Chapter 10, Problem 115A

Interpretation Introduction

Interpretation:

The number of atoms of silver present in sample having mass $1\times {10}^{-8}\text{ g}$ should be calculated.

Concept introduction:

Number of moles of a compound is defined as the ratio of given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{mass of the compound}}{\text{molar mass of the compound}}$

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

Answer to Problem 115A

The number of atoms of silver present in sample is $0.056\times {10}^{15}\text{ atoms}$.

Explanation of Solution

The mathematical expression for the calculation of number of moles is given by:

Number of moles = $\frac{\text{mass of the compound}}{\text{molar mass of the compound}}$

Molar mass of silver = 107.868 g/mole

Mass of silver = $1\times {10}^{-8}\text{ g}$

Put the values,

Number of moles = $\frac{\text{mass of the compound}}{\text{molar mass of the compound}}$

Number of moles = $\frac{\text{1}\times {\text{10}}^{-8}\text{ g}}{\text{107}\text{.868 g/mole}}$

Number of moles of silver = $0.0093\times {10}^{-8}\text{ mole}$

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

Thus, the number of atoms of silver present in sample

= $0.0093\times {10}^{-8}\text{ mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

= $0.056\times {10}^{15}\text{ atoms}$