6.5.2 Mole-Particles Calculations

This topic explains how to convert between moles and the number of particles (atoms, molecules, or formula units) using Avogadro's number.

Definition

Mole-particle calculations involve converting between the number of moles of a substance and the number of particles (atoms, molecules, or formula units) it contains.

Simple explanation: If you know the moles, you can find the number of particles. If you know the number of particles, you can find the moles.

Main Idea

The key relationship is:

Number of particles = Number of moles × N_A

Or rearranged:

Number of moles = Number of particlesN_A

Where:

N_A = 6.022 × 10²³ particles/mol

Simple explanation: One mole always contains 6.022 × 10²³ particles — no matter what the substance is.

Core Concept

The Conversion Factor

Simple explanation: Multiply by Avogadro's number to go from moles to particles; divide to go from particles to moles.

What Are "Particles"?

The term representative particles refers to:

• Atoms — for elements (e.g., Zn, Al, C)
• Molecules — for molecular compounds (e.g., CH₄, SO₂, H₂O)
• Formula units — for ionic compounds (e.g., NaCl, MgO)

Simple explanation: The "particles" can be atoms, molecules, or formula units, depending on the substance.

Detailed Explanation

Example 6.7: Calculating the number of atoms in given moles

1. Zinc (Zn) is a silvery metal used to galvanize steel to prevent corrosion. How many atoms are there in 1.25 moles of Zn?

Problem Solving Strategy: Remember that symbols Zn and Al stand for one mole of Zn and Al atoms respectively.

Solution:

1 mole of Zn contains = 6.022 × 10²³ atoms

1.25 moles of Zn contain = 6.022 × 10²³ × 1.25

= 7.53 × 10²³ Zn atoms

Final Answer: 1.25 moles of Zn contains 7.53 × 10²³ Zn atoms.

2. Aluminium (Al) foil is used as a wrapper in food industries. How many atoms are present in a foil that contains 0.2 moles of aluminium?

Solution:

1 mole of Al contains = 6.022 × 10²³ atoms

0.2 moles of Al will contain = 6.022 × 10²³ × 0.2

= 1.2044 × 10²³ atoms

Final Answer: 0.2 moles of Al contains 1.2044 × 10²³ Al atoms.

Simple explanation: Multiply the number of moles by 6.022 × 10²³ to get the number of atoms.

Example 6.8: Calculating the number of molecules in given moles of a substance

1. Methane (CH₄) is the major component of natural gas. How many molecules are present in 0.5 moles of a pure sample of methane?

Problem Solving Strategy: Remember that CH₄ is a molecular compound, thus 1 mole of methane will have 6.022 × 10²³ molecules.

Solution:

1 mole of CH₄ contains = 6.022 × 10²³ molecules

0.5 moles of CH₄ will contain = 6.022 × 10²³ × 0.5

= 3.011 × 10²³ molecules

Final Answer: 0.5 moles of CH₄ contains 3.011 × 10²³ molecules.

2. Sulphur dioxide (SO₂) — at high temperature, hydrogen sulphide gas given off by a volcano is oxidized by air to sulphur dioxide. Sulphur dioxide reacts with water to form acid rain. How many molecules are there in 0.25 moles of SO₂?

Solution:

1 mole of SO₂ contains = 6.022 × 10²³ molecules

0.25 moles of SO₂ will contain = 6.022 × 10²³ × 0.25

= 1.5055 × 10²³ molecules

Final Answer: 0.25 moles of SO₂ contains 1.5055 × 10²³ molecules.

Simple explanation: Same rule — multiply moles by 6.022 × 10²³ to get the number of molecules.

Example 6.9: Calculating the number of moles in the given number of atoms

Titanium (Ti) is a corrosion-resistant metal used in rockets, aircraft, and jet engines. Calculate the number of moles of this metal in a sample containing 3.011 × 10²³ Ti atoms.

Problem Solving Strategy: Remember that 1 mole of an element contains 6.022 × 10²³ atoms.

Thus:

6.022 × 10²³ atoms = 1 mole

3.011 × 10²³ atoms = ? moles

Solution:

6.022 × 10²³ Ti atoms = 1 mole of Ti

3.011 × 10²³ Ti atoms = 16.022 × 10²³ × 3.011 × 10²³

= 0.5 moles of Ti

Final Answer: 3.011 × 10²³ Ti atoms = 0.5 moles of Ti.

Simple explanation: Divide the number of particles by 6.022 × 10²³ to get the number of moles.

Example 6.10: Calculating number of moles in the given number of molecules

Formaldehyde (CH₂O) is used to preserve dead animals. Its molecular formula is CH₂O. Calculate the number of moles that would contain 3.011 × 10²³ molecules of this compound.

Problem Solving Strategy: Remember that 1 mole of any compound contains 6.022 × 10²³ molecules.

