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## Example: Find the total charge for a mole of electrons

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 $e = -1.602\cdot10^{-19} \text{ C}$.

#### 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{align*} N &= 1 \text{ mol} \cdot 6.022 \cdot 10^{23} \text{ mol}^{-1} \\ &= 6.022 \cdot 10^{23} \end{align*} We now have $N$ and $e$. The total charge $Q$ is then given by \begin{align*} 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{align*}