Question

A student makes a solution by mixing 160.0 g of H₂O with 56.56 g of an unknown nonelectrolyte. The student then measures the freezing point of the solution and finds that it is -14.2 ^∘C. What is the molar mass of the nonelectrolyte

Answer 1

Answer -

Given,

Mass of H2O = 160.0 g or 0.16 kg [1 g = 0.001 kg]

Mass of unknown Electrolyte = 56.56 g

Molar Mass of Water = 18.01 g/mol

Freezing point of the solution = -14.2 $\degree$C

Molar Mass of unknown = ?

We know that,

$\Delta$T = i * Kf * molality

where,

$\Delta$T = TH2O - Tsoln

i = Vant' hoff factor (For non-electrolyte, i = 1)

Kf = 1.86 °C/m for water

Frezing point of water = 0$\degree$C

So,

TH2O - Tsoln = i * Kf * molality

Put the values,

0 $\degree$C - (-14.2 $\degree$C) = 1 * 1.86 °C/m * molality

14.2 $\degree$C = 1.86 °C/m * molality

molality = 14.2 $\degree$C / 1.86 °C/m

molality = 7.63 m

Now,

Molality = moles of solute / mass of solvent in kg

So,

Moles of Solute = Molality * mass of solvent in kg

Moles of Solute = 7.63 m * 0.16 kg

Moles of Solute = 1.2208 mol

Now,

Moles = Mass / Molar Mass

So,

Molar Mass = Mass /Moles

Molar Mass of non electrolyte = 56.56 g / 1.2208 mol

Molar Mass of non electrolyte = 46.33 g/mol [ANSWER]