A solution is prepared with an unknown compound with an empirical formula of C3H7NO.

The solution is made by dissolving 30.0 mg of compound in 1.200 g of the organic solvent biphenyl. The freezing point was depressed by 1.37C. What are the molar mass and molecular formula of the compound?

delta T = Kf*molality

Solve for molality.

molality = moles/kg solvent
Solve for moles

moles = grams/molar mass
Solve for molar mass.

molar mass/empirical mass and round to the nearest whole number = n
molecular formula is (empirical formula)n

To determine the molar mass and molecular formula of the compound, you can use colligative properties, specifically freezing point depression.

First, let's calculate the freezing point depression using the formula:

ΔT = Kf * m

Where:
- ΔT is the freezing point depression
- Kf is the cryoscopic constant of the solvent (biphenyl)
- m is the molality of the compound in the solution

In this case, you're given that the freezing point depression (ΔT) is 1.37°C and the mass of the solvent biphenyl is 1.200 g. To calculate the molality (m), you need to determine the number of moles of the unknown compound dissolved in the biphenyl solvent.

1. Convert the mass of the compound from milligrams to grams:
Mass of the compound = 30.0 mg = 0.030 g

2. Calculate the number of moles of the compound using its empirical formula:
Number of moles of compound = Mass of compound / Molar mass of compound
Number of moles of compound = 0.030 g / Empirical molar mass (C3H7NO)

Now, to determine the molar mass and molecular formula, you need to compare the freezing point depression with the expected freezing point depression based on the number of moles of solute in the solution.

The expected freezing point depression can be calculated using the formula:

ΔT = Kf * (molality of solute)

Since you have the ΔT and Kf values, you can rearrange the equation to solve for the molality of solute:

molality of solute = ΔT / Kf

Now, substitute the given values (ΔT and Kf) into the equation to calculate the molality of solute.

Finally, compare the number of moles of the compound (from step 2) with the molality of solute. If they are the same, the empirical formula represents the molecular formula. Otherwise, you will need to determine the molecular formula based on the ratio of the empirical formula to the molecular formula.

Using this procedure, you should be able to determine the molar mass and molecular formula of the compound.