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| 184_notes:examples:week2_moleoelectrons [2018/01/18 16:34] – tallpaul | 184_notes:examples:week2_moleoelectrons [2018/05/17 15:16] (current) – curdemma | ||
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| - | + | [[184_notes: | |
| - | ===== Find the total charge for a mole of electrons ===== | + | ===== 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? | ||
| - | |||
| - | ====Solution==== | ||
| ===Facts=== | ===Facts=== | ||
| - | * The Avogadro constant is $N_A = 6.022 \cdot 10^{23} \text{ mol}^{-1}$ | + | * 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. We could also write this unit as $mol^{-1}=\frac{1}{mol}$. | * 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 $e = -1.602\cdot10^{-19} \text{ C}$. | ||
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| * Find the amount of charge in 1 mole of electrons. | * 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 $N$: | 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*} | ||
| - | |||
| - | |||
| - | --- | ||
| - | ===Approximations & Assumptions=== | ||
| - | * None, we have all the information we need. | ||
| - | |||
| - | ===Representations=== | ||
| - | * The total number of particles $N$ can be found from the number of moles $m$ using the Avogadro constant: $N = m \cdot N_A$. | ||
| - | * The total charge $Q$ can be written as the number of particles $N$ times the charge of each particle ($e$, for electrons): $Q=N\cdot e$. | ||
| - | |||
| - | The total number of electrons $N$ is given by | ||
| \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} \\ | ||