#### Partial Molar Quantities: Screencast

Presents the definition of partial molar quantities and describes how they could be measured.

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Uses molar quantity of solution and the Gibbs-Duhem equation to derive an equation for partial molar quantities in terms of a total derivative. Shows how to determine partial molar quantities from graph of molar quantity of mixture versus mole fraction of mixture.

We suggest you list the important points in this screencast as a way to increase retention.

##### Important Equations:

Partial Molar Quantity:

$\overline{M_i} \equiv \left( \frac{\partial M^{total}}{\partial n_i} \right) _{T,P,n_{j \neq i}}$

$M = \sum_i {x_i\overline{M_i}}$

where $$M$$ represents a state variable per mole for a mixture
$$M^{total}$$ represents a total value of a state variable (not per mole)
$$\overline{M}$$ is a partial molar quantity
$$x_i$$ is the mole fraction of component $$i$$

For a binary mixture, enthalpy per mole of mixture is:

$H = x_1\overline{H}_1 + x_2\overline{H}_2$

The partial derivative for a binary mixture:

$\overline{G}_i \equiv \left( \frac{\partial \underline{G}}{\partial n_i} \right) _{T,P,n_{j \neq i}} = \mu _i \hspace{1mm}(chemical \hspace{1mm} potential)$

Also for a binary mixture:

$\overline{M_1} = M +x_2\frac{dM}{dx_1} \hspace{8mm} \overline{M_2} = M – x_1\frac{dM}{dx_1}$