Chapter 3.3, Problem 40SP

Interpretation Introduction

Interpretation : The number of atoms in $5.00\text{g}$ of gold is to be calculated.

Concept Introduction : A conversion factor is a ratio of equivalent measurements. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements in another.

Answer to Problem 40SP

The number of atoms in $5.00\text{g}$ of gold is $1.53\times {10}^{22}\text{atoms}$ .

Explanation of Solution

Given information :

The mass of gold atom is $3.271\times {10}^{-22}\text{g}$ .

The given mass is $5.00\text{g}$ .

The molar mass of gold is $196.97\text{g}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The formula for the number of moles is given as:

  $\text{No}\text{.}\text{of}\text{moles}=\frac{\text{given mass}}{\text{molar mass}}$

To calculate the number of moles of $5.00\text{g}$

of gold, substitute the values in the above formula:

  $\begin{array}{c}\text{No}\text{.}\text{of}\text{moles}=\frac{\text{given mass}}{\text{molar mass}}\\ \text{No}\text{.}\text{of}\text{moles}=\frac{5.00\text{g}}{196.97\text{g}}\\ =0.0253\text{g}\end{array}$

The number of gold atoms is given as:

  $\begin{array}{c}\text{No}\text{.}\text{of}\text{atoms}\text{=}\text{moles×Avogadro}\text{number}\\ \text{= }0.0253\text{g}\times 6.022\times {10}^{23}\\ =0.1528\times {10}^{23}\text{ g}\\ =1.53\times {10}^{23}\text{ g}\end{array}$