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| 184_notes:examples:week2_moleoelectrons [2017/08/24 17:19] – [Example: How much total charge is in one mole of electrons?] tallpaul | 184_notes:examples:week2_moleoelectrons [2018/05/17 15:16] (current) – curdemma | ||
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| - | + | [[184_notes: | |
| - | ===== Example: | + | ===== Example: |
| How much total charge (in coulombs) is in one mole of electrons? | How much total charge (in coulombs) is in one mole of electrons? | ||
| ===Facts=== | ===Facts=== | ||
| - | * The Avogadro constant is $6.022 \cdot 10^{23} \text{ mol}^{-1}$ | + | * 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. | + | * 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 $e$ = $-1.602\cdot10^{-19} \text{ C}$. | + | * All electrons have the same charge, which is $e = -1.602\cdot10^{-19} \text{ C}$. |
| - | ===Lacking=== | + | ===Goal=== |
| - | * Total Charge | + | * Find the amount of charge in 1 mole of electrons. |
| - | ===Approximations & Assumptions=== | ||
| - | * None here, we have all the information we need. | ||
| - | ===Representations=== | ||
| - | * The total charge $Q$ can be written as the number of particles $N$ times the charge of each particle ($e$, for electrons): $Q=N\cdot e$. | ||
| ====Solution==== | ====Solution==== | ||
| - | The total number of electrons $N$ is given by | + | 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*} | \begin{align*} | ||
| N &= 1 \text{ mol} \cdot 6.022 \cdot 10^{23} \text{ mol}^{-1} \\ | N &= 1 \text{ mol} \cdot 6.022 \cdot 10^{23} \text{ mol}^{-1} \\ | ||
| &= 6.022 \cdot 10^{23} | &= 6.022 \cdot 10^{23} | ||
| \end{align*} | \end{align*} | ||
| - | The total charge $Q$ is given by | + | We now have $N$ and $e$. The total charge $Q$ is then given by |
| \begin{align*} | \begin{align*} | ||
| Q &= N \cdot e \\ | Q &= N \cdot e \\ | ||
| &= 6.022 \cdot 10^{23} \cdot -1.602 \cdot 10^{-19} \text{ C} \\ | &= 6.022 \cdot 10^{23} \cdot -1.602 \cdot 10^{-19} \text{ C} \\ | ||
| - | &= 9.647 \cdot 10^4 \text{ C} | + | & |
| \end{align*} | \end{align*} | ||