if the freezing point of the solution had been incorrectly determined to be lower than the true freezing point, how would that affect the calculated molar mass? Explain.

The molecular weight would be higher if the true freezing point is bigger than the determined freezing point. It’s higher because ....

delta T = Kf*m

m = mols/kg solvent
mols = g/molar mass.

If delta T is too large, molality will be to large.
If molality is too large, mols will be too large.
If mols is too large, then molar mass will be too small.(from molar mass = g/mols).

yes

To understand how an incorrectly determined freezing point affects the calculated molar mass, we need to first understand the concept of freezing point depression and its relationship to molar mass.

Freezing point depression is a colligative property, meaning it depends solely on the number of solute particles present in a solution and not on the nature of the solute. According to Raoult’s law, the freezing point of a solution is lower than that of the pure solvent, and the extent to which it is lowered is directly proportional to the concentration of solute particles.

The mathematical relationship between freezing point depression and molar mass can be expressed by the equation ΔT = Kf * m, where ΔT is the freezing point depression, Kf is the cryoscopic constant, and m is the molality of the solute.

Now, if the freezing point of the solution has been incorrectly determined to be lower than the true freezing point, it implies that the calculated freezing point depression (ΔT) would also be incorrect. This incorrect value of ΔT would lead to an incorrect value of m, which is the molality of the solute.

Since the molar mass is directly proportional to the molality of the solute, an incorrect value of m will result in an incorrect calculation of the molar mass. Specifically, the calculated molar mass would be higher than the actual value if the true freezing point is larger than the determined freezing point.

In summary, an incorrectly determined freezing point lower than the true freezing point would result in an overestimation of the molality of the solute, leading to an overestimation of the molar mass of the solute.