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| 184_notes:examples:week2_moleoelectrons [2017/08/24 17:24] – [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 NA=6.022⋅1023 mol−1 | + | * The Avogadro constant is NA=6.022⋅1023 mol−1. This is easy to look up, which is what we did. |
| - | * Note: When we write the unit as mol−1, we mean particles per mole. | + | * Note: When we write the unit as mol−1, we mean particles per mole. We could also write this unit as mol−1=1mol. |
| - | * 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⋅10−19 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 number of particles N can be found from the number of moles m using the Avogadro constant: N=m⋅NA. | ||
| - | * The total charge Q can be written as the number of particles N times the charge of each particle (e, for electrons): Q=N⋅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⋅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} \\ | ||
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| 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*} | ||