Chapter 12, Problem 12.70QP

A solution was prepared by dissolving 0.800 g of sulfur, S_g, in 100.0 g of acetic acid, HC₂H₃O₂. Calculate the freezing point and boiling point of the solution.

Interpretation Introduction

Interpretation:

The boiling point and freezing point of $0.800\text{ g}$ Sulfur in $100.0\text{ g}$ of acetic acid have to be determined.

Concept Introduction:

Elevation in boiling point is a colligative property which refers to increase in boiling point of the solution due to the addition of non-volatile solute. It is expressed as,

$\Delta T_b=K_b.c_m$

Where,

$\begin{array}{l}{\text{ΔT}}_{\text{b}}\text{= elevation in boiling point}\\ {\text{K}}_{\text{b}}\text{= boiling point elevation constant}\\ {\text{c}}_{\text{m}}\text{= molal concentration}\end{array}$

Depression in freezing point is a colligative property which refers to decrease in freezing point of the solution due to the addition of non-volatile solute. It is expressed as,

$\Delta T_f=K_f.c_m$

Where,

$\begin{array}{l}{\text{ΔT}}_{\text{f}}\text{= depression in freezing point}\\ {\text{K}}_{\text{f}}\text{= freezing point depression constant}\\ {\text{c}}_{\text{m}}\text{= molal concentration}\end{array}$

Molality or molal concentration is one of the many parameters that is used to express concentration of a solution.  It is expressed as,

$\text{Molality = }\frac{number\text{ of }molesof\text{ solute}}{mass\text{ of solvent in kg}}$

Answer to Problem 12.70QP

The boiling point of $0.800\text{ g}$ Sulfur in $100.0\text{ g}$ of acetic acid is determined as $118.6°C.$

The freezing point of $0.800\text{ g}$ Sulfur in $100.0\text{ g}$ of acetic acid is determined as $16.49°C.$

Explanation of Solution

Given that mass of solvent acetic acid is $\text{100}\text{.0 g}$ which is equivalent to $\text{0}\text{.1000 kg}$. Mass of Sulfur is $0.800g$

Number of moles of sulfur is,

$\begin{array}{l}No.of\text{ moles of sulfur}\text{= }\frac{mass\text{ of Sulfur}}{molar\text{ mass of Sulfur}}\\ =\frac{0.800\text{ g}}{256.52\text{ g/mol}}\\ =\text{ 0}\text{.003119 g/mol}\end{array}$

Molality of the solution is,

$\begin{array}{l}Molality=\frac{0.003119\text{ mol}}{0.1000\text{ kg}}\\ =\text{ 0}\text{.03119 m }\approx 0.0312\text{ m}\end{array}$

From the data given in the table $\text{12}\text{.3}$ in text book, for acetic acid, ${\text{K}}_{\text{f}}\text{= 3}\text{.59°C/m}$

Therefore, depression in freezing point is,

${\text{ΔT}}_{\text{f}}{\text{ = K}}_{\text{f}}{\text{.c}}_{\text{m}}$

Substitute the values,

$\begin{array}{l}{\text{ΔT}}_{\text{f}}\text{= 3}\text{.59}°\text{C/m }\times \text{ 0}\text{.0312 m}\\ \text{= 0}\text{.1120}°\text{C}\end{array}$

The depression in freezing point is equivalent to the difference between freezing temperature of pure solvent and solution. Hence freezing point of the solution is,

$\begin{array}{l}\Delta T_f{\text{= T}}_f(solvent){\text{ - T}}_f(solution)\\ 0.1120°C=\text{ 16}\text{.60}°\text{C - }{T}_f(solution)\\ T_f(solution)=\text{ 16}\text{.60}°\text{C - 0}\text{.1120}°\text{C}\\ \text{= 16}\text{.49}°\text{C}\end{array}$

From the data given in the table $\text{12}\text{.3}$ in text book, for Acetic acid, ${\text{K}}_{\text{b}}\text{= 3}\text{.08°C/m}$

Therefore, elevation in boiling point is,

${\text{ΔT}}_{\text{b}}{\text{ = K}}_{\text{b}}{\text{.c}}_{\text{m}}$

Substitute the values,

$\begin{array}{l}{\text{ΔT}}_{\text{b}}\text{= 3}\text{.08}°\text{C/m }\times \text{ 0}\text{.0312 m}\\ \text{= 0}\text{.096096}°\text{C}\end{array}$

The elevation in boiling point is equivalent to the difference between boiling temperature of and solution and pure solvent. Hence boiling point of the solution is,

$\begin{array}{l}\Delta T_b{\text{= T}}_b(solution){\text{ - T}}_b(solvent)\\ 0.096096°C=T_b(solution)-\text{100}°\text{C}\\ T_f(solution)=\text{ 118}\text{.5}°\text{C + 0}\text{.096096}°\text{C}\\ \text{= 118}\text{.59}°\text{C = 118}\text{.6}°\text{C}\end{array}$

Conclusion

Depression in freezing point and elevation in boiling point are colligative properties that depend upon the concentration of the solute in solution.  The molal concentration of the solute, depression in freezing point and elevation in boiling point are the key parameters to determine freezing point and boiling point of the solution.