Question

How many atoms are in $7.10$ grams of chlorine atoms?

Answer 1

Hint: We will use the Avogadro number to determine the number of atoms in the given gram. For this first, we have to calculate the moles of chlorine in the given gram. For this, we will use the mole formula. Then by using the Avogadro number we will determine the numbers of atoms.

Formula used: ${\text{mole}}\,\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,\,{\text{mass}}}}$

Complete step by step answer:
We will use the mole formula to determine the number of moles of chlorine as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$

The molar mass of chlorine is $35.45$ g/mol.
On substituting $7.10$ grams for the mass of chlorine and $35.45$for molar mass of chlorine,
$ \Rightarrow {\text{mole}}\,{\text{ = }}\,\dfrac{{7.10}}{{35.45}}$
$ \Rightarrow {\text{mole}}\,{\text{ = }}\,0.20$
So, the moles of the chlorine is $0.20$ mol.

According to the Avogadro, one mole of any substance contains$\,6.02 \times {10^{23}}$ atoms, molecules or ions of that substance. This number $\,6.02 \times {10^{23}}$ is known as Avogadro number.
According to the Avogadro number,
- One mole of any substance = $\,6.02 \times {10^{23}}$ atoms.
- So, one mole =$\,6.02 \times {10^{23}}$ atoms of chlorine
- So, $3.3 \times {10^{ - 3}}$moles of chlorine will have, $0.20$ mole of gold = $\,1.22 \times {10^{23}}$ atoms of chlorine.
$ \Rightarrow \,1.22 \times {10^{23}}$ atoms of chlorine.
So, $\,1.22 \times {10^{23}}$ atoms of chlorine are present in $7.10$ g of chlorine.

Therefore, $\,1.22 \times {10^{23}}$ atoms is the correct answer.

Note: The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. In the case of monoatomic, one mole of a substance contains an Avogadro number of atoms. Chlorine is diatomic gas but here, gram amount of chlorine atom is given so, we calculate the mole of chlorine atoms. The molar mass of chlorine is the sum of the number of protons and neutrons. We can also determine the total number of molecules and ions by using the Avogadro number. For this, we have to multiply the Avogadro with a total number of molecules or ions.