Q.Given that $1\ \text{mol}$ of an ideal gas occupies $22.4$ litres at STP and Avogadro's number is $6.022 \times 10^{23}\ \text{mol}^{-1}$, find the number of molecules present in $1\ \text{cm}^3$ of the gas at STP.

One mole occupies $22.4\ \text{litres} = 22{,}400\ \text{cm}^3$ at STP and contains $N_A = 6.022\times 10^{23}$ molecules. The number of molecules per $\text{cm}^3$ is therefore

$\frac{N_A}{22{,}400\ \text{cm}^3} = \frac{6.022\times 10^{23}}{2.24\times 10^{4}} \approx 2.69\times 10^{19}\ \text{molecules/cm}^3$ …

Convert the molar volume from litres to $\text{cm}^3$, then divide Avogadr …

• Forgetting to convert $22.4$ litres to $22{,}400\ \text{cm}^3$ (a factor-of-$1000$ error, since $1\ \text{litre}=1000\ \text{cm}^3$). …