^{-1}mo{l}^{-1}]$

Answer 1

Mass $=1$ gm

Change in temperature $\Delta T=6^{o}C$

Specific heat $=1.25kJ/K$

Heat change $q=c\times \Delta T=1.25\times 6=7.5kJ$

$\because$ the reaction is exothermic, $\Delta H=-7.5$ kJ

Molar mass of $N{H}_{4}N{O}_3=(2\times 14.0)+(4\times 1)+(3\times 16)$

$=80.0=80g$ (where M & N$=14.0,H=1$ & $O=16$)

$\therefore 1$g corresponds to $\frac{1}{80}=0.0125$ mol

Molar heat of decomposition:- $\Delta H=\frac{-7.5}{0.0125}kJ/mol=600kJ/mol$.