Chapter 10, Problem 147A

Interpretation Introduction

Interpretation:

The number of chloride ions in 10.75 g of magnesium chloride should be calculated.

Concept introduction:

The number of moles of a compound is defined as the ratio of the given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 147A

Number of chloride ions = $1.36\times 10\text{ions}$

Explanation of Solution

The given compound is magnesium chloride.

The molecular formula of magnesium chloride = ${\text{MgCl}}_2$

The molar mass of ${\text{MgCl}}_2$ = $1\left(24.31\text{ g/mole}\right)+2\left(35.45\text{ g/mole}\right)$

= $95.21\text{ g/mole}$

Mass of ${\text{MgCl}}_2$ = 10.75 g

Number of moles of ${\text{MgCl}}_2$ = $\frac{\text{10}\text{.75 g}}{95.21\text{ g/mole}}$

= $\text{0}\text{.113 mole}$

${\text{MgCl}}_2$ contains one mole of magnesium and two moles of chlorine.

Or,

${\text{MgCl}}_2$ dissociated as:

${\text{MgCl}}_2\to {\text{Mg}}^{\text{2+}}{\text{+2Cl}}^{-}$

Number of moles of ${\text{Cl}}^{-}$ = $\text{0}\text{.113 mole}\times \text{2}$

= $0.226\text{ mole}$

Number of chloride ions = $\text{Number of moles × 6}\text{.022}\times {\text{10}}^{23}\frac{\text{ions}}{\text{mole}}$

= $0.226\text{ mole}\times \text{ 6}\text{.022}\times {\text{10}}^{23}\frac{\text{ions}}{\text{mole}}$

= $1.36\times 10\text{ions}$