# How do you do freezing point depression problems?

Feb 4, 2017

#### Explanation:

Given an amount of a solute and a volume of solvent, calculate the molar concentration of the solute and multiply it by the molar freezing point depression constant of the particular solvent to find the freezing point depression. Subtract that from the normal freezing point to find the new freezing point.

Given a freezing point depression and a solvent, you can calculate the molarity of the solute. Given a mass in addition to that, you can calculate the molecular weight of the solvent.

REMEMBER that the Boiling Point elevation and Freezing Point depression constants are DIFFERENT from each other, and that they are a function of the SOLVENT, not the solute!

For an example calculation, go here: http://www.chem.purdue.edu/gchelp/solutions/freeze.html

Feb 4, 2017

Depends on the problem, but as a general idea, some form of this equation will be used:

$\Delta {T}_{\text{trs" = T_"trs" - T_"trs"^"*" = pmiK_"trs}} m$
(${T}_{\text{trs"^"*}}$ is the pure phase transition point of the solvent)

As defined, you could either have a negative sign for freezing or positive sign for boiling.

That aside, you may be asked to solve for any of the following:

• $m$, the molality, which is $\text{mols solute"/"kg solvent}$.
• ${T}_{\text{trs}}$, the new phase transition point for the SOLVENT in the solution in $\text{^@ "C}$ for a ${K}_{\text{trs}}$ in units of $\text{^@ "C/m}$.
• $\Delta {T}_{\text{trs}}$, the change in phase transition point, which is always negative for freezing point depression and positive for boiling point elevation.

It's technically possible to ask to solve for ${K}_{f}$ or $i$, but I haven't seen that asked. ${K}_{f} = {1.86}^{\circ} \text{C/m}$ for water, so yeah, why would you solve for that?

Usually, you are given ${K}_{f}$, implicitly asked to estimate or are given $i$ for electrolytes (or assume $i = 1$ for nonelectrolytes), and given enough information to determine $m$.

Some example generic problems:

What is the change in freezing point for a solution of 50% $\text{w/w}$ ethanol in water? Assume $i \approx 1$.

What is the freezing point for a solution of glucose in water if $\text{____}$ $\text{g}$ of glucose (${\text{C"_6"H"_(12)"O}}_{6}$) is dissolved in $\text{____}$ $\text{mL}$ of water? Assume water has a density of $\text{1 g/mL}$ at the temperature of the solution.

Using a van't Hoff factor of $1.9$ for $\text{NaCl}$, determine the molality of an aqueous solution whose freezing point has dropped by $\text{____"^@ "C}$.

It is worth noting that if you know how to do freezing point depression problems, boiling point elevation problems are analogous and are quite similar. The only difference is that ${T}_{b}^{\text{*}}$ for water is not ${0}^{\circ} \text{C}$ and ${K}_{b} = \text{0.512"^@ "C/m} \ne {K}_{f}$.

(The equations are practically identical in form.)