Chapter 6, Problem 9A

Interpretation Introduction

Interpretation : The number of atoms present in a sample having atomic mass of element in grams is to be determined.

Concept Introduction : One mole is defined as the quantity that is composed of as many numbers of particles as there are particles present in $12.0\text{g}$ of carbon-12.

Answer to Problem 9A

A sample equal to the atomic mass of an element in grams contains $\underset{\_}{\text{6}\text{.022}\times {\text{10}}^{\text{23}}}$ atoms.

Explanation of Solution

One mole of any substance consists of $6.022\times {10}^{23}$ particles. These particles can be ions, atoms or molecules depending on the type of species. The molecular weight of any substance is equal to mass of one mole of that substance. The number of moles is calculated as shown below.

  $\text{Number of moles}=\frac{\text{Given mass}}{\text{Atomic mass in grams}}$ . (1)

The number of moles is also calculated as shown below.

  $\text{Number of moles}=\frac{\text{Given number of particles}}{\text{Avogadro number}}$ . (2)

On combining the above two equations the final equation is given as shown below.

  $\frac{\text{Given mass}}{\text{Atomic mass in grams}}=\frac{\text{Given number of particles}}{\text{Avogadro number}}$

As it is given that given mass of sample is equal to atomic mass in grams. Thus, on rearraging the equation is given as shown below.

  $\begin{array}{c}\text{Given number of particles}=\frac{\text{Given mass}}{\text{Atomic mass in grams}}\times \text{Avogadro number}\\ =\frac{\text{Atomic mass in grams}}{\text{Atomic mass in grams}}\times \text{6}\text{.022}\times {\text{10}}^{\text{23}}\\ =\text{6}\text{.022}\times {\text{10}}^{\text{23}}\end{array}$

Conclusion

A sample equal to the atomic mass of an element in grams contains $\underset{\_}{\text{6}\text{.022}\times {\text{10}}^{\text{23}}}$ atoms.