# How would you estimate the number of gas molecules in one cubic meter of air in the classroom on an average day?

May 11, 2016

We would use the molar volume of an ideal gas at $\text{SLC}$ as an approximation. There are are approx 41 moles of air, thus $41 \cdot m o l \times {N}_{A}$ $=$ $\text{number of gas molecules}$

#### Explanation:

Given the molar volume, we know that 1 mole of an ideal gas occupies $24.5 \cdot L$ at $\text{SLC}$, i.e. the molar volume is $24.5 \cdot L \cdot m o {l}^{-} 1$.

Knowing that $1$ ${m}^{3}$ $=$ $1000 \cdot L$ we simply divide this quantity by the first:

$\text{Number of moles}$ $=$ $\frac{1000 \cdot L}{24.5 \cdot L \cdot m o {l}^{-} 1}$ $=$ $41 \cdot \text{moles}$

Each mole of gas contains ${N}_{A}$ gas molecules, whose behaviour is assumed to be ideal.

Thus, $\text{number of gas molecules}$ $41 \cdot m o l \times {N}_{A}$ $=$ $41 \cdot m o l \times 6.022 \times {10}^{23} \cdot m o {l}^{-} 1$ .