Chapter 14, Problem 80A

Interpretation Introduction

Interpretation:

The molality of KCl solution is to be calculated.

Concept Introduction:

Molality: Molality is defined as the number of moles of solute per kg of the solvent.

In expression,

  $\text{Molality}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{o}\text{l}\text{u}\text{t}\text{i}\text{o}\text{n}=\frac{\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f} \text{t}\text{h}\text{e} \text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}{ \text{M}\text{a}\text{s}\text{s} \text{o}\text{f} \text{t}\text{h}\text{e} \text{s}\text{o}\text{l}\text{v}\text{e}\text{n}\text{t}(\text{i}\text{n}\text{K}\text{g})}$

Thus, $\text{Number}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}=\frac{\text{M}\text{a}\text{s}\text{s}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}{\text{M}\text{o}\text{l}\text{e}\text{c}\text{u}\text{l}\text{a}\text{r}\text{w}\text{e}\text{i}\text{g}\text{h}\text{t}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}$

Answer to Problem 80A

The molality of KCl solution is 10.63 mol/kg.

Explanation of Solution

Given information:

Mass of KCl = 75.3 gm

Mass of the solvent water = 95 gm = 0.095 kg

Write the expression for Molality.

  $\text{Molality}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{o}\text{l}\text{u}\text{t}\text{i}\text{o}\text{n}=\frac{\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f} \text{t}\text{h}\text{e} \text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}{ \text{M}\text{a}\text{s}\text{s} \text{o}\text{f} \text{t}\text{h}\text{e} \text{s}\text{o}\text{l}\text{v}\text{e}\text{n}\text{t}(\text{i}\text{n}\text{K}\text{g})}$

Calculate the number of moles of $\text{K}\text{C}\text{l}$ .

  $\begin{array}{l}\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}=\frac{\text{M}\text{a}\text{s}\text{s}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}{\text{M}\text{o}\text{l}\text{e}\text{c}\text{u}\text{l}\text{a}\text{r}\text{w}\text{e}\text{i}\text{g}\text{h}\text{t}\text{o}\text{f}\text{t}\text{h}\text{e}\text{s}\text{o}\text{l}\text{u}\text{t}\text{e}}\end{array}$

  $\begin{array}{c}\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{K}\text{C}\text{l}=\frac{\text{M}\text{a}\text{s}\text{s}\text{o}\text{f}\text{K}\text{C}\text{l}}{\text{M}\text{o}\text{l}\text{e}\text{c}\text{u}\text{l}\text{a}\text{r}\text{w}\text{e}\text{i}\text{g}\text{h}\text{t}\text{o}\text{f}\text{K}\text{C}\text{l}}\end{array}$

  $\begin{array}{c}\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{K}\text{C}\text{l}=\frac{75.3\text{g}\text{m}}{74.6\text{g}\text{m}/\text{m}\text{o}\text{l}}=1.01\text{m}\text{o}\text{l}\text{e}\end{array}$

(Note: Molecular weight of KCl = 74.6 gm/mol)

Calculate the Molality of $\text{K}\text{C}\text{l}$ .

  $\begin{array}{l}\text{M}\text{o}\text{l}\text{a}\text{l}\text{i}\text{t}\text{y}\text{o}\text{f}\text{K}\text{C}\text{l}\text{s}\text{o}\text{l}\text{u}\text{t}\text{i}\text{o}\text{n}=\frac{\text{N}\text{u}\text{m}\text{b}\text{e}\text{r}\text{o}\text{f}\text{m}\text{o}\text{l}\text{e}\text{s}\text{o}\text{f}\text{K}\text{C}\text{l}}{ \text{M}\text{a}\text{s}\text{s} \text{o}\text{f} \text{w}\text{a}\text{t}\text{e}\text{r}}\end{array}$

  $\begin{array}{c}\text{M}\text{o}\text{l}\text{a}\text{l}\text{i}\text{t}\text{y}\text{o}\text{f}\text{K}\text{C}\text{l}\text{s}\text{o}\text{l}\text{u}\text{t}\text{i}\text{o}\text{n}=\frac{1.01\text{m}\text{o}\text{l}\text{e}}{ 0.095\text{k}\text{g}}=10.63\text{m}\text{o}\text{l}/\text{k}\text{g}\end{array}$