Question

Chlorophyll contains $2.68$ % of Mg by weight. Then the number of Mg atom in $2.00$ g of chlorophyll is:
(Atomic mass of Mg = $24$)

Answer 1

We will use the Avogadro number to determine the number of atoms of Mg in the given gram of chlorophyll. For this first, we have to calculate the moles of Mg 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 of Mg.

Complete solution:
It is given that chlorophyll contains $2.68$ % of Mg by weight it means in $100$g chlorophyll, $2.68$ g Mg is present so, the amount of Mg present in $2.00$g chlorophyll is,
$100$g chlorophyll = $2.68$ g Mg
$2.00$g chlorophyll = $0.0536$ g Mg
We will use the mole formula to determine the number of moles of Mg as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
Molar mass of Mg is $24$g/mol
On substituting $0.0536$ grams for mass of Mg and $24$for molar mass of Mg,
${\text{mole}}\,{\text{ = }}\,\dfrac{{0.0536}}{{24}}$
${\text{mole}}\,{\text{ = }}\,2.23 \times {10^{ - 3}}$
So, the moles of the Mg present in $2.00$g chlorophyll is$2.23 \times {10^{ - 3}}$ mol.
According to the Avogadro number,
One mole of any substance =$\,6.02 \times {10^{23}}$ atoms
So,
One mole of Mg =$\,6.02 \times {10^{23}}$ atoms of Mg
So, $2.23 \times {10^{ - 3}}$moles of Mg will have,
$\,6.02 \times {10^{23}}\, \times \,2.23 \times {10^{ - 3}}$ atoms of Mg
$1.34 \times {10^{21}}$atoms of Mg
So, the number of Mg atoms is$1.34 \times {10^{21}}$.
Therefore, $1.34 \times {10^{21}}$ is the correct answer.

Note: The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. Here, the number of Mg atoms present in one mole chlorophyll is not given so we assume it as one. If the number of atoms of Mg in a mole of chlorophyll is given then we have to multiply the Avogadro number with the mole of Mg and number of Mg present in one mole of chlorophyll.