Vapour Pressure lowering of a solution
The commonality in these properties is that the effects are entropy effects. Take, for example, the vapor pressure of a pure liquid versus one in which a solute has been dissolved. In the former case, the difference in entropy for the phase-change reaction is greater than that for the latter since the process of dissolving the solute into the liquid has slightly increased the entropy of the liquid (more random since the solute is spacing out the solvent molecules a bit). Hence, the vapor pressure of the pure liquid is higher than that of the solution.
Psolvent = csolvent P°solvent
where Psolvent = vapour pressure of the solvent in solution,
csolvent = mole fraction of the solvent
= # moles of solvent molecules
Total number of moles
and P°solvent = vapor pressure of the pure solvent.
Recall that the total pressure of a solution is the sum of the partial pressures of the solvent and solute
psolution = psolvent + psolute = csolvent P°solvent + csolute P°solute
If the solute is non-volatile (no vapor pressure: P°solute = 0) then the total vapor pressure of solution is
psolution = psolvent = csolvent P°solvent
To see this in graphical form, see the phase diagram for pure water, below. Three lines are present indicating the phase transition (read equilibrium) between solid, liquid and gas. Where all three lines meet is the triple point where all three phases are in equilibrium. We see that at an external pressure of 1 atm. The normal melting point and normal boiling point are indicated. If the pressure is lowered, we note that the boiling point will be lowered and the melting point raised (very slightly; it’s exaggerated here).
Now, look at the following diagram indicating the phase transitions for pure water and for water with some solute dissolved in it (not to scale).
Here we see that the curves for equilibrium between the liquid and the other phases are lowered. Look, for example at the vertical line indicating the normal boiling point of water crosses the solution’s lower pressure, i.e., the vapor pressure at that (and any other) temperature is lower for the solution. One could, in principle, calculate the concentration of solute which would be required to create a given VP lowering.