Chapter 3.4, Problem 3.16AFP

Interpretation Introduction

Interpretation:

The number of aluminum atoms that reacts with iron (III) oxide to form $1.00\text{ g}$ of aluminum oxide is to be determined. A road map to show the solution is to be included.

Concept introduction:

One mole is defined as the amount of substance that contains the same number of entities such as molecules, ions, atoms as the number of atoms in $12\text{ g}$ of $\text{C-12}$. This number is called Avogadro’s number. The value of Avogadro’s number is $\text{6}\text{.022}\times {\text{10}}^{23}\left(\text{entitites/mol}\right)$.

In a balanced chemical equation, the total mass of reactants and products are equal in a balanced chemical equation, thus, it obeyed the law of conservation of mass. Also, the amounts of substances in a balanced chemical reaction are stoichiometrically equivalent to each other.

Following are the steps to determine the number of atoms of a substance when the mass of other substance present in the chemical reaction is given.

Step 1: Divide the given mass of the substance by its molar mass to calculate the moles of that compound. The expression to calculate the amount of a chemical substance in moles is as follows:

$\text{Amount}\left(\text{mol}\right)=\frac{\text{Mass }\left(\text{g}\right)}{\text{Molar mass}\left(\text{g/mol}\right)}$ (1)

Step 2: Determine the molar ratio between the substance whose mass is given and the substance whose amount is to be calculated from the balanced chemical equation. Multiply the calculated moles in step 1 by the molar ratio to obtain the amount of the substance.

Step 3: Multiply the amount calculated in step 2 by Avogadro’s number to calculate the number of atoms. The expression to calculate the number of atoms from the moles of a substance is as follows:

$\text{Number of atoms}=\left(\text{Amount}\left(\text{mol}\right)\right)\left(\frac{6.022\times {10}^{23}\text{ atoms}}{1\text{ mol}}\right)$ (2)