When 271. mg of a certain molecular compound X are dissolved in 25.0g of benzene C6H6, the freezing point of the solution is measured to be 0.5°C. Calculate the molar mass of X. If you need any additional information on benzene, use only what you find in the ALEKS Data resource. Also, be sure your answer has a unit symbol, and is rounded to 2 significant digits.
molal freezing point depression constant (Kf)
°C·kg·mol−1 of benzene is 5.07

11g/mol is the molar mass of X

Explanation:

The freezing point depression occurs in a solvent by the addition of a solute. The equation is:

ΔT = Kf*m*i

Where ΔT is change in freezing point (5.5°C - 0.5°C = 5.0°C)

Freezing point of benzene is 5.5°C

Kf is molal freezing point depression of benzene (5.07°C*kg/mol)

m is molality of the solution in moles/kg of solvent

And i is Van't Hoff factor (1 for all solutes dissolved in benzene)

Replacing to solve molality:

5.0°C = 5.07°C*kg/mol*m*1

0.986mol / kg = molality

As the mass of the solvent is 25.0g = 0.025kg:

0.025kg * (0.986mol/kg) = 0.0247 moles

As molar mass of X is the ratio between mass in grams and moles, the molar mass of X is:

0.271g / 0.0247moles =

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