A solution of 0.64 g of adrenaline in 36.0 g of CCl_4 (K_b = 5.02 degrees celcius/m) causes an elevation of 0.49 degrees celcius in the boiling point. What is its molar mass?

Expert Answers
mvcdc eNotes educator| Certified Educator

The extent of elevatoin in boiling point (a colligative property) is directly proportional to the amount of solute (molal concentration) according to the following equation:

`Delta T_b = k_b m_B`

where:

`k_b` is the ebullioscopic constant and is dependent on the properties of the solvent.

`m_B` is the molality of the solution. Molality is the ratio of the moles of solute to kilograms of the solvent.

Note also the following:

`n = (mass)/(MW)`

We are given the following:

`mass_(solute) = 0.64 g`

`mass_(solvent) = 36.0 g = 36.0 x 10^(-3) kg`

`k_b = 5.02 (deg.Cel.)/m` 

`Delta T_b = 0.49 deg.Cel.`

To solve for the MW:

`Delta T_b = k_b (n_(solute)/(kg_(solvent)))`

`Delta T_b = k_b (((m_(solute))/(MW))/(kg_(solvent)))`

Hence,

`MW = (m_(solute) k_b)/(kg_(solvent) Delta T_b)`

`MW = (0.64*5.02)/(36x10^(-3) * 0.49) = 182.13`  

The molecular mass is 182.1315 grams/mole.