Question

How many grams are in $1.25 \times {10^{22}}$ atoms of oxygen?

Answer 1

We can determine the answer by using Avogadro number and mole formula. First, we will use the Avogadro number to determine the number of moles in the given number of atoms. Then we will calculate the mass of oxygen by using mole formula.

Complete solution:
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,
$\,6.02 \times {10^{23}}$ atoms = One mole of any substance
So,
$\,6.02 \times {10^{23}}$ atoms of oxygen = One mole of oxygen
So, $1.25 \times {10^{22}}$atoms of oxygen will have,
$1.25 \times {10^{22}}$ atoms of oxygen =$1.25 \times {10^{22}}/\,6.02 \times {10^{23}}$ mole of oxygen
= $0.021$ mole of oxygen
So, $0.021$moles of oxygen are present in$1.25 \times {10^{22}}$atoms of oxygen.
We will use the mole formula to determine the grams of oxygen as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
The molar mass of oxygen is $16.00$ g/mol.
On substituting $0.021$ mol for the mole of oxygen and $16.00$for molar mass of oxygen atom,
${\text{0}}{\text{.021}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{16.00}}$
${\text{mass}}\, = \,\,{\text{0}}{\text{.021}} \times {\text{16}}{\text{.00}}$
${\text{mass}}\, = \,\,0.332$ gram
So, the mass of oxygen is $0.332$gram.
Therefore, $0.332$ grams are present in $1.25 \times {10^{22}}$ atoms of oxygen.

Note: The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. The molar mass of oxygen 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. In the case of monoatomic, one mole of a substance contains an Avogadro number of atoms.