# CfE: $\Delta H_{mix}$ vs. $\Delta H_{sol}$

### $\Delta H_{mix}$ vs. $\Delta H_{sol}$

Sometimes the tabulated values of property changes upon mixing and reported in terms of a change per unit mass/mole solvent rather than per solution.

##### Definition:

The $\Delta H_{sol}$ or "delta H of solution" is measured as the enthalpy change when 1 mol of solute is mixed with a specified amount of solvent (rather than solution).

This definition leads to a simple relationship between $\Delta H_{mix}$ and $\Delta H_{sol}$. That is:

$\Delta H_{sol} = \frac{\Delta H_{mix}}{x_{solute}}$

or:

$\Delta H_{mix} = x_{solute}\Delta H_{sol}$

where $x_{solute}$ is the mole fraction of the solute (dissolved or minor component).

##### Outcome:

Calculate the enthalpy of solution from the enthalpy of mixing and vice versa.

##### Note:

Typically, one can find tabulated values of $\Delta H_{mix}$ and $\Delta V_{mix}$, but not other properties. This is due to the fact that often the $\Delta S_{mix}$ is assumed to be given by the ideal gas result. That is $\Delta S_{mix} = -\sum_i R n_i \ln (y_i)$. By combining the tabulated values with this result for $\Delta S_{mix}$, one can calculate most other mixing values.

##### Note:

This expression for $\Delta S_{mix}$ will be true for "regular" solutions. We will discuss deviations from this behavior in the next section.