Avogadro Number, Mole Concept, Molar Volume and Ideal Gas Equation for SS 1

Class: SS 1
Term: Third Term
Week: 2
Age: 15 years
Duration: 60 minutes
Subject: Chemistry
Curriculum Theme: The chemical world
Focal competence: Illustrating the gas laws with appropriate equations and solving problems related to the laws
Key competencies/values: Critical Thinking
Skills:

• Deriving the gas equation from statements of gas laws

Previous Lesson: Gas Laws, Charles’ Law, Celsius–Kelvin Conversion and Avogadro’s Law
Topic: Gas Laws: Avogadro Number And The Mole Concept
Subject Matter: Avogadro number and the mole concept, Molar volume of gases, Ideal gas equation, Applications of the gas laws in industrial processes

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• State the relationship between the rate of diffusion and density.
• Describe the mole-volume relationship in the combined gas equation.
• Prove that PV=nRT as the general gas equation.
• Describe some applications of gas laws in industrial processes.

Affective Domain

• Appreciate the importance of gas laws in everyday life and industrial applications.
• Participate actively in group discussions and problem-solving activities.

Psychomotor Domain

• Solve mathematical problems involving the ideal gas equation.
• Demonstrate the diffusion of gases using appropriate materials.

Social Domain

• Collaborate effectively with peers in group activities.
• Communicate ideas clearly during brainstorming sessions.

Reference Materials

The following resources were used in planning this lesson:

• 2025 New Revised Senior Secondary Education Curriculum (SSEC)
• Relevant State Unified Scheme of Work
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)
• A suitable Chemistry textbook for Senior Secondary School 1

Instructional Materials

The teacher will teach this lesson with the aid of:

• Pictures/Charts on the applications of gas laws in industrial processes.
• Cotton wool
• Ammonia solution
• Concentrated HCl solution
• Thermometer
• Stopwatch
• Long glass tube

Rationale for the Lesson

This lesson is important because it introduces students to fundamental principles governing the behaviour of gases, which are crucial for understanding many chemical reactions and physical phenomena. It provides the mathematical tools to quantify gas properties and explains their practical applications in various industrial processes, linking theoretical knowledge to real-world scenarios.

Prerequisite/Previous Knowledge

Students should have a basic understanding of states of matter, kinetic theory of matter, and simple gas laws (Boyle’s Law, Charles’s Law, Gay-Lussac’s Law).

Lesson Content/Board Summary

Gas Laws: Avogadro Number And The Mole Concept

Avogadro Number and the Mole Concept

The mole is the SI unit for the amount of substance. One mole of any substance contains Avogadro’s number of particles (atoms, molecules, ions, or electrons).

Avogadro’s number, denoted as (N_A), is approximately (6.02 times 10^{23}) particles per mole.

The mole concept provides a way to relate the macroscopic mass of a substance to the microscopic number of particles it contains.

Molar Volume of Gases

The molar volume of a gas is the volume occupied by one mole of that gas at a specific temperature and pressure.

At Standard Temperature and Pressure (STP), which is (0^circ C) (273 K) and 1 atmosphere (101.325 kPa) pressure, one mole of any ideal gas occupies a volume of (22.4 dm^3) (or 22.4 litres).

This relationship is a direct consequence of Avogadro’s Law, which states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules (or moles).

Relationship between Rate of Diffusion and Density (Graham’s Law)

Graham’s Law of Diffusion states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass or density, provided the temperature and pressure are constant.

Mathematically, it can be expressed as:

( frac{Rate_1}{Rate_2} = sqrt{frac{M_2}{M_1}} = sqrt{frac{d_2}{d_1}} )

Where:

1. (Rate_1) = rate of diffusion of gas 1
2. (Rate_2) = rate of diffusion of gas 2
3. (M_1) = molar mass of gas 1
4. (M_2) = molar mass of gas 2
5. (d_1) = density of gas 1
6. (d_2) = density of gas 2

This means lighter gases diffuse faster than heavier gases.

Ideal Gas Equation (PV=nRT)

The Ideal Gas Equation combines Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, and Avogadro’s Law into a single relationship that describes the behaviour of an ideal gas.

