Manufacturers of headache remedies routinely claim that their own brands are more potent pain relievers than the competing brands. Their way of making the comparison is to compare the number of molecules in the standard dosage. Tylenol uses 325 mg of acetaminophen (C8H9NO2) as the standard dose, while Advil uses 2.00 x 102 mg of ibuprofen (C13H18O2). Find the number of molecules of pain reliever in the standard doses of

(a) Tylenol and

(b) Advil.

a) 12.95*10^20 molecules

b) 5.84*10^20 molecules

Explanation:

a) Tylenol

Mass of Tylenol = 325 mg

(m) = 325*10^-3 g

Molecular weight of Tylenol (M) = 151.16256 g/mol

the number of moles present

n = m/M

= 325*10^-3 g / 151.1656 g/mol

= 2.15 * 10^-3 mol

the number of molecules present

N = nNa

= (2.15*10^ - 3 mol) (6.023*10^23 molecules/mol)

N=12.95*10 ^20 molecules

b) Advil

Mass of Advil = 200 mg

m=200*10^-3 g

Molecular weight of Advil (M) = 206.28082 g/mol

the number of moles

n=m/M

=200*10^ - 3 g / 206.28082 g/mol

=0.96955*10^ - 3 mol

the number of molecules resent

N=nNa

= (0.96955*10^ - 3) (6.023*10^ 23 molecules / mol)

N=5.84*10^20 molecules