When of a certain molecular compound X are dissolved in of benzonitrile , the freezing point of the solution is measured to be . Calculate the molar mass of X. If you need any additional information on benzonitrile, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to significant digit.

49.0g/mol is molar mass of X

Explanation:

551mg of X are dissolved in 100g of benzonitrile

Freezing point of solution: -13.4°C

The freezing point depression of a solution (Colligative property) follows the equation:

ΔT = Kf*m*i

Where ΔT is change in freezing point from the pure solvent (Benzonitrile: -12.8°C) to the solution (-13.4°C)

Kf is freezing point depression of benzonitrile: 5.34°C/m

m is molality of the solution (Moles X / kg of benzonitrile)

And i is Van't Hoff factor (1 for any solute in benzonitrile)

ΔT = -12.8°C - (-13.4°C) = 0.6°C

Solving for molality of the solution:

ΔT = Kf*m*i

0.6°C = 5.34°C/m*m*1

0.1124m = molality of the solution

Moles of X are:

0.1124mol/kg benzonitrile * 0.1kg benzonitrile = 0.01124 moles X

In 551mg = 0.551g:

Molar mass:

0.551g / 0.01124mol =

49.0g/mol is molar mass of X