IB MYP 4-5 Chemistry -The mole concept and Avogadro’s constant- Study Notes - New Syllabus

The Mole Concept and Avogadro’s Constant

The mole is the standard scientific unit used to measure the amount of substance. It allows chemists to count particles (atoms, ions, or molecules) by weighing them.

Key Idea: One mole of any substance contains the same number of particles — this number is known as Avogadro’s constant.

Avogadro’s Constant (\( \mathrm{N_A} \))

 Avogadro’s constant (\( \mathrm{N_A} \)) is the number of particles (atoms, molecules, or ions) in one mole of a substance.

\( \mathrm{N_A = 6.022 \times 10^{23}\ particles\ mol^{-1}} \)

Meaning:

• 1 mole of atoms = \( \mathrm{6.022 \times 10^{23}} \) atoms.
• 1 mole of molecules = \( \mathrm{6.022 \times 10^{23}} \) molecules.
• 1 mole of ions = \( \mathrm{6.022 \times 10^{23}} \) ions.

Example: 1 mole of water (\( \mathrm{H_2O} \)) contains:

• \( \mathrm{6.022 \times 10^{23}} \) molecules of water
• \( \mathrm{(6.022 \times 10^{23}) \times 3 = 1.807 \times 10^{24}} \) atoms (2 H + 1 O)

Relationship Between Mass, Moles, and Molar Mass

Formula:

\( \mathrm{n = \dfrac{m}{M}} \)

Where:

• \( \mathrm{n} \) = number of moles
• \( \mathrm{m} \) = mass of the substance (in grams)
• \( \mathrm{M} \) = molar mass (g/mol)

Rearranged Forms:

• \( \mathrm{m = nM} \)
• \( \mathrm{M = \dfrac{m}{n}} \)

 Relationship Between Number of Particles and Moles

Formula:

\( \mathrm{n = \dfrac{N}{N_A}} \)

Where:

• \( \mathrm{N} \) = number of particles (atoms, molecules, or ions)
• \( \mathrm{N_A} \) = Avogadro’s constant
• \( \mathrm{n} \) = number of moles

Rearranged Forms:

• \( \mathrm{N = n \times N_A} \)
• \( \mathrm{n = \dfrac{N}{N_A}} \)

Relationship Between Volume and Moles (for Gases)

At standard temperature and pressure (STP: 0°C and 1 atm), 1 mole of any gas occupies:

\( \mathrm{22.4\ dm^3 = 22,400\ cm^3} \)

Formula:

\( \mathrm{n = \dfrac{V}{V_m}} \)

Where:

• \( \mathrm{n} \) = number of moles
• \( \mathrm{V} \) = volume of gas (in dm³)
• \( \mathrm{V_m} \) = molar volume = \( \mathrm{22.4\ dm^3\ mol^{-1}} \) at STP

Molar Mass and Relative Atomic Mass

The molar mass (\( \mathrm{M} \)) of a substance is the mass of one mole of that substance.

\( \mathrm{M = Relative\ Atomic\ or\ Molecular\ Mass\ (in\ g/mol)} \)

Examples:

• 1 mole of \( \mathrm{H_2} \) = 2 g
• 1 mole of \( \mathrm{O_2} \) = 32 g
• 1 mole of \( \mathrm{H_2O} \) = 18 g

Summary Table of Relationships