Derivation:

1. Boyle’s Law: (V propto frac{1}{P}) (at constant n, T)
2. Charles’s Law: (V propto T) (at constant n, P)
3. Avogadro’s Law: (V propto n) (at constant P, T)

Combining these proportionalities, we get:

(V propto frac{nT}{P})

Introducing a proportionality constant, R (the ideal gas constant), we get the Ideal Gas Equation:

(PV = nRT)

Where:

1. (P) = Pressure of the gas (in atmospheres, Pascals, or mmHg)
2. (V) = Volume of the gas (in litres or cubic metres)
3. (n) = Number of moles of the gas
4. (R) = Ideal gas constant ((0.0821 L cdot atm cdot mol^{-1} cdot K^{-1}) or (8.314 J cdot mol^{-1} cdot K^{-1}))
5. (T) = Absolute temperature of the gas (in Kelvin)

Example 1

Question: Calculate the volume occupied by 0.5 moles of an ideal gas at (27^circ C) and 2 atm pressure. (Given R = (0.0821 L cdot atm cdot mol^{-1} cdot K^{-1}))

Solution:

Step 1: Write the formula and convert temperature to Kelvin.

(PV = nRT)

(T = 27^circ C + 273 = 300 K)

Step 2: Rearrange the formula to solve for V and substitute the values.

(V = frac{nRT}{P})

(V = frac{0.5 text{ mol} times 0.0821 L cdot atm cdot mol^{-1} cdot K^{-1} times 300 K}{2 text{ atm}})

Step 3: Simplify and write the answer.

(V = frac{12.315}{2} L)

(V = 6.1575 L)

Answer: (6.16 L) (to 3 significant figures)

Example 2

Question: A gas occupies a volume of 10 L at (127^circ C) and 3 atm pressure. If the gas weighs 16 g, calculate its molar mass. (Given R = (0.0821 L cdot atm cdot mol^{-1} cdot K^{-1}))

Solution:

Step 1: Write the formula and convert temperature to Kelvin.

(PV = nRT)

(T = 127^circ C + 273 = 400 K)

Step 2: Substitute (n = frac{mass}{Molar Mass}) into the ideal gas equation and rearrange to solve for Molar Mass (M).

(PV = frac{mass}{M}RT)

(M = frac{mass times RT}{PV})

(M = frac{16 text{ g} times 0.0821 L cdot atm cdot mol^{-1} cdot K^{-1} times 400 K}{3 text{ atm} times 10 L})

Step 3: Simplify and write the answer.

(M = frac{525.44}{30} text{ g/mol})

(M = 17.5146 text{ g/mol})

Answer: (17.5 text{ g/mol}) (to 3 significant figures)

Applications of Gas Laws in Industrial Processes

Gas laws are fundamental to many industrial processes, including:

1. Ammonia Production (Haber Process): High pressure and specific temperatures are used to shift the equilibrium towards ammonia formation, based on Le Chatelier’s principle which is influenced by gas laws.
2. Oxygen and Nitrogen Production (Fractional Distillation of Liquid Air): Air is compressed and cooled to a liquid state, then separated into its components based on their different boiling points, a process involving changes in pressure and temperature.
3. Hot Air Balloons: The principle of buoyancy, driven by the expansion of hot air (Charles’s Law), allows the balloon to rise.
4. Refrigeration and Air Conditioning: These systems work by compressing and expanding gases (refrigerants) to absorb and release heat, relying heavily on the relationship between pressure, volume, and temperature.
5. Tyre Inflation: Understanding the relationship between pressure, volume, and temperature (Ideal Gas Law) is critical for safe and efficient tyre inflation, especially with temperature changes.
6. Aerosol Cans: These operate by storing a gas under high pressure, which expands rapidly when the valve is opened, propelling the contents.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Problem Solving, Pair Work, Group Work

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Questioning/Recall

Teacher’s Activity: The teacher greets the students and reviews previous knowledge on simple gas laws (Boyle’s, Charles’, Gay-Lussac’s) by asking questions like, “What happens to the volume of a gas when pressure increases at constant temperature?”

Pupils’ Activity: Pupils respond to the questions, recalling their knowledge of basic gas laws.

Learning Point: Review of gas laws

Step 2: Avogadro Number and Mole Concept

Time: 10 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher introduces Avogadro’s number and the mole concept, explaining their significance in quantifying the amount of substance. The teacher defines molar volume and states its value at STP.

Pupils’ Activity: Pupils listen attentively, ask questions for clarification, and note down key definitions.

Learning Point: Mole concept introduction

Step 3: Relationship between Rate of Diffusion and Density

Time: 10 minutes

Teaching Skill: Demonstration/Explanation

Teacher’s Activity: The teacher demonstrates Graham’s Law using a long glass tube, cotton wool soaked in concentrated ammonia, and another soaked in concentrated HCl. Students observe the formation of ammonium chloride ring and discuss which gas diffused faster. The teacher then explains Graham’s Law and its formula.

