Question

When 240 mg of a certain molecular compound X are dissolved in 35.0 g of dibenzyl ether ((C6H5CH2)2O), the freezing point of the solution is measured to be 1.0 °C. Calculate the molar mass of X If you need any additional information on dibenzyl ether, 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

Answer: MM = 16.55 g/mol

Explanation: Freezing point depression is a phenomena that explains why adding a solute to a solvent decreases the solvent freezing point: when a substance begins to freeze, its molecules slows down and rearrange itself forming a solid. If a solute is added, the molecules from the solvent interfere in the formation of the solid. To guarantee the transformation, the solution has to cooled down even more.

Freezing point and molality concentration is related by

$\Delta T=T_{f}_{(solvent)}-T_{f}_{(solution)}=K_{f}.m$

where

ΔT is freezing point depression

$T_{f}_{(solvent)}$ and $T_{f}_{(solution)}$ are freezing point of solvent and solution, respectively

$K_{f}$ is freezing point depression constant

m is molality concentration

Dibenzyl ether is the solvent and has the following properties: $K_{f}=$ 6.27 and $T_{f}$ = 3.6°C.

Molality concentration is

$m=\frac{T_{(solvent)}-T_{(solution)}}{K_{f}}$

$m=\frac{3.6-1}{6.27}$

m = 0.415

Molality concentration is moles (n) of solute dissolved in a mass, in kilogram, of solvent.

$m=\frac{moles}{mass(kg)}$

n = m(mass of solvent in kg)

n = 0.415(0.035)

n = 0.0145

Molar mass (M) is the weight of one sample mole and can be calculated as

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

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

m in grams

Molar mass of compound X is

$M=\frac{0.24}{0.0145}$

M = 16.55

Molar mass of molecular compound X is 16.55g/mol