Step-by-step explanation:
X = liquid
K = 3.97 °C-kg-mol
T f = -0.10 °C
T f' = -1.80 °C
m = 750. g
m (KBr) = ?
The freezing point depression equation is:
ΔT f = K·m·i
where ΔT f is the freezing point depression, K is the freezing point depression constant, m is the molality of the solution, and i is the van't Hoff factor.
Since we are given the mass of liquid X (750 g), we can calculate the molality of the solution:
m = 750/M (X)
where M (X) is the molar mass of X. We are not given this value, so we must assume it to be 100 g/mol.
m = 750/100 = 7.50 mol/kg
We can now use the freezing point depression equation to calculate the mass of KBr:
ΔTf = K·m·i
-1.8 = 3.97·7.50·i
i = -1.8/29.78 = 0.060
The van't Hoff factor for KBr is 2, so the mass of KBr is:
m (KBr) = i/2 = 0.060/2 = 0.030 kg = 30.0 g (to 3 sig. figs.)