Solution:
Enthalpy change for a response (∆H) is given by the articulation,
![\[H\text{ }=\text{ }U\text{ }+\text{ }ngRT\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ac52f5668747eb15b53474cba2b55079_l3.png "Rendered by QuickLaTeX.com")
Where,
![\[\begin{array}{*{35}{l}} U\text{ }=\text{ }change\text{ }in\text{ }inside\text{ }energy \\ ~ \\ ng\text{ }=\text{ }change\text{ }in\text{ }number\text{ }of\text{ }moles\text{ }For\text{ }the\text{ }given\text{ }response, \\ ~ \\ ng\text{ }=\text{ }\sum ng\text{ }\left( items \right)\text{ }\text{ }\sum ng\text{ }\left( reactants \right)\text{ }=\text{ }\left( 2\text{ }\text{ }2.5 \right)\text{ }moles \\ ~ \\ ng\text{ }=\text{ }\text{ }0.5\text{ }moles\text{ }And,\text{ }U\text{ }=\text{ }\text{ }742.7\text{ }kJ\text{ }mol1 \\ ~ \\ T\text{ }=\text{ }298\text{ }K \\ ~ \\ R\text{ }=\text{ }8.314\text{ }\times \text{ }103\text{ }kJ\text{ }mol1\text{ }K\text{ }\text{ }1 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f7f1addc92bffa0d040e96cd00e2ef71_l3.png "Rendered by QuickLaTeX.com")
Subbing the qualities in the statement of ∆H:
![\[\begin{array}{*{35}{l}} H\text{ }=\text{ }\left( \text{ }742.7\text{ }kJ\text{ }mol1\text{ } \right)\text{ }+\text{ }\left( \text{ }0.5\text{ }mol \right)\text{ }\left( 298\text{ }K \right)\text{ }\left( 8.314\text{ }\times \text{ }103\text{ }kJ\text{ }mol1\text{ }K\text{ }\text{ }1\text{ } \right) \\ ~ \\ =\text{ }\text{ }742.7\text{ }\text{ }1.2 \\ ~ \\ H\text{ }=\text{ }\text{ }743.9\text{ }kJ\text{ }mol1 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-335f8c9c1163aeb0b8bb129169456bd1_l3.png "Rendered by QuickLaTeX.com")
The response of cyanamide, NH2CN(s), with dioxygen was done in a bomb calorimeter, and ∆U was observed to be – 742.7 kJ mol–1 at 298 K. Ascertain enthalpy change for the response at 298 K.
![\[NH2CN\left( g \right)\text{ }+\text{ }3/2\text{ }O2\left( g \right)\text{ }\to \text{ }N2\left( g \right)\text{ }+\text{ }CO2\left( g \right)\text{ }+\text{ }H2O\left( l \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6cb518a194b0305964737ad87e3d7289_l3.png "Rendered by QuickLaTeX.com")
