Chapter 14, Problem 85A

Interpretation Introduction

Interpretation:

The mole fraction of MgCl₂ in the solutionis to be calculated.

Concept introduction:

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 85A

The mole fraction of MgCl₂ in the solution is 0.125.

Explanation of Solution

Given information:

Mass of MgCl₂ = 132.1 gm

Volume of water = 175 mL

Mass of water = 175 gm

Calculate the number of Moles of $MgC{l}_2$.

$\mathrm{Number}ofmolesofMgC{l}_2=\frac{132.1gm}{95.2gm/mol}=1.387mole$

(Note: Molecular weight of MgCl₂ = 95.2 gm/mol)

$\mathrm{Number}ofmolesofwater=\frac{175gm}{18gm/mol}=9.72mole$

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

Calculate the number of Mole fractions of $MgC{l}_2$

$\begin{array}{l}MolefractionofMgC{l}_2=\frac{NumberofmolesofMgC{l}_2}{NumberofmolesofMgC{l}_2+Numberofmolesofwater}\\ =\frac{1.387mol}{1.387mol+9.72mol}=0.125\end{array}$

The mole fraction of MgCl₂ in the solution is 0.125.