Chapter 10, Problem 146A

Interpretation Introduction

Interpretation:

The number of moles of aluminum ions that are present in 250.0 g of aluminum oxide 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 146A

Number of moles of ${\text{Al}}^{\text{3+}}$ = $4.9\text{ mole}$

Explanation of Solution

The given compound is aluminium oxide.

The molecular formula of aluminum oxide = ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$

The molar mass of ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ = $2\left(26.98\text{ g/mole}\right)+3\left(15.999\text{ g/mole}\right)$

= $102\text{ g/mole}$

Mass of ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ = 250.0 g

Number of moles of ${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ = $\frac{\text{250}\text{.0 g}}{102\text{ g/mole}}$

= $\text{2}\text{.45 mole}$

${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ contains two moles of aluminum and three moles of oxygen.

Or,

${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}$ dissociated as:

${\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\to {\text{2Al}}^{\text{3+}}{\text{+3O}}^{\text{2-}}$

Number of moles of ${\text{Al}}^{\text{3+}}$ = $\text{2}\text{.45 mole}\times \text{2}$

= $4.9\text{ mole}$