Question

Find the total number of atoms in a sample of cocaine hydrochloride, C17H22ClNO4, of mass 24.0 mg ?

Find the total number of atoms in a sample of cocaine hydrochloride, C17H22ClNO4, of mass 24.0 mg .

Answer 1

`4.25*10^19 \ "molecules of" \ C_17H_22ClNO_4`

Explanation:

We first need to convert that amount into moles.

Cocaine hydrochloride `(C_17H_22ClNO_4)` has a molar mass of `339.816 \ "g/mol"`.

Now, we need to convert `24 \ "mg"` into `"g"`.

We know that `1 \ "g"=1*10^3 \ "mg"`

`:.24 \ "mg" = 24*10^-3 \ "g"`

So, there are approximately

`(24*10^-3cancel"g")/(339.816cancel"g""/mol")=7.06*10^-5 \ "mol of" \ C_17H_22ClNO_4`

In one mole of molecules, there exist `6.02*10^23` molecules.

Therefore in here, there exists a total of

`7.06*10^-5*6.02*10^23~~4.25*10^19 \ "molecules of" \ C_17H_22ClNO_4`