Question

calculate the no of gold atom in 300mg of a gold ring of 20 carat gold (atomic mass of gold =197,pure gold is 24 carat)

Answer 1

∵ 300mgof a gold ring is 20 of 20 Carat . It means in 300 mg ring , 20 part is pure gold and 4 part is other metal.
∴ weight of pure gold in 300mg =300 × (20/24) × 100 = 250mg

Now, weight of pure gold = 250mg = 0.25g
molecular weight of pure gold = 197g/mol
∴ mole = weight of gold/molecular weight of gold
= 0.25/197

Now, number of gold atoms = number of mole of gold × 6.023 × 10²³
= 0.25/197 × 6.023 × 10²³
= 7.64 × 10²⁰

Answer 2

197g of gold contains 6.02 *10^23 atoms.

So,300/1000g contains 6.02*10^23/197 x 300/1000

=0.0916*10^22 atoms.

So,24 carat gold contains 9.16x10^20 atoms

Likewise, 20 carat contains 9.16 x10^20/24 *20

=7.6*10^20.

Hope this will consume less time.