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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] (current) – curdemma
@@ Line 1: / Line 1: @@
+[[184_notes:charge|Return to Electric Charge Page]]
-===== Example: How much total charge is in one mole of electrons? =====
+===== Example: Find the total charge for a mole of electrons =====
-How much total charge (in coulombs) is in one mole ($n=6.022*10^{23} \text{ particles/mole}$) of electrons?
+How much total charge (in coulombs) is in one mole of electrons?
 ===Facts===
-  * $1 \text{ mol} = 6.022 \cdot 10^{23} \text{ particles}$
+  * 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.
-  * 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 per mole. We could also write this unit as $mol^{-1}=\frac{1}{mol}$.
+  * All electrons have the same charge, which is $e = -1.602\cdot10^{-19} \text{ C}$.
-===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====
-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*}
 Q &= N \cdot e \\
-  &= 1 \text{ mol} \cdot 1.602*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*}
-The number of electrons in one mole is obtained by multiplying the number of moles by Avogodro's number.
-$$N=(1 mole)*6.022*10^{23}$$
-$$N=6.022*10^{23} electrons$$
-Therefore, the total charge $Q$ is given by...
-$$Q=N*e$$
-$$Q=(6.022*10^{23})*(1.602*10^{19} C)$$
-$$Q=96472.44 C$$