Chapter 13, Problem 125E

Interpretation Introduction

Interpretation:

With the help of mass of unknown compound, mass of water and the freezing point, molar mass of the unknown compound is to be calculated.

Concept introduction:

Molality is the number of moles of solute to the mass of solvent.

Relation between number of moles $\left(n\right)$ and molar mass is as follows:$n=\frac{\text{mass}}{\text{molar mass}}$

To convert $\text{g}$ to kilograms $\left(\text{kg}\right)$, conversion factor will be $\left(\frac{{10}^{-3}\text{ kg}}{\text{1 g}}\right)$

The mass of the solvent should be in kilograms $\left(\text{kg}\right)$.

Calculate molality as follows:

$m=\frac{\text{Moles solute}}{\text{Kilograms solvent}}$ …… (1)

The temperature at which change of liquid state to solid state takes place is called freezing point.

The freezing point depression is as follows:

$\Delta T_{\text{f}}=m\times K_{\text{f}}$ …… (2)

Here, $\Delta T_{\text{f}}$ is the change in temperature of the freezing point in $\text{C}$, $m$ is the

Molality of the solution in $\frac{\text{mol solute}}{\text{kg solvent}}$ and $K_{\text{f}}$ is the freezing point depression

Constant for the solvent.

For water:

$K_{\text{f}}=1.86\frac{\text{C}\text{ kg solvent}}{\text{mol solute}}$