What would be the heat released when an aqueous solution containing...

0.5 mole of $\mathrm{HNO}_3$ equivalents to 0.5 mole of $\mathrm{H}^{+}$. But only 0.3 mole of $\mathrm{OH}^{-}$ions are available. Thus, 0.3 mole of $\mathrm{H}^{+}$ions will combine with 0.3 mole of $\mathrm{OH}^{-}$ions to form 0.3 mole of $\mathrm{H}_2 \mathrm{O}$ and 0.2 mole of $\mathrm{H}^{+}$ions will remain unreacted. Heat evolved when 1 mole of $\mathrm{H}^{+}$ions combine with 1 mole of $\mathrm{OH}^{-}$ions $=57.1 \mathrm{~kJ}$. Therefore, heat evolved wher 0.3 mole of $\mathrm{H}^{+}$ions combine with 0.3 mole of $\mathrm{OH}^{-}$ions $=0.3 \times 57.1=17.13 \mathrm{~kJ}$.