If the initial state of the component is a pure liquid (presuming the solution is liquid), the dilution process is equal to its dissolution process and the heat of dilution is the same as the heat of solution.
The differential heat of dilution is viewed on a micro scale, which is associated with the process in which a small amount of solvent is added to a large quantity of solution.
The molar differential heat of dilution is thus defined as the enthalpy change caused by adding a mole of solvent at a constant temperature and pressure to a very large amount of solution.
Because of the small amount of addition, the concentration of dilute solution remains practically unchanged.
Mathematically, the molar differential heat of dilution is denoted as:[1]
where ∂∆ni is the infinitesimal change or differential of mole number of the dilution.
The integral heat of dilution, however, is viewed on a macro scale.
The enthalpy change in this process, normalized by the mole number of solute, is evaluated as the molar integral heat of dilution.
Mathematically, the molar integral heat of dilution is denoted as:
If the infinite amount of solvent is added to a solution with a known concentration of solute, the corresponding change of enthalpy is called as integral heat of dilution to infinite dilution.
In both processes, similar final statuses of solutions are reached.
In a dilution process, on the other hand, the solution is changed from one concentration to another, illustrated as:
Consider an extreme condition for the dilution process.
It is worth noting that this expression is just the second stage of the dissolution process.
Viewed from a microscopic perspective, the dissolution and dilution processes involve three steps of molecular interaction: the breaking of attraction between solute molecules (lattice energy), the breaking of attraction between solvent molecules, and the forming of attraction between a solute and a solvent molecule.
As a result, the enthalpy change caused by breaking and forming attraction is canceled, and the dilution of an ideal solution causes no enthalpy change.
[3] However, if the solute and solvent cannot be treated identically when considered in terms of molecular attraction, which makes the solution non-ideal, the net change of enthalpy is nonzero.
In other words, the heat of dilution results from the non-ideality of the solution.