Question

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.

Answer 1

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

Answer 2

Tylenol contains more molecules of active ingredient hence it is a more effective drug.

We have to find the number of molecules in each of the drugs. In the drug, tylenol, the molar mass of the compound C8H9NO2 is;

8(12) + 9(1) + 14 + 2(16) = 96 + 9 + 14 + 32 =151 g/mol

Number of moles = 325 × 10^-3 g/151 g/mol = 0.0022 moles

1 mole contains 6.02 × 10^23 molecules

0.0022 moles contains  0.0022 moles ×  6.02 × 10^23 molecules /1 mole = 1.32 × 10^21 molecules

For Advil;

Molecular mass= 13(12) + 18(1) + 2(16) = 156 + 18 + 32 = 206 g/mol

Number of moles = 0.2 g/ 206 g/mol = 0.00097 moles

1 mole contains 6.02 × 10^23 molecules of advil

0.00097 moles contains  0.00097 moles × 6.02 × 10^23 molecules /1 mole = 5.8  × 10^20

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