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`
`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)))`
`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.