Freezing-point depression can be used to determine the molecular mass of a compound. Suppose that 1.28 g of an unknown molecule were added to 19.9 g of water and the freezing point of the solution determined. If the new freezing point of water were found to be -1.50°C, what would you predict to be the molecular mass of the compound?

To determine the molecular mass of the compound using freezing-point depression, we need to use the formula:

ΔT = Kf * m * i

Where:
- ΔT is the change in freezing point of the solution (in Celsius),
- Kf is the cryoscopic constant (water's constant is 1.86 °C/m),
- m is the molality of the solution (moles of solute per kilogram of solvent),
- i is the van't Hoff factor (the number of particles the solute breaks into in solution).

First, let's calculate the molality of the solution:
Molality (m) = moles of solute / kg of solvent

Given that the mass of the unknown molecule is 1.28 g and the mass of water is 19.9 g, we need to convert the masses into moles:

Moles of solute = 1.28 g / molar mass of the compound
Moles of water = 19.9 g / molar mass of water

To find the molar mass of the compound, we need to rearrange the equation:

Molar mass of the compound = 1.28 g / moles of solute

Next, we need to determine the change in freezing point, ΔT:
ΔT = initial freezing point - new freezing point
= 0 °C - (-1.50 °C)
= 1.50 °C

Now, we know the value of Kf for water is 1.86 °C/m.

Let's assume that the van't Hoff factor (i) is equal to 1, which means the unknown compound does not dissociate or associate in water.

Finally, we can substitute all the values into the formula to find the molecular mass of the compound:
1.50 °C = 1.86 °C/m * molality * 1

Rearranging the equation:

molality = 1.50 °C / (1.86 °C/m)
molality = 0.8065 m

Now we can calculate the molar mass of the compound:
Molar mass of the compound = 1.28 g / molality

By substituting the calculated values into the equation, you can find the molecular mass of the compound.