## 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\quad$0.30 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\quad$151.18 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.