Answer
The simplest formula of the compound: $C_8H_{11}O_3N_1$
Work Step by Step
Let's assume that we have 100g of norepinephrine.
$mass carbon=Total mass\times percent composition=100\times\frac{56.8}{100}=56.8g$
$mass hydrogen=Total mass\times percent composition=100\times\frac{6.56}{100}=6.56g$
$mass oxygen=Total mass\times percent composition=100\times\frac{28.4}{100}=28.4g$
$mass nitrogen=Total mass\times percent composition=100\times\frac{8.28}{100}=8.28g$
We can then calculate the number of moles of each element using the formula:
$Number of moles=\frac{mass}{molecular mass}$
$Number of moles of carbon=\frac{56.8}{12}\approx4.733mol$
$Number of moles of hydrogen=\frac{6.56}{1}=6.56mol$
$Number of moles of oxygen=\frac{28.4}{16}=1.775mol$
$Number of moles of nitrogen=\frac{8.28}{14}\approx0.5914mol$
To find the number of atoms of each element in the compound simplest formula we divide each element's number of moles with the lowest element number of moles:
Number of carbon atoms=$\frac{number of molesofcarbon}{number of moles of nitrogen}=\frac{4.733}{0.5914}\approx8$
Number of hydrogen atoms=$\frac{number of molesofhydrogen}{number of moles of nitrogen}=\frac{6.56}{0.5914}\approx11$
Number of oxygen atoms=$\frac{number of molesofoxygen}{number of moles of nitrogen}=\frac{1.775}{0.5914}\approx3$
The simplest formula of epinephrine contains 8 carbon 11 hydrogen 3 oxygen and 1 nitrogen.
The simplest formula: $C_8H_{11}O_3N_1$
