You use the formula for freezing point depression.
EXAMPLE
What is the freezing point depression caused by adding 31.65 g of sodium chloride to 220.0 g of water. ##K_”f”## for water is ##”1.86 °C·kg·mol”^”-1″##.
Solution
The formula for freezing point depression expression is
##color(blue)(|bar(ul(color(white)(a/a) ΔT_”f” = iK_”f”m color(white)(a/a)|)))” “##
where
##ΔT_”f”## is the freezing point depression,
##i## is the van’t Hoff factor,
##K_”f”## is the molal freezing point depression constant for the , and
##m## is the of the solution.
Step 1: Calculate the molality of the NaCl
##”moles of NaCl” = 31.65 color(red)(cancel(color(black)(“g NaCl”))) × (1″mol NaCl”)/(58.44 color(red)(cancel(color(black)(“g NaCl”)))) = “0.5416 mol NaCl”##
##”mass of water” = 220.0 color(red)(cancel(color(black)(“g H”_2″O”))) × (1″kg H”_2″O”)/(1000 color(red)(cancel(color(black)(“g H”_2″O”)))) = “0.220 kg H”_2″O”##
##m = “moles of NaCl”/”kilograms of water” = “0.5416 mol”/”0.220 kg” = “2.46 mol/kg”##
Step 2: Determine the van’t Hoff factor
The van’t Hoff factor, ##i##, is the number of moles of particles obtained when 1 mol of a dissolves.
Nonelectrolytes such as sugar do not dissociate in water. One mole of solid sugar gives one mole of dissolved sugar molecules.
For nonelectrolytes, ##i = 1##.
Electrolytes such as ##”NaCl”## completely dissociate into ions.
##”NaCl” → “Na”^+ + “Cl”^”-“##
One mole of solid ##”NaCl”## gives two moles of dissolved particles: 1 mol of ##”Na”^+## ions and 1 mol of ##”Cl”^”-“## ions. Thus, for ##”NaCl”, i = 2##.
Step 3: Calculate ##ΔT_”f”##
##ΔT_”f” = iK_”f”m = 2 × “1.86 °C·”color(red)(cancel(color(black)(“kg·mol”^”-1″))) × 2.46 color(red)(cancel(color(black)(“mol·kg”^”-1″))) = “9.16 °C”##
The freezing point depression is 9.16 °C.
Here’s a video on how to calculate freezing point depression.