Thus:

6.022 × 10²³ molecules = 1 mole of compound

3.011 × 10²³ molecules = ? moles

Solution:

6.022 × 10²³ molecules = 1 mole of formaldehyde

1 molecule = 16.022 × 10²³ moles

3.011 × 10²³ molecules = 16.022 × 10²³ × 3.011 × 10²³

= 0.05 moles of formaldehyde

Final Answer: 3.011 × 10²³ molecules = 0.05 moles of formaldehyde.

Simple explanation: Divide the number of molecules by 6.022 × 10²³ to get the number of moles.

Intermediate Level

What Is Avogadro's Number Again?

N_A = 6.022 × 10²³ particles/mol

This is the number of particles in one mole of any substance.

Particles Can Be Atoms, Molecules, or Formula Units

Simple explanation: The "particle" depends on what kind of substance you have.

Concept Assessment Exercise 6.5 (from the book)

1. Aspirin — contains carbon, hydrogen, and oxygen; used as a painkiller. An aspirin tablet contains 1.25 × 10¹⁰ molecules. How many moles of this compound are present in the tablet?

Solution:

Moles = 1.25 × 10¹⁰6.022 × 10²³

= 2.08 × 10^-14 moles

2. Magnesium — a method used to prevent rusting in ships and underground pipelines involves connecting the iron to a block of a more active metal such as magnesium (cathodic protection). How many moles of magnesium are present in 1 billion (1 × 10⁹) atoms of magnesium?

Solution:

Moles = 1 × 10⁹6.022 × 10²³

= 1.66 × 10^-15 moles

Common Conversions

Important Points

• - Mole-particle calculations: converting between moles and particles.
• - Formula:
• - Particles = Moles × 6.022 × 10²³
• - Moles = Particles ÷ 6.022 × 10²³
• - **N_A** = 6.022 × 10²³ particles/mol.
• - Particles can be atoms, molecules, or formula units.
• - 1 mole of any substance contains 6.022 × 10²³ particles.
• - Examples:
• - 1.25 moles of Zn = 7.53 × 10²³ atoms
• - 0.2 moles of Al = 1.2044 × 10²³ atoms
• - 0.5 moles of CH₄ = 3.011 × 10²³ molecules
• - 0.25 moles of SO₂ = 1.5055 × 10²³ molecules
• - 3.011 × 10²³ Ti atoms = 0.5 moles
• - 3.011 × 10²³ CH₂O molecules = 0.05 moles

Remember

• - **Moles × 6.022 × 10²³ = Particles**
• - **Particles ÷ 6.022 × 10²³ = Moles**
• - **N_A** = 6.022 × 10²³ particles/mol.
• - **1 mole** = 6.022 × 10²³ particles.
• - **1.25 moles of Zn** = 7.53 × 10²³ atoms.
• - **0.5 moles of CH₄** = 3.011 × 10²³ molecules.
• - **3.011 × 10²³ Ti atoms** = 0.5 moles.

Common Mistakes

• 1. Forgetting Avogadro's number. It is 6.022 × 10²³.
• 2. Multiplying when you should divide. Moles to particles = multiply; particles to moles = divide.
• 3. Thinking "particles" always means atoms. It can be atoms, molecules, or formula units.
• 4. Forgetting to use the correct particle for the substance. Zn has atoms; CH₄ has molecules; NaCl has formula units.
• 5. Forgetting the exponent. 6.022 × 10²³ is not the same as 6.022.
• 6. Confusing mole-particle calculations with mole-mass calculations. Mole-particle uses Avogadro's number; mole-mass uses molar mass.

Quick Revision

• Mole-particle calculations: converting between the number of moles and the number of particles (atoms, molecules, or formula units).
• Formula:
• Particles = Moles × 6.022 × 10²³
• Moles = Particles6.022 × 10²³
• **N_A** = 6.022 × 10²³ particles/mol.
• Examples:
• 1.25 moles of Zn → 1.25 × 6.022 × 10²³ = 7.53 × 10²³ Zn atoms
• 0.2 moles of Al → 0.2 × 6.022 × 10²³ = 1.2044 × 10²³ Al atoms
• 0.5 moles of CH₄ → 0.5 × 6.022 × 10²³ = 3.011 × 10²³ CH₄ molecules
• 0.25 moles of SO₂ → 0.25 × 6.022 × 10²³ = 1.5055 × 10²³ SO₂ molecules
• 3.011 × 10²³ Ti atoms → 0.5 moles
• 3.011 × 10²³ CH₂O molecules → 0.05 moles
• Particles can be atoms, molecules, or formula units depending on the substance.

60-Second Revision

• **Moles × 6.022 × 10²³ = Particles**
• **Particles ÷ 6.022 × 10²³ = Moles**
• **1.25 moles of Zn** = 7.53 × 10²³ atoms.
• **0.5 moles of CH₄** = 3.011 × 10²³ molecules.
• Warning: don't confuse mole-particle calculations with mole-mass calculations — one uses Avogadro's number, the other uses molar mass.