## Q. 6.2

How many objects are there in each of the following quantities?
a. 0.23 mole of aspirin molecules         b. 1.6 moles of oxygen atoms

## Verified Solution

Dimensional analysis (Section 2.8) will be used to solve each of these problems. Both of the problems are similar in that we are given a certain number of moles of substance and want to find the number of objects present in the given number of moles. We will need Avogadro’s number to solve each of these moles-to-particles problems.
$\quad\quad\quad\quad \boxed{\ Moles of\\ Substance}\xrightarrow[involving Avogadro’s number]{Conversion factor}\boxed{Particles of\\ Substance}$
a. The objects of concern are molecules of aspirin. The given quantity is 0.23 mole of aspirin molecules, and the desired quantity is the number of aspirin molecules.
$\quad\quad\quad\quad$0.23 mole aspirin molecules = ? aspirin molecules
Applying dimensional analysis here involves the use of a single conversion factor, one that relates moles and molecules.
$\quad\quad\quad\quad 0.23 \cancel{ mole aspirin molecules}\times (\frac{6.02\times 10^{23} aspirin molecules}{1 \cancel{ mole aspirin molecules}})\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad =1.4\times 10^{23}$ aspirin molecules
b. This time we are dealing with atoms instead of molecules. This switch does not change the way we work the problem. We will need the same conversion factor.
$\quad\quad$The given quantity is 1.6 moles of oxygen atoms, and the desired quantity is the actual number of oxygen atoms present.
$\quad\quad\quad\quad$1.6 moles oxygen atoms = ? oxygen atoms
The setup is
$\quad\quad\quad\quad 1.6 \cancel{moles oxygen atoms}\times (\frac{6.02\times 10^{23} oxygen atoms}{1 \cancel{mole oxygen atoms}})\\\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad =9.6\times 10^{23}$ oxygen atoms