To solve freezing point depression problems, you need to know the following things:
-- the identity of the solute (the thing you are adding to the liquid)
-- the identity of the solvent (the liquid)
-- whether the solute is molecular or ionic, and if ionic, how many ions it forms
-- the amount of solute (in grams or moles)
-- the amount of solvent (in kilograms)
-- the value of Kf of the solvent (for water, it is -1.858 K·kg/mol (or -1.858 °C molal-1)
Then you use the following equation:
∆T = i * Kf * m
where ∆T is the change in the freezing point, "i" is the number of molecules or ions formed upon addition to the solvent, Kf
is the freezing point depression constant, and "m" is the molality of
the solution.
The Kf of water for a freezing point depression is known and is equal to -1.858 °C·kg/mol (or -1.858 °C molal-1)
The value of "i" has to do with what you add to the water. If
you added sugar, a molecular compound the value of "i" is 1.0. If you
add a ionic compound like NaCl, the value of "i" is 2.0 because for
every 1 molecule of NaCl, you make 2 ions: one Na+ and one Cl- in water. For MgCl2, the value of "i" is thus 3.0 (for each MgCl2 you get one Mg2+ and two Cl- ions, so a total of 3 ions).
To find "m," the molality of a solution you need to know the number of
moles of solute and the number of kilograms of solvent (m = moles/kg).
If you are given the number of grams of solute, the number of moles is found from the mass and the molar mass of the solute.
grams of solute ÷ molar mass of solute = moles of solute
To find the molality, just divide the moles of solute by the kilograms of solvent
moles of solute ÷ kilograms solvent = molality
Note: If you are given the volume of the solvent instead of the mass, use the density of the solvent to convert -- the density of water is 1 kilogram per liter)
Liters of solvent * density of solvent = kilograms of solvent
Now just plug all the numbers into the equation at the top of the answer!