Question

19.7 kg of gold was recovered from a smuggler. The atoms of gold recovered are:
A. 100
B. $6.023\times {{10}^{23}}$
C. $6.023\times {{10}^{24}}$
D. $6.023\times {{10}^{25}}$

Answer 1

Hint There is a formula to calculate the number of moles of an element and it is as follows.
Number of moles of an element $\text{=}\dfrac{\text{weight of the element}}{\text{molecular weight of the element}}$
The number of atoms present in one gram of the compound is equal to the Avogadro number of atoms.

Complete step by step answer:
- In the question it is given that to calculate the number of atoms present in the 19.7 kg of gold which is recovered from a smuggler.
- The mass of the given gold is 19.7 kg = (19.7) (1000) = 19700 grams.
- The molecular weight of the gold is 197 g/mol.
- We can calculate the number of moles of the gold by using the below formula from the above data and it is as follows.
Number of moles of gold
\[\begin{align}
&\implies\text{}\dfrac{\text{weight of the gold in grams}}{\text{molecular weight of the gold}} \\
&\implies\dfrac{19700}{197} \\
&\implies100moles \\
\end{align}\]
- Therefore the number of moles of gold present in 19.7 kg of gold is 100 moles.
- Now we can get the number of atoms of gold by multiplying the 100 moles with Avogadro's number and it is as follows.
- The number of atoms of gold present in 100 moles of the gold is
\[\begin{align}
  &\implies\left( 100 \right)\text{ }(6.023\times {{10}^{23}}) \\
 &\implies 6.023\times {{10}^{25}}atoms. \\
\end{align}\]
- Therefore the number of atoms present in 19.7 kg of gold is $6.023\times {{10}^{25}}$ atoms.

- So, the correct option is D.

Note: Whenever we are going to calculate the number of atoms from the moles of the compound we have to multiply the number moles of the particular compound with Avogadro number. We should consider the amount of the compound in grams while calculating the number of moles.