Question

In a particular mass of kau(cn)2, there are 6.66 × 1020 atoms of gold. What is the total number of atoms in this sample?

Answer 1

Total number of atoms in the sample is the sum of number of atoms of all the elements present in the sample.

Number of gold, $Au$ atoms in $KAu(CN)_2$ = $6.66\times 10^{20}$ atoms     (given)

From the formula of compound that is $KAu(CN)_2$ it is clear that the number of potassium and gold are same whereas those of carbon and nitrogen are 2 times of them.

So, the number of atoms of each element is:

Number of potassium, $K$ atoms in $KAu(CN)_2$ = $6.66\times 10^{20}$ atoms    

Number of carbon, $C$ atoms in $KAu(CN)_2$ = $2\times6.66\times 10^{20}$ atoms = $13.32\times 10^{20}$

Number of nitrogen, $N$ atoms in $KAu(CN)_2$ = $2\times6.66\times 10^{20}$ atoms = $13.32\times 10^{20}$

Total number of atoms in $KAu(CN)_2$ = Number of gold, $Au$ atoms+Number of potassium, $K$ atoms +Number of carbon, $C$ atoms + Number of nitrogen, $N$ atoms

Total number of atoms in $KAu(CN)_2$ = $6.66\times 10^{20}+6.66\times 10^{20}+13.32\times 10^{20}+13.32\times 10^{20}$

Total number of atoms in $KAu(CN)_2$ = $39.96\times 10^{20}$ atoms

Hence, the total number of atoms in $KAu(CN)_2$ is $3.996\times 10^{21}$ atoms.