184_notes:examples:week2_moleoelectrons

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184_notes:examples:week2_moleoelectrons [2018/01/18 16:34] – tallpaul184_notes:examples:week2_moleoelectrons [2018/05/17 15:16] (current) – curdemma
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- +[[184_notes:charge|Return to Electric Charge Page]] 
-===== Find the total charge for a mole of electrons =====+===== Example: Find the total charge for a mole of electrons =====
 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 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. We could also write this unit as mol−1=1mol.     * 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⋅10−19 C.   * All electrons have the same charge, which is e=−1.602⋅10−19 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⋅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⋅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⋅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. 
- 
-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} \\
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