Example: Find the total charge for a mole of electrons
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How much total charge (in coulombs) is in one mole of electrons?
Facts
- The Avogadro constant is $N_{A} = 6.022 \cdot 10^{23}\text{~mol}^{- 1}$. This is easy to look up, which is what we did.
- Note: When we write the unit as $\text{~mol}^{- 1}$, we mean particles per mole. We could also write this unit as $mol^{- 1} = \frac{1}{mol}$.
- All electrons have the same charge, which is $e = - 1.602 \cdot 10^{- 19}\text{~C}$.
Goal
- Find the amount of charge in 1 mole of electrons.
Solution
The total charge $Q$ can be written as the number of particles $N$ times the charge of each particle ($e$, for electrons): $Q = N \cdot e$. We know $e$, and since we know we are interested in exactly 1 mole, we can find $N$:
$$ \begin{matrix} N & = 1\text{~mol} \cdot 6.022 \cdot 10^{23}\text{~mol}^{- 1} \\ & = 6.022 \cdot 10^{23} \end{matrix} $$We now have $N$ and $e$. The total charge $Q$ is then given by
$$ \begin{matrix} Q & = N \cdot e \\ & = 6.022 \cdot 10^{23} \cdot - 1.602 \cdot 10^{- 19}\text{~C} \\ & = - 9.647 \cdot 10^{4}\text{~C} \end{matrix} $$