# How do freezing point, boiling point, and vapor pressure for the solvent change upon addition of a solute?

May 2, 2017

Freezing point decreases, boiling point increases, and vapor pressure decreases.

Whenever ANYTHING at all is added to a solvent, it blocks some solvent particles at the surface of the solution, or attracts solvent particles towards it.

Thus, the higher the concentration of ANYTHING added, the harder it is for solvent particles to:

• Leave the surface of the solution (i.e. boil). The solute particles block the solvent particles from leaving the solution, thereby making it more difficult to boil.

$\Delta {T}_{b} = i {K}_{b} m$

$\implies$ as $m \uparrow$, $\Delta {T}_{b} \uparrow$

($i , {K}_{b} , m > 0$).

• Congregate into a proper network solid (i.e. freeze). The solute particles attract the solvent particles around them, and make it more difficult for the solvent to freeze.

$\Delta {T}_{f} = - i {K}_{f} m$

$\implies$ as $m \uparrow$, $\Delta {T}_{f} \uparrow$

($i , {K}_{f} , m > 0$).

As a result, we also have that vapor pressure decreases; evidently, if it is more difficult to boil, it must be that the vapor pressure is lower (less gases formed... therefore lower pressure of the gas, i.e. vapor pressure).

The change in vapor pressure can be determined as follows ($\text{*}$ indicates pure solvent):

$\textcolor{b l u e}{\Delta {P}_{v a p}} = {P}_{v a p} - {P}_{v a p}^{\text{*}}$

$= {\chi}_{\text{solvent"P_(vap)^"*" - P_(vap)^"*}}$ (Raoult's Law)

= (1-chi_("solute"))P_(vap)^"*" - P_(vap)^"*"

= color(blue)(-chi_("solute")P_(vap)^"*")

Since $\chi$, the mol fraction, is ALWAYS positive, it follows that the change in vapor pressure is ALWAYS negative.