Question

How many gold atoms are contained in $0.650$ grams of gold?

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 gold 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.

Complete solution:
We will use the mole formula to determine the number of moles of gold as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
The molar mass of gold is $196.96$ g/mol.
On substituting $0.650$ grams for the mass of gold and $196.96$for molar mass of gold,
${\text{mole}}\,{\text{ = }}\,\dfrac{{0.650}}{{196.96}}$
${\text{mole}}\,{\text{ = }}\,3.3 \times {10^{ - 3}}$
So, the moles of the gold is$3.3 \times {10^{ - 3}}$.
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 gold
So, $3.3 \times {10^{ - 3}}$moles of gold will have,
$3.3 \times {10^{ - 3}}$mole of gold =$\,6.02 \times {10^{23}}\, \times \,3.3 \times {10^{ - 3}}$ atoms of gold
=$\,1.98 \times {10^{21}}$ atoms of gold
So, $\,1.98 \times {10^{21}}$ atoms of gold are present in $0.650$ g of gold.

Therefore, $\,1.98 \times {10^{21}}$ 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. Gold is monoatomic. In molecules, the subscript after each atom represents the numbers of that atom. The superscript represents the charge of an ion not the number of that ion. 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.