Sagot :
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 freezing point depression and molality. With this last one, is possible to calculate molar mass or molar weight of a compound.
Freezing Point Depression occurs when a solute is added to a solvent: the freezing point of the solvent decreases when a non-volatile solute is incremented.
Molality or molal concentration is a quantity of solute dissolved in a certain mass, in kg, of solvent. Its symbol is m and it's defined as
[tex]m=\frac{moles(solute)}{kg(solvent)}[/tex]
Freezing point depression and molal are related as the following:
[tex]\Delta T_{f}=K_{f}.m[/tex]
where
[tex]\Delta T_{f}[/tex] is freezing point depression of solution
[tex]K_{f}[/tex] is molal freezing point depression constant
m is molality
Now, to determine molar mass, first, find molality of the mixture:
[tex]\Delta T_{f}=K_{f}.m[/tex]
[tex]m=\frac{\Delta T_{f}}{K_{f}}[/tex]
For benzene, constant is 5.12°C/molal. Then
[tex]m=\frac{3.5}{5.12}[/tex]
m = 0.683 molal
Second, knowing the relationship between molal and moles of solute, determine the last one:
[tex]m=\frac{moles(solute)}{kg(solvent)}[/tex]
[tex]mol(solute)=m.kg(solvent)[/tex]
mol(solute) = 0.683(0.065)
mol(solute) = 0.044 mol
The definition for Molar mass is the mass in grams of 1 mol of substance:
[tex]n(moles)=\frac{m(g)}{MM(g/mol)}[/tex]
[tex]MM=\frac{m}{n}[/tex]
In the mixture, there are 0.044 moles of X, so its molecular mass is
[tex]MM=\frac{2.1}{0.044}[/tex]
MM = 47.30 g/mol
The molecular compound X has molecular mass of 47.30 g/mol.