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Q. The reaction of cyanamide, $NH _2$ $CN _{(s)}$ with oxygen was run in a bomb calorimeter and $\Delta U$ was found to be $742.24 \, kJ\, mol ^{-1}$.The magnitude of $\Delta H _{298}$ for the reaction $NH _2 CN _{( s )}+\frac{3}{2} O _2 g \rightarrow N _2( g )+ O _2( g )+ H _2 O _{(1)}$ is $- X \, kJ$. Value of $X$ is: (Rounded off to the nearest integer) [Assume ideal gases and $R =8.314 \, J \, mol ^{-1}\, K ^{-1}$ ]

NTA AbhyasNTA Abhyas 2022

Solution:

$NH _{2} CN ( s )+\frac{3}{2} O _{2}( g ) \longrightarrow N _{2}( g )+ CO _{2}( g )+ H _{2} O (\ell)$
$\Delta n _{ g }=(1+1)-\frac{3}{2}=\frac{1}{2}$
$\Delta H =\Delta U +\Delta n _{ g } \quad RT$
$=-742.24+\frac{1}{2}\times \frac{8 . 314 \times 298}{1000}$
$=-742.24+1.24$
$=-741kJ/mol$
$X=741$