Final answer:
To calculate the van't Hoff factor for ammonium chloride in a mystery solvent, the freezing point depression data from a known non-electrolyte like urea is used to find the solvent's cryoscopic constant, which is then applied to the data for ammonium chloride. The resulting van't Hoff factor reveals the degree of ammonium chloride's dissociation in the solvent.
Step-by-step explanation:
To calculate the van't Hoff factor for ammonium chloride in the mystery solvent X, we can use the information given for urea and ammonium chloride's effect on the freezing point of X. We start by assuming that the depression in freezing point (ΔTf) is directly proportional to the molality (m) of the solution, which is given by the formula ΔTf = Kf x i x m, where Kf is the cryoscopic constant (or molal freezing-point depression constant) of the mystery solvent, i is the van't Hoff factor (which represents the degree of dissociation or ionization of the solute in the solvent), and m is the molality of the solution.
To find the Kf for the mystery solvent X using urea, which is a non-electrolyte and thus has a van't Hoff factor of 1, we can set up the equation with the given values: ΔTf = Kf x 1 x m. Plugging in the given values, we get 7.6°C = Kf x (0.118 kg / 1.500 kg). Solving for Kf gives us the value needed to proceed with ammonium chloride.
Next, we use the ammonium chloride data with the calculated Kf to find its van't Hoff factor. The new equation using ammonium chloride's ΔTf (15.3°C) is 15.3°C = Kf x i x (0.118 kg / 1.500 kg). With Kf known from the urea calculation, we can solve for i, which is the van't Hoff factor for ammonium chloride in X. This would allow us to assess the degree of ammonium chloride's dissociation in the mystery solvent.
To understand why the van't Hoff factor obtained may differ from the theoretical or ideal one, we can look at factors such as ion pairing, intermolecular forces, or the nature of the solvent that may affect the actual dissociation of the ionic compound in solution.