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The question is incomplete. Here is the complete question.
When 2.10 g of a certain molecular compound X are dissolved in 65.0 g of benzene (C₆H₆), the freezing point of the solution is measured to be 3.5°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.
Answer: MM = 47.30 g/mol.
Explanation: There is a relationship between <u>freezing</u> <u>point</u> <u>depression</u> and <u>molality</u>. With this last one, is possible to calculate <u>molar</u> <u>mass</u> or molar weight of a compound.
<u>Freezing</u> <u>Point</u> <u>Depression</u> occurs when a solute is added to a solvent: the freezing point of the solvent decreases when a non-volatile solute is incremented.
<u>Molality</u> or <u>molal</u> <u>concentration</u> is a quantity of solute dissolved in a certain mass, in kg, of solvent. Its symbol is m and it's defined as
Freezing point depression and molal are related as the following:
where
is freezing point depression of solution
is molal freezing point depression constant
m is molality
Now, to determine molar mass, first, find molality of the mixture:
For benzene, constant is 5.12°C/molal. Then
m = 0.683 molal
Second, knowing the relationship between molal and moles of solute, determine the last one:
mol(solute) = 0.683(0.065)
mol(solute) = 0.044 mol
The definition for <u>Molar</u> <u>mass</u> is the mass in grams of 1 mol of substance:
In the mixture, there are 0.044 moles of X, so its molecular mass is
MM = 47.30 g/mol
The molecular compound X has molecular mass of 47.30 g/mol.