Question

The number of gold atoms in 300 mg of a gold ring of 20-carat gold ($Au=197$: pure gold is 24 carat) is:

• A. $4.5\times {10}^{20}$
• B. $6.8\times {10}^{15}$
• C. $7.6\times {10}^{20}$
• D. $9.5\times {10}^{20}$

Answer 1

Answer: (C)

$7.6\times {10}^{20}$

We have given in question: $300mg$ of a gold ring is $20of24Carat$.

It means in $300mg$ ring has $20$ part is pure gold and $4$ part is other metal.

$\therefore$ Weight of pure gold in $300mg=300\times \left(\frac{20}{24}\right)\times 100=250mg$

Now, weight of pure gold $=250mg=0.25g$
The molecular weight of pure gold $=197g/mol$

$\therefore mole=\frac{weightofgold}{molecularweightofgold}$

$=\frac{0.25}{197}$

Now,

$numberofgoldatoms=numberofmoleofgold\times 6.023\times {10}^{23}$

$=\frac{0.25}{197}\times 6.023\times {10}^{23}$

$=7.64\times {10}^{20}$

Option $C$ is correct.