Calculate the number of gold atoms in 300 mg of a gold ring of 20-carat gold.
Calculate the number of gold atoms in 300 mg of a gold ring of 20-carat gold.
We are given that the ring is made up of 20 carrat gold. 20 carrat gold means 20 parts of gold and 4 parts of other metal (usually copper or silver). Thus, the percentage of gold in 20 carrat gold will be
= (20 / 24) X 100
= 83.333 %
We can now calculate the mass of gold in the ring. We are given that the ring weighs 300 mg. So, the mass of gold in ring will be
= (83.333 / 100) X 300
= 250 mg
Thus, the mass of gold in 300 mg of the ring is 250 mg.
Now the molar mass of gold is 197 g. This means that there are 6.023 X 10^23 atoms of gold in 197g of gold. Thus
197g of gold = 6.023 X 10^23 atoms of gold
1g of gold = (6.023 X 10^23 ) / 197 atoms of gold
250 mg or 0.25g of gold = (6.023 X 10^23 X 0.25) / 197 atoms of gold
= 7.643 X 10^20 atoms of gold
We are given that the ring is made up of 20 carrat gold. 20 carrat gold means 20 parts of gold and 4 parts of other metal (usually copper or silver). Thus, the percentage of gold in 20 carrat gold will be
= (20 / 24) X 100
= 83.333 %
We can now calculate the mass of gold in the ring. We are given that the ring weighs 300 mg. So, the mass of gold in ring will be
= (83.333 / 100) X 300
= 250 mg
Thus, the mass of gold in 300 mg of the ring is 250 mg.
Now the molar mass of gold is 197 g. This means that there are 6.023 X 10^23 atoms of gold in 197g of gold. Thus
197g of gold = 6.023 X 10^23 atoms of gold
1g of gold = (6.023 X 10^23 ) / 197 atoms of gold
250 mg or 0.25g of gold = (6.023 X 10^23 X 0.25) / 197 atoms of gold
= 7.643 X 10^20 atoms of gold
