Question

When of a certain molecular compound X are dissolved in of benzene , the freezing point of the solution is measured to be . 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 the correct number of significant digits.

Answer 1

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

$m=\frac{moles(solute)}{kg(solvent)}$

Freezing point depression and molal are related as the following:

$\Delta T_{f}=K_{f}.m$

where

$\Delta T_{f}$ is freezing point depression of solution

$K_{f}$ is molal freezing point depression constant

m is molality

Now, to determine molar mass, first, find molality of the mixture:

$\Delta T_{f}=K_{f}.m$

$m=\frac{\Delta T_{f}}{K_{f}}$

For benzene, constant is 5.12°C/molal. Then

$m=\frac{3.5}{5.12}$

m = 0.683 molal

Second, knowing the relationship between molal and moles of solute, determine the last one:

$m=\frac{moles(solute)}{kg(solvent)}$

$mol(solute)=m.kg(solvent)$

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:

$n(moles)=\frac{m(g)}{MM(g/mol)}$

$MM=\frac{m}{n}$

In the mixture, there are 0.044 moles of X, so its molecular mass is

$MM=\frac{2.1}{0.044}$

MM = 47.30 g/mol

The molecular compound X has molecular mass of 47.30 g/mol.