As discussed previously, mixtures do not simply exhibit the weighted average properties of their component parts. We have spent the last several sets of notes showing exactly how to calculate the contribution of each of the components to the mixture. That is, we have recognized that:

$V \ne \sum n_i v_i$

Instead:

$V = \sum n_i \bar V_i$

so that, in general:

$v_i \ne \bar V_i$

Besides the methods previously discussed, a typical way to
experimentally handle this fact is to define *property changes
of mixing*, such as the $\Delta V_{mix}, as:$

$\Delta V_{mix} = V - \sum n_i v_i$

That is, $\Delta V_{mix}$ specifically accounts for the difference between the naive assumption (that mixtures yield the weighted average) and reality. Another way to write this is

$\Delta V_{mix} = \sum n_i (\bar V_i - v_i)$

or graphically, the $\Delta V_{mix}$ (or $\Delta v_{mix}$ if we speak in terms of intensive rather than extensive volume):

The value of $\Delta V_{mix}$ (or $\Delta v_{mix}$) goes to zero at the two endpoints (pure component solutions), and varies in magnitude as concentration varies.

When $\Delta V_{mix}$ is measured experimentally, it is typically tabulated for the mixture in question, so that it may be used to determine the total solution property by rearranging its definition:

$V = \sum n_i v_i + \Delta V_{mix}$

One should note that the property changes are measured *per
unit mass/mole or* **mixture/solution**. Also, a
particularly useful property change that one can find tabulated is
$\Delta H_{mix}$.

Explain the origin of enthalpy, entropy, and volume changes due to mixing.