Question 8.6.1: Calculations of Partial Molar Enthalpies from Experimental D...

First we must obtain values of enthalpy versus concentration at 65.6°C. The values read from this figure and converted to a molar basis are given below.

These data are fit reasonably well with the simple expression

and

Therefore,

and

Also,

and

Finally, from Eq. 8.6-9b, we have

\begin{aligned}\Delta_{\text {mix }} \underline{H}-\left.x_{2} \frac{\partial\left(\Delta_{\text {mix }} \underline{H}\right)}{\partial x_{2}}\right|_{T, P} &=\Delta_{\text {mix }} \underline{H}+\left.x_{2} \frac{\partial\left(\Delta_{\text {mix }} \underline{H}\right)}{\partial x_{1}}\right|_{T, P} \\&=\left(\bar{H}_{1}-\underline{H}_{1}\right)\end{aligned} (8.6-9b)

and

Note that in this case the pure component and partial molar enthalpies differ considerably. Consequently, we say that this solution is quite nonideal, where, as we shall see in Chapter 9, an ideal solution is one in which some partial molar properties (in particular the enthalpy, internal energy, and volume) are equal to the pure component values. Further, here the solution is so nonideal that at the temperature chosen the pure component and partial molar enthalpies are even of different signs for both water and sulfuric acid. For later reference we note that, at x_{ H _{2} SO _{4}}=0.5, we have