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184_notes:examples:week2_moleoelectrons [2017/08/24 17:11] – [Example: How much total charge is in one mole of electrons?] tallpaul | 184_notes:examples:week2_moleoelectrons [2018/05/17 15:16] – curdemma | ||
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- | + | [184_notes: | |
- | ===== Example: | + | ===== Example: |
- | How much total charge (in coulombs) is in one mole ($n=6.022*10^{23} \text{ particles/ | + | How much total charge (in coulombs) is in one mole of electrons? |
===Facts=== | ===Facts=== | ||
- | * $1 \text{ mol} = 6.022 \cdot 10^{23} \text{ particles}$ | + | * The Avogadro constant is $N_A = 6.022 \cdot 10^{23} \text{ |
- | * All electrons have the same charge, which is $e$ = $-1.602\cdot10^{-19} \text{ C}$. | + | * Note: When we write the unit as $\text{ mol}^{-1}$, we mean particles |
+ | * 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 charge $Q$ 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*} | ||
+ | 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*} | \begin{align*} | ||
Q &= N \cdot e \\ | Q &= N \cdot e \\ | ||
- | & | + | & |
- | & | + | & |
\end{align*} | \end{align*} | ||
- | The number of electrons in one mole is obtained by multiplying the number of moles by Avogodro' | ||
- | $$N=(1 mole)*6.022*10^{23}$$ | ||
- | $$N=6.022*10^{23} electrons$$ | ||
- | Therefore, the total charge $Q$ is given by... | ||
- | $$Q=N*e$$ | ||
- | $$Q=(6.022*10^{23})*(1.602*10^{19} C)$$ | ||
- | $$Q=96472.44 C$$ |