In this experiment, you will determine the standard enthalpy changes for a series of reactions of the following type: \[\ce{MX_{(s)} --> M_{(aq)}^+ + X_{(aq)}^-}\] where \(\ce{M_{(aq)}^+}\) is one mole of a cation, \(\ce{M^+}\), in an infinitely dilute aqueous solution and \(\ce{MX_{(s)}}\) is one mole of the solid. The energy released when an ionic solid dissolves in solution is normally described as heat of solution . When a solute is dissolved in a solvent, heat may be absorbed or evolved. The integral heat of solution is the enthalpy change for the solution of 1 mole of solute in \(n\) moles of solvent. When reporting heats of solution, the concentration of the final solution must also be stated. The integral heats of solution for \(\ce{H2SO4}\), \(\ce{NaOH}\), and \(\ce{NH4NO3}\) are plotted versus the amount of water per mole of solute in Figure \(\PageIndex{1}\). As the amount of water is increased, the integral heats of solution reach limiting values and no further heat change occurs on addition of more water. Experimentally, the integral heat of solution at infinite dilution is found by measuring the integral heats of solution at progressively higher dilutions until the enthalpy change per mole of solute no longer changes. The integral heat of dilution is the heat liberated or absorbed when a solution of known concentration is mixed with a sufficient amount of solvent to produce a more dilute solution of new and known concentration. Heat capacities relate the differential transfer of heat in a system to its differential temperature change, \( {dq}= {CdT}\), and are usually expressed on a molar basis. If a process is carried out at constant pressure, the heat capacity is designated as \( {C}_{ {p}}\), and, since the heat capacity itself may be a function of temperature, the heat involved would be given by: \[ {q}_{ {p}}=\int_{ {T}_1}^{ {T}_2} {C}_{ {p}} {dT}\] The reaction in this experiment is performed under constant (atmospheric) pressure in a thermally insulated calorimeter. Thus, the reaction conditions are adiabatic (q_p = 0) and not isothermal (constant temperature). The relationship between isothermal and adiabatic conditions is shown in Figure \(\PageIndex{1}\). Enthalpy is a state function and therefore \(\Delta {H}\) is independent of the path taken (in general \(q\) is not). Therefore \[\Delta {H}=\Delta {H}\left( {T}_1\right)+\int_{ {T}_1}^{ {T}_2} {C}_{ {p}} {dT} \label{eq7}\] where \(\Delta {H}\left( {T}_1\right)\) is the enthalpy change for the isothermal part of the path shown in Figure \(\PageIndex{2}\). The temperature change for the reaction is generally small enough for \( {C}_{ {p}}\) to be considered constant and therefore Equation \ref{eq7} becomes \ref{eq8}: \[\Delta {H}=\Delta {H}\left(\Delta {H}\right)+ {C}_{ {p}}\left( {T}_2- {T}_1\right) \label{eq8}\] Under adiabatic conditions, \(\Delta {H}= {qp}=0\) and thus Equation \ref{eq8} simplifies to \ref{eq9}: \[\Delta {H}_{ {T}_1}=- {C}_{ {p}}\left( {T}_2- {T}_1\right) \label{eq9}\] and finally \[\Delta {H}\left( {T}_1\right)=-\left[ {C}_{ {p}, {cal}}+ {C}_{ {p}, \text { products }}\right]\left( {T}_2- {T}_1\right)\] The enthalpy change, which occurs upon dissolution of TRIS (tris(hydroxymethyl)amino-methane hydrochloride) in aqueous hydrochloric acid, or of KCl dissolved in deionized water, is known with precision. The heat capacity of the products is given by the product mass multiplied by its specific heat capacity, which for aqueous solutions is assumed to be \(4.18 {~J} {~K}^{-1} {~g}^{-1}\). Therefore, if one measures the temperature change (\( {T}_2\) - \( {T}_1\)) that occurs during either of these reactions, the heat capacity of the calorimeter at constant pressure (\( {C}_{ {p}, {cal}}\)) may be determined. Knowing (\( {C}_{ {p}, {cal}}\)), we can measure the heat of solution (enthalpy change \(\Delta {H}_{ {T}_1}\)) of other salts by measurement of the temperature change during the reaction.