# Question 0c399

Jan 28, 2016

$2.09 \cdot {10}^{- 5}$

#### Explanation:

A mole of molecules is simply a very large collection of molecules. In order to have one mole of oxygen molecules, you need to have exactly $6.022 \cdot {10}^{23}$ molecules of oxygen.

This very large number, which is known as Avogadro's number, allows you to convert from moles of a substance to molecules of a substance.

In your case, the problem tells you that you have a total of $1.26 \cdot {10}^{19}$ molecules of oxygen gas, ${\text{O}}_{2}$. Right from the start, you can compare this number to Avogadro's number and say that this many molecules will amount to significantly less than one mole, since

$1.26 \cdot {10}^{19} < 6.022 \cdot {10}^{23}$

To determine exactly how many moles of oxygen you have, use Avogadro's number as a conversion factor

1.26 * 10^(19) color(red)(cancel(color(black)("molecules O"_2))) * overbrace("1 mole O"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules O"_2)))))^(color(blue)("Avogadro's number")) = color(green)(2.09 * 10^(-5)"moles O"_2)#

Alternatively, you can express this number in standard notation to get

$n = \textcolor{g r e e n}{{\text{0.0000209 moles O}}_{2}}$

The answer is rounded to three sig figs, the number of sig figs you have for the number of molecules of oxygen.