Question

When 1.04 g of an unknown non-electrolyte is dissolved in 50.0 g of cyclohexane, the freezing point decreased by 3.91 degrees C. If the Kfp of the solvent is 20.1 K/m, calculate the molar mass of the unknown solute.

Answer 1

The molar mass of the unknown solute is 106,9 g/m

Step-by-step explanation:

Cryoscopic descent formula to solve this

ΔT = Kf . m

Be careful because units in Kfp are K/m, so let's get the ΔT degrees °C in K

3,91°C = 3,91 K

It's a difference, in the end it does not matter

For example you can have 5° C as the final temperature and as initial, 1,09 °C -- ΔT is 5 - 1.09 = 3.91

What happens in Kelvin?

5°C + 273 = 278 K

1,09° C + 273 = 274,09 K

ΔT = 278 K - 274,09 K = 3,91 K

3,91 K = 20,1 K/m * m

3,91 K / 20,1 m/K = m

0,194 = m (molality)

Molality means moles from solute in 1 kg of solvent.

1kg = 1000 g

1000 g ________ 0,194 moles

50 g _________ x

x = (50 g * 13,77 moles) / 1000 g = 9,72 *10-3 moles

Moles = mass / molar mass

Molar mass = mass / moles

Molar mass = 1,04 g / 9,72 *10-3 moles

Molar mass = 106,9 g/m