A solution containing an unknown solute is prepared by dissolving 25 grams of the solute in 500 grams of a solvent. The freezing point depression of the solution is found to be 4.8°C. The freezing point depression constant for the solvent is 10.2 °C kg/mol. What is the molar mass of the solute?Select one:a.80.0 g/molb.100.0 g/molc.200.0 g/mold.160.0 g/mol

To find the molar mass of the solute, we can use the formula for freezing point depression:

ΔTf = Kf * m

where ΔTf is the freezing point depression, Kf is the freezing point depression constant, and m is the molality of the solution.

First, we need to find the molality of the solution. Molality is defined as the number of moles of solute per kilogram of solvent. We know the mass of the solute (25 grams) and the mass of the solvent (500 grams), but we need to convert the mass of the solvent to kilograms:

500 grams * (1 kg / 1000 grams) = 0.5 kg

Next, we can rearrange the formula for freezing point depression to solve for molality:

m = ΔTf / Kf = 4.8°C / 10.2 °C kg/mol = 0.4706 mol/kg

Now that we have the molality, we can find the number of moles of solute. We know that molality is the number of moles of solute per kilogram of solvent, so:

0.4706 mol/kg * 0.5 kg = 0.2353 mol

Finally, we can find the molar mass of the solute by dividing the mass of the solute by the number of moles:

25 grams / 0.2353 mol = 106.2 g/mol

So, the molar mass of the solute is closest to 100.0 g/mol (option b).