I need help understanding this problem. What is the Molar Mass of the unknown solute in g/mol?

Question

A solution is prepared by dissolving 18.49 g of an unknown non-electrolyte solute in 65.10 g of cyclohexane. The freezing point of the solution is found to be -2.30 ^oC. What is the molar mass of the unknown solute in g/mol?

answer is 648 g.mol

Answer 1

Hi Angela!

For this problem, we're going to be dealing with freezing point depression, using the equation:

ΔT_F = m * K_F * i

ΔT_F is the change in freezing point of the solution

m is the molality of the solution

K_F is the freezing point depression constant of cyclohexane (20.1 °C/m)

i is the Van't Hoff factor -- the number of particles the solute dissociates into.

(In this case, it is 1, because the solute is a non-electrolyte!)

We also need to know the normal freezing point of cyclohexane, which is 6.50 °C. The difference between that and our new freezing point will be:

6.50 °C - (-2.30 °C) = 8.8 °C

So... 8.8 °C = (20.1 °C/m) * (m) * (1)

Which gives us a molality of...0.438 molal.

Remember, molality is equivalent to moles of solute per kg of solvent, so using that, we can determine how many moles of solute we have in our solution!

0.438 molal = X mol solute / 0.0651 kg cyclohexane

Which gives us .0285 moles of solute.

Finally, since we're looking for a molar mass (g/mol), let's take the grams and divide by moles!

18.49g solute / .0285 mol solute = 648 g/mol!

Hope that helps clear it up :)

-Niral