# How many hydrogen atoms are in 4.5 moles of methane molecules?

$\text{Well there are 18 moles of hydrogen atoms..........}$
Instead of $\text{moles}$, I could use $\text{dozens}$ as my metric. How many hydrogen atoms are in $4$ $\frac{1}{2}$ $\text{dozen}$ methane molecules? Well clearly each methane molecule contributes $4$ hydrogen atoms; therefore there are $4 \times 4.5 \times 12 = 216$ $\text{hydrogen atoms}$.
In a $\text{mole}$, $\text{a Chemist's dozen}$, there are $6.022 \times {10}^{23}$ individual particles; ${N}_{A} = 6.022 \times {10}^{23} \cdot m o {l}^{-} 1$.
So in $4.5 \cdot m o l$ of $C {H}_{4}$, there are $4.5 \cdot m o l \times {N}_{A} \times 4$ $\text{hydrogen atoms}$ $=$ $18 \times {N}_{A}$ $\text{hydrogen atoms}$.