Answer
The simplest formula of cocaine is $C_{17}H_{21}NO_{4}$.
Work Step by Step
Recall that the definition of percent composition by mass is the mass of a component divided by the mass of the entire system. Therefore, in a 100 g sample of cocaine, there is 67.30 g of C, 6.930 g of H, 21.15 g of O, and 4.62 g of N.
Now let's calculate the number of moles of each element in the sample.
$ n(C)=\frac{m(C)}{M(C)}=\frac{67.30}{12.01}$ mol $= 5.604 $ mol
$ n(H)=\frac{m(H)}{M(H)}=\frac{6.930}{1.008}$ mol $= 6.875 $ mol
$ n(O)=\frac{m(O)}{M(O)}=\frac{21.15}{16.00}$ mol $= 1.322 $ mol
$ n(N)=\frac{m(N)}{M(N)}=\frac{4.62}{14.01}$ mol $= 0.330 $ mol
The next step is to divide those numbers by the smallest one of them and round the results to whole numbers.
$N(C)=\frac{n(C)}{n(N)}=17$
$N(H)=\frac{n(H)}{n(N)}=21$
$N(O)=\frac{n(O)}{n(N)}=4$
$N(N)=\frac{n(N)}{n(N)}=1$
The simplest formula of cocaine is $C_{17}H_{21}NO_{4}$.
