Chapter 6

Q. 6.3

Acetaminophen, the pain-killing ingredient in Tylenol formulations, has the formula C_{8}H_{9}O_{2}N. Calculate the mass, in grams, of a 0.30-mole sample of this pain reliever.


Verified Solution

We will use dimensional analysis to solve this problem. The relationship between molar mass and formula mass will serve as a conversion factor in the setup of this problem.
\quad\quad\quad\quad \boxed{\ Moles  of\\ Substance}\xrightarrow[involving  molar  mass]{Conversion  factor}\boxed{Grams  of\\ Substance}
The given quantity is 0.30 mole of C_{8}H_{9}O_{2}N, and the desired quantity is grams of this same substance.
\quad\quad\quad\quad0.30 mole C_{8}H_{9}O_{2}N= ? grams C_{8}H_{9}O_{2}N
The calculated formula mass of C_{8}H_{9}O_{2}N is 151.18 amu. Thus,
\quad\quad\quad\quad151.18 grams C_{8}H_{9}O_{2}N = 1 mole C_{8}H_{9}O_{2}N
With this relationship in the form of a conversion factor, the setup for the problem becomes
\quad\quad\quad\quad 0.30  \cancel{moles  C_{8}H_{9}O_{2}N}\times (\frac{151.18  g  C_{8}H_{9}O_{2}N}{1  \cancel{moles  C_{8}H_{9}O_{2}N}})=45  C_{8}H_{9}O_{2}N

Molar masses are conversion factors between grams and moles for any substance. Because the periodic table is the usual source of the atomic masses needed to calculate molar masses, the periodic table can be considered to be a useful source of conversion factors.