Chapter 10, Problem 100A

Interpretation Introduction

Interpretation:

The time taken to count one mole of atoms should be calculated when two atoms are counted every second. The calculated time should be compared with the age of earth that is $4.5\times {10}^9\text{ years old}$.

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

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

Answer to Problem 100A

Time taken to count one mole of atoms = $9.54487\times {10}^{15}\text{ years}$.

$9.54487\times {10}^{15}\text{ years}$ is $2.12\times {10}^6$ times the age of earth.

Explanation of Solution

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

It is given that; two atoms are counted every second.

Therefore, time taken to count one mole of atoms = $6.022\times {10}^{23}\text{ atoms}\times \frac{1\text{ s}}{2\text{ atoms}}$

= $3.011\times {10}^{23}\text{ s}$

Now, convert the seconds in year.

Since, 1 second = $3.17\times {10}^{-8}\text{ year}$

Number of seconds in a year = $3.011\times {10}^{23}\text{ s}\times \frac{3.17\times {10}^{-8}\text{ year}}{1\text{ s}}$

= $9.54487\times {10}^{15}\text{ year}$

Thus, the time taken to count one mole of atoms = $9.54487\times {10}^{15}\text{ years}$

The age of earth = $4.5\times {10}^9\text{ years old}$

$9.54487\times {10}^{15}\text{ years}$ is required to count one mole of atoms which is $2.12\times {10}^6$ times the age of earth.