Derive expression $\Delta H =\Delta U +\Delta n _{ g } R T$.
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Answer
For any gaseous reaction if at constant pressure and temperature volume of reactant is $V _{ A }$ and that of product is $U_B$ and $n_A$ and $n_B$ are moles of reactants and products respectively their according to ideal gas equation : $ \begin{array}{ll} & pV_{A}=n_{A} RT \\ \text { and } & pV V_{B}=n_{B} RT \\ \text { or } & pV V_{B}-pV_{A}=n_{B} RT-n_{A} RT=\left(n_{B}-n_{A}\right) RT \\ & p\left(V_{B}-V_{A}\right)=\left(n_{B}-n_{A}\right) RT \\ & p \Delta V=\Delta n_{g} RT \end{array} $ Here $\Delta_{ ng }=$ moles of product - moles of reactant On putting value of $p \Delta V$ in equation $ \begin{array}{c} \Delta H=\Delta V+p \Delta V \\ \Delta H=\Delta U+\Delta n_{g} RT \end{array} $
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