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--- 184_notes:examples:week2_moleoelectrons [2017/08/24 17:10] – [Solution] 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 mole = $6.022\cdot10^{23}$ 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...
- $Q=N*e$
- $Q=(6.022*10^{23})*(1.602*10^{19} C)$
- $Q=96472.44 C$