The Mole

The Mole and Avogadro's Constant

Avogadro's constant: $6.02 \times 10^{23}$ , representing the number of particles (atoms, molecules, or ions) in one mole of any substance.
Particles may be atoms (for elements) or molecules (for compounds).
The mole (mol) is the SI unit for the amount of substance.
One mole contains exactly Avogadro's number of particles.

Standard Temperature and Pressure (STP)

Standard temperature and pressure (STP) are conditions used as a reference for gas calculations.
- Temperature: 273 K (0°C)
- Pressure: 1 atmosphere (101.3 kPa)
Under STP, 1 mole of any gas occupies a volume of 22.4 litres.
- This is known as the molar volume at STP.

Molar Mass and Relative Molecular Mass (Mr)

Molar mass (g/mol): The mass of one mole of a substance in grams. It is numerically equal to the substance's relative molecular mass (Mr).
Relative molecular mass (Mr): The sum of the relative atomic masses of all atoms in a molecule.

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Example: For water $H_2O$

Mr = 2(1) + 16 = 18 \, \text{g/mol}

Converting Between Units

Moles to Mass (Grams):

To calculate mass from moles:

\text{Mass (g)} = \text{Moles} \times \text{Molar Mass (g/mol)}

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Example: Calculate the mass of 0.5 moles of calcium hydroxide

\text{Ca(OH)}_2 \text{where}\ (Mr = 74)

Using the formula:

\text{Mass} = 0.5 \times 74

= :success[37 \, \text{g}]

Mass to Moles:

To calculate moles from mass:

\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}

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Example: Calculate the moles in 0.64 g of oxygen gas

O_2\ \text{where}\ (Mr = 32)

Using the formula:

\text{Moles} = \frac{0.64}{32}

= :success[0.02 \, \text{moles}]

Moles to Number of Particles:

To calculate the number of particles from moles:

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

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Example: Find the number of molecules in 0.02 moles of water:

Using the formula:

\text{Number of Molecules} = 0.02 \times 6.02 \times 10^{23}

= :success[1.2 \times 10^{22} \, \text{molecules}]

Volume of Gas to Moles (at STP):

To calculate moles from the volume of gas:

\text{Moles} = \frac{\text{Volume (litres)}}{22.4 \, \text{L/mol}}

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Example: Find the number of moles in 1.12 litres of oxygen gas at STP

Using the formula:

\text{Moles} = \frac{1.12}{22.4}

= :success[0.05 \, \text{moles}]

Moles to Number of Atoms (Molecular Species):

For molecules, multiply by the number of atoms in each molecule.

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Example: 1 molecule of water $H_2O$ contains 3 atoms. If you have $1.2 \times 10^{22}$ molecules of water, the number of atoms is:

Multiplying by the number of atoms in each molecule:

\text{Number of Atoms} = 1.2 \times 10^{22} \times 3

= :success[3.6 \times 10^{22} \, \text{atoms}]

Determination of Mr Using a Mass Spectrometer

In a mass spectrometer, the relative molecular mass (Mr) of a substance can be determined through the following steps:

Vaporisation: The sample is vaporised.
Ionisation: The vaporised atoms are ionised, usually by losing an electron.
Acceleration: The ions are accelerated through an electric field.
Separation: The ions are separated based on their mass-to-charge ratio.
Detection: The ions are detected, and their abundance is measured to determine the relative molecular mass.

The Mole Simplified Revision Notes for Leaving Cert Chemistry

The Mole

The Mole and Avogadro's Constant

Standard Temperature and Pressure (STP)

Molar Mass and Relative Molecular Mass (Mr)

Converting Between Units

Moles to Mass (Grams):

Mass to Moles:

Moles to Number of Particles:

Example: Find the number of molecules in 0.02 moles of water:

Volume of Gas to Moles (at STP):

Example: Find the number of moles in 1.12 litres of oxygen gas at STP

Moles to Number of Atoms (Molecular Species):

Determination of Mr Using a Mass Spectrometer

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