Question

5.6x10-12 l of carbon dioxide gas is equal to how many molecules?

Explanation:

Step1: Use the ideal gas law at standard temperature and pressure (STP)

At STP ($T = 273\ K$, $P= 1\ atm$), 1 mole of any ideal gas occupies $V_m=22.4\ L$.
The number of moles $n$ of a gas is given by $n=\frac{V}{V_m}$, where $V = 5.6\times10^{-12}\ L$ is the volume of $CO_2$ gas.
So, $n=\frac{5.6\times 10^{-12}\ L}{22.4\ L/mol}=2.5\times10^{-13}\ mol$.

Step2: Use Avogadro's number

Avogadro's number $N_A = 6.022\times 10^{23}\ molecules/mol$.
The number of molecules $N$ of $CO_2$ is $N=n\times N_A$.
Substitute $n = 2.5\times10^{-13}\ mol$ and $N_A=6.022\times 10^{23}\ molecules/mol$ into the formula:
$N=(2.5\times 10^{-13}\ mol)\times(6.022\times 10^{23}\ molecules/mol)=1.5055\times 10^{11}\ molecules$.

Answer:

$1.5055\times 10^{11}$ molecules