# The Mole and Avogadro's Constant

A LevelAS LevelAQA

## The Mole and Avogadro’s Constant

One mole of a substance contains $6.02\times10^{23}$ particles. This number is known as Avogadro’s constant. Avogadro’s constant can be used to work out how many particles there are in a particular amount of moles.

## Key Definitions

Relative Atomic Mass: The average mass of an atom of an element when compared to 1/12th of the mass of an atom of carbon-12.

Relative Molecular Mass: The average mass of a molecule when compared to 1/12th of the mass of an atom of carbon-12.

A LevelAS LevelAQA

## Moles, Mass and Mr

The number of moles of a substance can be calculated using the mass and molar mass ($\text{M}_\text{r}$) of the substance.

Equation:

$\text{Moles}= \dfrac{\text{Mass}}{\text{M}_\text{r}}$

$\text{Moles: mol} \text{Mass: g} \text{M}_\text{r}\text{: g mol}^{-1}$

Mr is calculated by adding up all the mass numbers of the elements in a molecule/ compound.

Example: Calculate the number of moles in $15.0\text{ g}$ of $\text{KNO}_3$.

$\text{Moles}= \dfrac{\text{Mass}}{\text{M}_\text{r}}$

$\text{Moles}= \dfrac{15}{39.1+14+\left(16\times3\right)} = \dfrac{15}{101.1} = 0.148 \text{ mol}$

Note: Always put your answer to the same number of significant figures as are in the question.

A LevelAS LevelAQA

## Unit Conversions

Sometimes, you may be given a mass that is not in grams and you will need to convert between the different units.

Example: Calculate the moles of $\textcolor{#00bfa8}{83\text{ mg}}$ of $\text{Mg}\left(\text{OH}\right)_{2}$.

\begin{aligned}&\text{Mass in g} = \dfrac{\textcolor{#00bfa8}{83}}{1000}= \textcolor{#008d65}{0.083\text{ g}}\\&\text{Moles} =\dfrac{\text{Mass}}{\text{M}_{\text{r}}}\\ &\text{Moles} = \dfrac{0.083}{24.3+\left(2\times\left(16+1\right)\right)} = \dfrac{\textcolor{#00bfa8}{0.083}}{58.3}= \textcolor{#008d65}{1.4\times10^{-3}}\text{ mol}\end{aligned}

A LevelAS LevelAQA

Avogadro’s constant is the number of particles in one mole of substance.

$\text{Avogadro's Constant}=6.02 \times10^{23}$

The relationship between the number of moles, number of particles and Avogadro’s constant is represented in the equation:

$\text{Moles} = \dfrac{\text{Number of particles}}{\text{Avogadro's Constant}}$

Particles can be anything such as atoms, ions and molecules.

Example: Calculate the number of molecules in $\textcolor{#00bfa8}{0.0056}$ moles of water.

\begin{aligned}\text{Moles} &= \dfrac{\text{Number of particles}}{\text{Avogadro's Constant}}\\\text{Number of particles}& = \text{Moles}\times\text{Avogadro's Constant}\\ \text{Number of particles} &= \textcolor{#00bfa8}{0.0056}\times6.02\times10^{23}\\ &= \textcolor{#008d65}{3.37\times10^{21}\text{ molecules}}\end{aligned}

A LevelAS LevelAQA

## Example 1: Calculating Mass of a Substance

Calculate the mass of $\textcolor{#00bfa8}{0.036 \text{ moles}}$ of $\text{NaCl}$.

[2 marks]

\begin{aligned}&\text{Moles}= \dfrac{\text{Mass}}{\text{M}_\text{r}}\\&\text{Mass}=\text{Moles}\times\text{M}_\text{r}\\&\text{Mass}=\textcolor{#00bfa8}{0.036}\times\left(23+35.5\right) = 0.036\times58.5= \textcolor{#008d65}{2.11\text{ g}}\end{aligned}

A LevelAS LevelAQA

## Example 2:Calculating Moles of a Substance

Calculate the number of moles in $\textcolor{#00bfa8}{28.6\text{ g}}$ of $\text{CuSO}_{4}.5\text{H}_{2}\text{O}$.

[2 marks]

\begin{aligned}\text{Moles}&= \dfrac{\text{Mass}}{\text{M}_\text{r}}\\&= \dfrac{\textcolor{#00bfa8}{28.6}}{63.5+32.1+\left(16\times4\right)+\left(5\times\left(2+16\right)\right)}\\&=\dfrac{\textcolor{#00bfa8}{28.6}}{249.6}\\&=\textcolor{#008d65}{0.115\text{ mol}}\end{aligned}

A LevelAS LevelAQA

## The Mole and Avogadro's Constant Example Questions

$\text{Mass in g}=0.0347\times1000=34.7\text{g}$

$\text{Moles} =\dfrac{\text{Mass}}{\text{M}_{\text{r}}}$

$\text{Moles}= \dfrac{34.7}{159.6}$

$\text{Moles}= 0.217\text{ mol}$

Gold Standard Education

$\text{Moles} = \dfrac{\text{Number of particles}}{\text{Avogadro's Constant}}$

$\text{Moles} = \dfrac{3.23\times10^{23}}{6.02\times10^{23}}$

$\text{Moles} =0.536$

Gold Standard Education

$\text{Mass in g}= \dfrac{93}{1000}= 0.093\text{ g}$

$\text{Moles}=\dfrac{\text{Mass}}{\text{M}_{\text{r}}}= \dfrac{0.093}{233.4}$

$\text{Moles}= 3.98\times10^{-4}$

$\text{Moles} = \dfrac{\text{Number of particles}}{\text{Avogadro's Constant}}$

$\text{Number of atoms}= \text{Moles}\times\text{ Avogadro's Constant}$

$\text{Number of atoms}= 3.98\times10^{-4}\times6.02\times10^{23}= 2.4\times10^{20}$

Gold Standard Education

Product

### £19.99

/month

Learn an entire GCSE course for maths, English and science on the most comprehensive online learning platform. With revision explainer videos & notes, practice questions, topic tests and full mock exams for each topic on every course, it’s easy to Learn and Revise with the MME Learning Portal.