Question

An unknown sample weighing 0.3512g was added to 20.0 mL of cyclohexane. The density of cyclohexane is 0.779g/mL, and the freezing point depression was 5.2°C. Calculate the molar mass of the unknown.

Answer 1

Explanation:

It is known that density is mass of a substance divided by its volume.

Mathematically,         Density = $\frac{mass}{volume}$

Therefore, calculate the mass of cyclohexane as follows.

             mass of cyclohexane = Density × volume

                                  = $0.779 g/mL \times 20 mL$

                                   = 15.58 g

or,                              = 0.01558 kg           (as 1 kg = 1000 g)

As, K_{f} of cyclohexane = $20^{o}C/m$  

                 $\Delta T_{f} = K_{f} \times molality$

                           $5.2 = 20 \times molality$

                             molality = $\frac{5.2}{20}$

                                         = 0.26 m

Also, molality is the number of moles of solute present in kg of solvent.

Mathematically,      molality = $\frac{\text{no. of moles}}{\text{mass of solvent}}$

                         0.26 = $\frac{\text{no. of moles}}{0.01558}$

                       No. of moles  = $4.05 \times 10^{-3}$

As,             No. of moles = $\frac{mass}{\frac{molar mass}}$      

                    $4.05 \times 10^{-3} = \frac{0.3512}{\text{molar mass}}$

                             molar mass = 87.0 g/mol

Thus, we can conclude that molar mass of unknown substance is 87.0 g/mole.