Chapter 3, Problem 3.24P

Interpretation Introduction

Interpretation:

The number of oxygen atoms in $38.0\text{ g}$ of oxygen gas is to be calculated.

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 $\text{6}\text{.022}\times {\text{10}}^{23}\left(\text{entitites/mol}\right)$.

Molar mass is defined as the mass of $1\text{ mol}$ of a chemical substance in grams. The molecular formula of a compound tells the number of atoms/ions of each element present in the compound.

Following are the steps to calculate the number of atoms of an element in a compound.

Step 1: Convert the mass of the compound to moles by using the molar mass of that compound as follows:

$\text{Amount}\left(\text{mol}\right)=\left(\text{Given mass}\left(\text{g}\right)\right)\left(\frac{1\text{ mol}}{\text{No}\text{. of grams}}\right)$

Step 2: Determine the number of moles of atoms of an element from the molecular formula of the compound. The formula to calculate the moles of atoms of an element X is as follows:

$\text{Amount of element X}\left(\text{mol}\right)=\left(\begin{array}{l}\text{amount of}\\ \text{compound}\\ \left(\text{mol}\right)\end{array}\right)\left(\frac{\begin{array}{l}\text{moles of element X in}\\ \text{molecular formula}\end{array}}{1\text{ mol compound}}\right)$

Step 3: Determine the number of atoms of element X by multiplying its moles with the Avogadro’s number. The expression to calculate the number of atoms of an element X is as follows:

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