How do you calculate freezing point depression?

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    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 Ckgmol^-1##.
    Solution
    The formula for freezing point depression expression is
    ##color(blue)(|bar(ul(color(white)(a/a) T_f = iK_fm color(white)(a/a)|))) ##
    where
    ##T_f## is the freezing point depression
    ##i## is the vant 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))) (1mol 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_2O))) (1kg H_2O)/(1000 color(red)(cancel(color(black)(g H_2O)))) = 0.220 kg H_2O##
    ##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 ##T_f##
    ##T_f = iK_fm = 2 1.86 Ccolor(red)(cancel(color(black)(kgmol^-1))) 2.46 color(red)(cancel(color(black)(molkg^-1))) = 9.16 C##
    The freezing point depression is 9.16 C.
    Here’s a video on how to calculate freezing point depression.

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