Chapter 13, Problem 124E

Interpretation Introduction

Interpretation:

The freezing and boiling points of the final solution of ethylene glycol solution which is diluted are to be calculated.

Concept Introduction:

Molarity is the ratio of the number of moles of solute to the liter of solution.

Mathematically, molarity $\left(\text{M}\right)$ is:

$\text{M=}\frac{\text{Moles solute}}{\text{Liters solution}}$

The concentration of the solution can be expressed in terms of the molality $\left(m\right)$.

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

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

Formula of molality is:

$m=\frac{\text{Moles solute}}{\text{Kilograms solvent}}$

Freezing point is the temperature at which liquid state changes to solid state.

The freezing point depression is:

$\Delta T_{\text{f}}=m\times K_{\text{f}}$

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:

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

The temperature at which vapor pressure of the liquid becomes equal to the

atmospheric pressure is known as boiling point.

The boiling point elevation is:

$\Delta T_{\text{b}}=m\times K_{\text{b}}$

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

molality of the solution in $\frac{\text{mol solute}}{\text{kg solvent}}$ and $K_{\text{b}}$ is the boiling point elevation

constant for the solvent.

For water:

$K_{\text{b}}=0.512\frac{\text{C}\text{ kg solvent}}{\text{mol solute}}$