Question

A solution of 0.85 g of an organic compound in 100.0 g of benzene has a freezing point of 5.16°C. What are the molality of the solution and the molar mass of the solute?

Answer 1

The molar mass of the solute(organic compound)=128.012 g/mol

Further explanation  

Solution properties are the properties of a solution that don't depend on the type of solute but only on the concentration of the solute.  

Solutions from volatile substances have a higher boiling point and lower freezing points than the solvent  

For freezing point can be formulated

$\tt \Delta T_f=K_f.m$

K = molal freezing point constant  

m = molal solution  

ΔT for solution (freezing point for Benzene = 5.5 °C) :

$\tt \Delta T_f=5.5-5.16=0.34$

• molality of solution (m) :

$\tt m=\dfrac{\Delta T_f}{K_f}\rightarrow K_f~for~Benzene=5.12^oC/m\\\\m=\dfrac{0.34}{5.12}=0.0664$

• mol of organic compound :

molal  : the number of moles of solute in 1 kg of solvent  

$\tt 0.0664=\dfrac{mol}{0.1~kg~benzene}\\\\mol=0.0664\times 0.1=0.00664$

• the molar mass of the solute(organic compound)

mass of organic compound = 0.85 g

$\tt MW=\dfrac{mass}{mol}=\dfrac{0.85}{0.00664}=128.012~g/mol$