Pupils’ Activity: Pupils observe the demonstration, discuss their observations, and state the relationship between diffusion rate and density.

Learning Point: Graham’s Law explanation

Step 4: Derivation of Ideal Gas Equation

Time: 10 minutes

Teaching Skill: Derivation/Explanation

Teacher’s Activity: The teacher guides students through the derivation of the Ideal Gas Equation (PV=nRT) by combining Boyle’s, Charles’, and Avogadro’s laws. The teacher explains each variable and the ideal gas constant (R) with its units.

Pupils’ Activity: Pupils follow the derivation, ask questions, and understand how the individual gas laws combine.

Learning Point: Ideal Gas Equation derivation

Step 5: Solving Problems with Ideal Gas Equation

Time: 10 minutes

Teaching Skill: Guided Practice/Problem Solving

Teacher’s Activity: The teacher works through the provided examples of Ideal Gas Equation calculations on the board, explaining each step. The teacher then guides students to work in groups to solve similar mathematical problems involving the gas laws.

Pupils’ Activity: Pupils pay attention to the worked examples, participate in group problem-solving, and practice applying the formula.

Learning Point: Ideal Gas Equation application

Step 6: Applications of Gas Laws in Industry

Time: 5 minutes

Teaching Skill: Brainstorming/Discussion

Teacher’s Activity: The teacher guides students to brainstorm in groups and identify various applications of gas laws in industrial processes, using charts or pictures as prompts. The teacher facilitates a class discussion on their findings.

Pupils’ Activity: Pupils discuss in groups, identify applications, and share their ideas with the class.

Learning Point: Industrial gas law applications

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. State Graham’s Law of Diffusion.
2. What is the molar volume of an ideal gas at STP?
3. Write down the Ideal Gas Equation and state the meaning of each symbol.
4. Mention two industrial applications of gas laws.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Assessment of understanding

Step 8: Note-Taking

Time: 10 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on Avogadro’s number, molar volume, Graham’s Law, Ideal Gas Equation, and its applications into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson notes

Step 9: Conclusion

Time: 5 minutes

Teaching Skill: Reinforcement

Teacher’s Activity: The teacher briefly summarizes the key concepts learned: Avogadro’s number, molar volume, Graham’s Law, and the Ideal Gas Equation, emphasizing their importance in chemistry and real-world applications. The teacher encourages students to review their notes.

Pupils’ Activity: Pupils listen to the summary and prepare for the next lesson.

Learning Point: Lesson consolidation

Continuous Assessment/Further Study

Type: Homework

Instruction: Answer the following questions in your notebook.

1. Calculate the number of moles in 44.8 L of an ideal gas at STP.
2. A gas has a volume of 5 L at 2 atm and (27^circ C). If the pressure is increased to 4 atm and the temperature to (127^circ C), what will be the new volume?
3. Explain how gas laws are applied in the operation of a refrigerator.
4. If gas A diffuses twice as fast as gas B, and the molar mass of gas A is 4 g/mol, what is the molar mass of gas B?

Lesson Keywords

• Avogadro Number – The number of particles ((6.02 times 10^{23})) in one mole of a substance.
• Mole Concept – A unit of measurement for the amount of substance, relating mass to the number of particles.
• Molar Volume – The volume occupied by one mole of a gas at a specific temperature and pressure.
• STP – Standard Temperature and Pressure ((0^circ C) and 1 atm).
• Ideal Gas Equation – (PV=nRT), a formula describing the relationship between pressure, volume, moles, and temperature of an ideal gas.
• Graham’s Law – States that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass or density.
• Diffusion – The spreading of particles from an area of higher concentration to an area of lower concentration.

Differentiation

Support: Provide simpler numerical problems for students struggling with calculations. Offer visual aids and step-by-step guides for deriving the ideal gas equation. Pair weaker students with stronger ones for group activities.

Extension: Challenge advanced students to research and present on more complex industrial applications of gas laws or to derive the combined gas law from the ideal gas equation. Encourage them to explore the limitations of the ideal gas law for real gases.

Suggested Lesson Videos

Search on YouTube for: “Avogadro’s number and mole concept SS1 Chemistry”, “Ideal Gas Law derivation and examples SS1”, “Graham’s Law of Diffusion experiment”