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?
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.