5.1 The Mole and Avogadro’s Number

Learning Objectives

  • Apply Avogadro’s number ([latex]6.022\times10^{23}[/latex]) to represent large amounts of a species through the mole within chemical contexts.

In speech, we use alternative units to describe amounts of items. For instance, [latex]1[/latex] dozen [latex]=12[/latex] objects, [latex]1[/latex] score [latex]=20[/latex] objects, [latex]1[/latex] ream [latex]=500[/latex] sheets paper, likewise in chemistry, chemist consider: 
[latex]1~\textrm{mole}=6.022\times10^{23}\textrm{objects}[/latex]

There are many interesting units and groupings in science! Leigh Mercer is most often credited with a famous mathematical limerick to assist in remembering rather odd values.

[latex]\frac{12+144+20+3*\sqrt{4}}{7}+(5\times11)=9^2+0[/latex]

A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.

The objects can be anything, such as houses, sand, eggs, oranges, etc. However, in chemistry, the objects we are concerned with are mainly atoms, ions or molecules – objects that are invisible to the naked eye!

One mole of anything contains [latex]6.022\times10^{23}[/latex] objects. For instance, one mole of eggs contains [latex]6.022\times10^{23}[/latex] eggs, one mole of carbon contains [latex]6.022\times10^{23}[/latex] carbon atoms, and one mole of carbon dioxide contains [latex]6.022\times10^{23}[/latex] carbon dioxide molecules.

The symbol of moles is “[latex]mol[/latex]”[1].

A black and white old looking sketch depicting Amedeo Avogadro.
Figure 5.1.1: Amedeo Avogadro – the unit is named after his contributions to chemistry.  Image attribution: Amadeo_Avogadro is licensed under a Public Domain license.
  • Thus, three moles (3 mol) of particles is three times [latex]6.022\times10^{23}[/latex] particles [latex]\left(3\times6.022\times10^{23}\right)[/latex], and ten moles (10 mol) of particles is ten times [latex]6.022\times10^{23}[/latex] particles [latex]\left(10\times6.022\times10^{23}\right)[/latex].
  • If we had [latex]3.011\times10^{24}[/latex] atoms of gold [latex]\left(\ce{Au}\right)[/latex], the number of moles of gold would be: [latex]\ce{n(Au)}=\frac{3.011\times10^{24}\textrm{atoms}}{6.022\times10^{23}\textrm{atoms mole}^{-1}}=5.000\textrm{mol}[/latex]

This exact number is a fundamental SI unit within science. Avogadro’s number [latex]N_A[/latex] is the term used for [latex]6.022\times10^{23}[/latex] objects.

Avogadro’s number is the link between the number of atoms (or molecules or ions) of a material and the number of moles of material. Understanding it allows chemical equations to be represented through the ratios of compounds and particles — enabling us to upscale reactions outside of individual atoms to notable masses and quantities for measurement and experimentation.

 

Key Takeaways

  • 1 mole is considered to be [latex]6.022\times10^{23}[/latex] atoms or molecules (Avogadro’s number).
  • Utilising moles as a unit is important to allow us to talk about specific atomic quantities easily.

 

Exercises

Practice Questions

Transcript

Media Attributions


  1. The plural of mole is moles, but when using it as a unit, there is no need to use mols (just mol; eg. 3 moles = 3 mol).
definition

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