Chapter 10, Problem 119A

Interpretation Introduction

Interpretation:

The total number of atoms present in the mixture 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 119A

Total number of atoms present in mixture = $\text{2}\text{.10709}\times {\text{10}}^{23}\text{ atoms}$

Explanation of Solution

Number of moles of $\text{Fe}$ = $\text{0}\text{.250 mole}$

Mass of carbon = 1.20 g

Molar mass of iron = 55.845 g/mole

Molar mass of carbon = 12.0107 g/mole

$\text{Number of moles of carbon = }\frac{\text{1}\text{.20 g}}{12.0107\text{ g/mole}}$

Number of moles of $\text{C}$ = $\text{0}\text{.0999 mole}$

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,

$\text{0}\text{.0999 mole}$ = $\text{Number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$\text{Number of atoms }=\text{0}\text{.0999 mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

Number of atoms of $\text{C}$ = $0.60159\times {\text{10}}^{23}\text{ atoms}$

Number of moles of $\text{Fe}$ = $\text{0}\text{.250 mole}$

Put the values,

$\text{0}\text{.250 mole}$ = $\text{Number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$\text{Number of atoms }=\text{0}\text{.250 mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

Number of atoms of iron = $1.5055\times {10}^{23}\text{ atoms}$

Total number of atoms present in mixture = number of atoms of iron + number of atoms of carbon

Total number of atoms present in mixture = $1.5055\times {10}^{23}\text{ atoms + }0.60159\times {\text{10}}^{23}\text{ atoms}$

= $\text{2}\text{.10709}\times {\text{10}}^{23}\text{ atoms}$