Chapter 10, Problem 140A

Interpretation Introduction

Interpretation:

The number of gold atoms should be calculated in 3.50 g gold.

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 140A

Number of atoms of gold = $1.07\times {10}^{22}\text{ atoms}$

Explanation of Solution

Mass of gold = 3.50 g

Molar mass of gold = 197 g/mole

Number of moles of gold = $\frac{3.50\text{ g}}{\text{197 g/mole}}$

Number of moles of gold = $0.01776\text{ mole}$

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,

$0.01776\text{ mole}$ = $\text{Number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$\text{Number of atoms }=0.01776\text{ mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

Number of atoms of gold = $1.07\times {10}^{22}\text{ atoms}$