Question

calculate molecular weight of substance whose 7.0%by mass solution in water freeze at 0.93C the cryoscopic constant for water is 1.86kg/mole​

Answer 1

I hope this helps ( ╹▽╹ )

Answer 2

Concept:

The freezing point is the temperature at which a liquid turns into a solid. The freezing point is often increased by increased pressure, just like the melting point.

Freezing point depression is the term used to describe how adding solutes lowers the freezing point of solvents. It is a colligative property of solutions that, in most cases, varies in proportion to the molality of the solute that has been added.

Given:

% of the solution by mass = 7%

The freezing point depression (Δ $T_{f}$ ) = 0.93 degree Celsius = (273.15 + 0.93) K = 274.08 K

The cryoscopic constant for water = 1.86 kg/mole​

Find:

Calculate molecular weight of substance.

Solution:

The depression in the freezing point of a solution can be described by the following formula.

                             Δ $T_{f}$ = i * $K_{f}$ * m

• Where Δ $T_{f}$ is the freezing point depression,

• i is Van’t Hoff factor = 1

• $K_{f}$ is the cryoscopic constant.

• m is the molality.

Mass of solute = 7% by mass = 7 g of solute in 100 g of solvent

Mass of solvent = 100 g = $\frac{100}{1000}$ Kg = 0.1 Kg

By substituting the given values in the above expression we get,

274.08 K = 1 * 1.86 Kg/mole * m

274.08 K = 1.86 Kg/mole * $\frac{number of moles of solute }{Mass of solvent in Kg}$

274.08 K = 1.86 Kg/mole * $\frac{Mass of solute }{ Molar mass of solute*Mass of solvent in Kg}$

274.08 K = 1.86 Kg/mole * $\frac{7 g}{ Molar mass of solute* 0.1 Kg}$

Molar mass of solute = $\frac{ 1.86 * 7}{274.08 * 0.1}$ = 0.475 g/mol

Hence, the molecular weight of the substance is 0.475 g/mol.

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