12.50g of an unknown compound (i=2) are dissolved in 50.00g of water and this solution freezes at –7.5 degrees C. What is the molar mass of this compound?

To find the molar mass of the compound, we need to use the concept of freezing point depression.

Freezing point depression is a colligative property that depends on the number of solute particles (in this case, the unknown compound) dissolved in a solvent (water). The equation for freezing point depression is:

ΔTf = Kf * i * m

Where:
ΔTf is the change in freezing point temperature,
Kf is the freezing point depression constant for the solvent,
i is the van't Hoff factor (the number of particles the compound dissociates into when dissolved),
m is the molality of the solution (moles of solute per kilogram of solvent).

In this case, we are given:
ΔTf = -7.5°C (the negative sign indicates a decrease in temperature),
Kf for water = 1.86°C/molal, and
i = 2 (as stated in the question).

First, we need to calculate the molality of the solution, which is given by the formula:

m = moles of solute / mass of solvent (in kg)

Mass of solvent = 50.00g = 0.05000 kg (since 1 kg = 1000g)

Now, we need to determine the moles of solute. We can calculate this by dividing the mass of the unknown compound by its molar mass:

moles of solute = mass of compound / molar mass of compound

So, let's divide the given mass (12.50g) by the molar mass of the compound to find the moles of solute.

The molar mass of the compound can be obtained by multiplying the moles of solute by the molality of the solution (m) and the freezing point depression constant (Kf).

Once we find the moles of solute, we can calculate the molar mass by dividing the mass of compound by the moles of solute.

Therefore, the steps to find the molar mass of the unknown compound are as follows:

1. Calculate the molality (m) of the solution: m = moles of solute / mass of solvent.
2. Determine the moles of solute: moles of solute = mass of compound / molar mass of compound.
3. Calculate the molar mass of the compound: molar mass = mass of compound / moles of solute.

By following these steps and plugging in the given values, you can find the molar mass of the unknown compound.