Final answer:
To calculate the mass of NH₄Cl dissolved, the freezing point depression formula is used. After finding the change in freezing point, the molality is calculated, and then the moles of NH₄Cl are determined. Multiplying this by the molar mass of NH₄Cl yields the mass dissolved, approximately 11.121 g.
Step-by-step explanation:
The student has asked to calculate the mass of ammonium chloride (NH₄Cl) dissolved in a liquid with a given normal freezing point and a freezing point depression constant. To find this, we use the freezing point depression formula ΔTf = Kf x m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution.
First, we calculate the change in freezing point (ΔTf) of the solvent, which is the difference between the normal freezing point of liquid X and the observed freezing point:
ΔTf = 3.30 °C - 1.6 °C = 1.7 °C.
Next, we find the molality (m) of the solution:
m = ΔTf / Kf = 1.7 °C / (-3.27 °C kg mol⁻¹) = -0.51957 mol/kg.
Note that the negative sign in the freezing point depression constant and ΔTf cancel each other out, giving a positive molality. Since we have 400 g of liquid X, which is 0.4 kg, we can calculate the number of moles of NH₄Cl:
number of moles = molality x mass of solvent = 0.51957 mol/kg x 0.4 kg = 0.20783 mol.
Finally, to find the mass of NH₄Cl dissolved, we use the molar mass of NH₄Cl (53.49 g/mol):
mass of NH₄Cl = number of moles x molar mass = 0.20783 mol x 53.49 g/mol = 11.121 g.
Therefore, approximately 11.121 g of NH₄Cl was dissolved in the solvent.