The freezing point of ethanol is -114.6 deg Celsius and its Kf value is 2.00degC/m. What is the freezing point for a solution prepared by dissolving 50.0g of glycerin in 200g ethanol?

I thought it may have been using the formula deltaT=Kf*m, but I'm not sure.

You have it right.

dT = 2.00*m

You need m. That is
m = mols/kg solvent and you can get mols by mol = grams/molar mass

After you have dT then subtract from normal freezing point to obtain new freezing point.

You are correct in thinking about using the formula ΔT = Kf * m. This formula is known as the Freezing Point Depression equation and is commonly used to calculate the change in freezing point of a solvent when a non-volatile solute is added.

In this case, the solvent is ethanol, and the solute is glycerin. To solve this problem, follow these steps:

1. Calculate the molality of the glycerin solution. Molality (m) is defined as the number of moles of solute (glycerin) per kilogram of solvent (ethanol).

First, convert the mass of glycerin (50.0g) to moles. To do this, divide the mass by the molar mass of glycerin, which is 92.09 g/mol:

Moles of glycerin = 50.0g / 92.09 g/mol = 0.5433 mol

Next, calculate the mass of ethanol in kilograms. Since the mass is given in grams (200g), divide that by 1000 to convert to kilograms:

Mass of ethanol = 200g / 1000 = 0.2 kg

Now, divide the moles of glycerin by the mass of ethanol in kilograms to calculate molality:

Molality (m) = 0.5433 mol / 0.2 kg = 2.7165 mol/kg

2. Use the freezing point depression equation to calculate the change in freezing point. ΔT represents the change in temperature, Kf is the freezing point depression constant (which is given as 2.00 degC/m), and m is the molality of the solution:

ΔT = Kf * m

Plug in the values:

ΔT = 2.00 degC/m * 2.7165 mol/kg

ΔT = 5.433 degC

3. Finally, subtract the change in freezing point (ΔT) from the freezing point of the pure solvent (ethanol's freezing point of -114.6 degC) to find the freezing point of the solution:

Freezing point of solution = -114.6 degC - 5.433 degC

Freezing point of solution = -120.033 degC

Therefore, the freezing point of the solution prepared by dissolving 50.0g of glycerin in 200g of ethanol is approximately -120.033 degrees Celsius.