Chapter 14, Problem 83A

Interpretation Introduction

Interpretation:

The molality of the solution and mole fraction of solute is to be calculated

Concept introduction:

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

In expression, $\mathrm{Molality}ofthesolution=\frac{Numberofmolesof the solute}{ Mass of the solvent(inKg)}$

Again $\mathrm{Number}ofmolesofsolute=\frac{Massofthesolute}{Molecularweightofthesolute}$

Mole fraction: Mole fraction defined as the number of moles of one component divided by total the number of moles in the mixture.

The mole fraction for the solute ( ${\chi }_A$ )and the mole fraction for the solvent ( ${\chi }_B$ )can be expressed as follows:Mole fraction ${\chi }_A=\frac{n_A}{ n_A+n_B}$ and ${\chi }_B=\frac{n_B}{ n_A+n_B}$ Where, n_A and n_Brepresent the number of moles of solute and solvent respectively.

Answer to Problem 83A

The molality of formic acid solution is 11.95 m and the mole fraction of formic acid in the solution is 0.177.

Explanation of Solution

Given information:

Percent by mass of formic acidsolution = 35.5

This above statement signifies that 35.5 g formic acid in 100 gm solution.

Mass of formic acid = 35.5 gm.

Calculate the number of moles of formic acids.

$\mathrm{Number}ofmolesofformicacid=\frac{35.5gm}{46.03gm/mol}=0.771mole$

(Note: Molecular weight of formic acid = 46.03 gm/mol)

Calculate the mass of water.

$\begin{array}{c}Massofwater=\left(100-35.5\right)gm\\ =64.5gm\\ =0.0645kg\end{array}$

$\mathrm{Number}ofmolesofwater=\frac{64.5gm}{18gm/mol}=3.58mole$

(Note: Molecular weight of water = 18 gm/mol)

Calculate the molality of formic solution.

$\begin{array}{l}Molalityofformicacidsolution=\frac{Numberofmolesofformicacid}{ Mass of water}\\ =\frac{0.771mole}{ 0.0645kg}=11.95m\end{array}$

Calculate the molefraction of $HCOOH$.

$\begin{array}{l}MolefractionofHCOOH=\frac{NumberofmolesofHCOOH}{NumberofmolesofHCOOH+Numberofmolesofwater}\\ =\frac{0.771mol}{0.771mol+3.58mol}=0.177\end{array}$

The molality of formic acid solution is 11.95 m and the mole fraction of formic acid in the solution is 0.177.