50.0 mL of 1.00 M hydrochloric acid is mixed with 50.0 mL of 1.00 M sodium hydroxide in a…

At constant pressure the heat taken in is $\Delta H$, and at constant volume it is $\Delta U$. For gases, $\Delta H = \Delta U + \Delta n_g R T$, where $\Delta n_g$ counts moles of gas only and $R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}$. Heat and temperature are linked by $q = C\Delta T = m c \Delta T$. A calorimeter takes up the heat the reaction gives out, so $\Delta H = -q$ per mole. For an ideal gas, $C_p - C_v = R$.