Chapter 10, Problem 120A

Interpretation Introduction

Interpretation:

The number of argon atoms should be calculated which is inhaled with each breath.

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 120A

Number of atoms of argon inhaled with each breath = $\text{8}\text{.445}\times {\text{10}}^{19}\text{ atoms}$

Explanation of Solution

Mass of air = 0.600 g

Percentage of argon present in air = 0.934 %

Mass of argon = $\frac{0.600\text{ g}\times \text{0}\text{.934 \%}}{100\text{ \%}}$

= $5.604\times {10}^{-3}\text{ g}$

Molar mass of argon = 39.948 g/mole

Number of moles = $\frac{\text{ 5}\text{.604}\times {\text{10}}^{-3}\text{ g}}{\text{39}\text{.948 g/mole}}$

Number of moles of $\text{Ar}$ = $0.1403\times {10}^{-3}\text{ mole}$

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

Number of moles = $\text{number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

Put the values,

$0.1403\times {10}^{-3}\text{ mole}$ = $\text{Number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$\text{Number of atoms }=0.1403\times {10}^{-3}\text{ mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

Number of atoms of $\text{Ar}$ = $\text{8}\text{.445}\times {\text{10}}^{19}\text{ atoms}$

Number of atoms of argon inhaled with each breath = $\text{8}\text{.445}\times {\text{10}}^{19}\text{ atoms}$