Question

Find the number of copper atoms present in $10g$ of $22$ carat gold. ($22$ carat gold means $22$ out of $24$ is gold and rest is copper) Atomic mass of copper =$63.5u$)

Answer 1

The gold containing $24$ carat is referred to as $100\%$ pure. The gold containing $22$ carat gold is the gold which is mixed with certain alloys and impurities.

Complete answer:
As per question the impurities present in $22$ carat gold is copper. The mole of copper is to be determined to find the number of copper atoms.
According to Avogadro’s law, one mole of a substance contains $6.023 \times {10^{23}}$ number of atoms. So the number of moles of copper multiplied by the Avogadro’s number gives the number of copper atoms present in $22$ carat gold.
At first the percentage of copper present in $22$ carat gold is calculated as below:
Percentage of copper in $22$ carat gold = $\dfrac{{24 - 22}}{{24}} \times 100 = \dfrac{1}{{12}}$.
The weight of $22$ carat gold given here is $10g$. Thus the mass of copper present in $10g$ = $\dfrac{1}{2} \times 10 = \dfrac{{10}}{{12}}g$ The moles of copper = $\dfrac{{weight{\text{ }}or{\text{ }}mass{\text{ }}of{\text{ }}copper}}{{molar{\text{ }}mass{\text{ }}of{\text{ }}copper}} = \dfrac{{\dfrac{{10}}{{12}}}}{{63.5}} = 0.013{\text{ }}mole$
Thus the number of copper atoms in $\dfrac{{10}}{{12}}g$ g of copper = number of mole of copper × Avogadro's number
= $0.013 \times 6.023 \times {10^{23}}$
= $7.9 \times {10^{21}}$ atoms.

Note: A mole of a substance is equivalent to the amount of substance which contains the exact $6.023 \times {10^{23}}$ number of atoms in that substance. Molar mass is defined as that mass of the substance present in one mole of the substance. Gram atomic mass is the mass of one mole of the element and Gram molecular mass is the mass of one mole of a compound.