Determination of Relative Apparent Molar Enthalpies

The relative apparent molar enthalpy, 4 L, is usually obtained from enthalpy of dilution measurements in which the moles of solute are held constant and additional solvent is added to dilute the starting solution. The process can be represented as 

The enthalpy change for this process is an integral enthalpy of dilution for which we saw earlier that 

To show how we can calculate relative apparent molar enthalpies from enthalpies of dilution, consider as an example, a process in which we start with a HC1 solution of molality m = 18.50 mol-kg-1 and dilute it to a concentration of m = 11.10 mol-kg-1. The initial solution contains 3 moles of H20 per mole of HC1 (A = 3) while the final solution has A = 5. The enthalpy change for that process is measured. Then the m = 11.10 mol-kg-1 solution is diluted to one with m = 4.63 mol-kg-1 and its enthalpy of dilution measured. The series continues as illustrated below, 

As indicated by the final equation, the dilution steps are continued until the infinitely dilute solution is approached. The sum of all of the steps represents the change to infinite dilution from the given starting solution. Thus, the sum of all 

Note that from this extrapolation, one can also obtain qL for all of the subsequent solutions, since 

---