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The relation between $\Delta H$ and $\Delta U$ for a reaction involving gases is:
A$\Delta H = \Delta U \cdot \Delta n_g R T$
B$\Delta H = \Delta U - \Delta n_g R T$
C$\Delta H = \Delta U + \Delta n_g R T$
D$\Delta H = \Delta U / \Delta n_g$
Answer & Solution
Correct answer: C. $\Delta H = \Delta U + \Delta n_g R T$
From the definition $H = U + pV$ and the ideal-gas relation $pV = n_g R T$, $\Delta H = \Delta U + \Delta(pV) = \Delta U + \Delta n_g R T$ at constant $T$, where $\Delta n_g$ is (moles of gaseous products) $-$ (moles of gaseous reactants). For reactions with $\Delta n_g = 0$, $\Delta H = \Delta U$.
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