Answer
There are 1.2 x $10^{21}$ molecules HCN in 56 mg HCN.
Work Step by Step
We have to convert mass HCN to number of molecules. So the conversion factors needed are two:
conversion factor to mol ( 1 mol/Molar mass) and
conversion factor to number of molecules ( Avogadro's number/ 1 mol ).
First find Molar mass for hydrogen cyanide HCN.
Molar mass HCN = 1 x 1.00 + 1 x 12.01 +1x 14.00
Molar mass HCN = 27.01 g/mol or 27.0 g/mol to three significant numbers.
Find number of molecules that are in 56 mg HCN ( or 56 x $10^{-3}$g HCN :
56 x $10^{-3}$g HCN x $\frac{1 mol (HCN)}{ 27.0 g (HCN)}$ x $\frac{6.02 \times 10^{23}(HCN molecules)}{1 mol(HCN)}$ =
2.0 x $10^{-3}$mol HCN x $\frac{6.02 \times 10^{23}(HCNmolecules)}{1 mol(HCN)}$ = 12.04 x $10^{20}$ molecules HCN.
To three significant numbers 12.0 x $10^{20}$ molecules HCN
Therefore 12.0 x $10^{20}$ molecules HCN or 1.2 x $10^{21}$ molecules HCN are in 56 mg HCN.
