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Gas laws — KCSE Chemistry

KCSE Chemistry · 78 practice questions · 4 syllabus objectives · 4 revision lessons

26 easy25 medium27 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

State and apply Boyle's law (P₁V₁ = P₂V₂) to solve problems at constant temperature

State and apply Charles's law (V₁/T₁ = V₂/T₂) to solve problems at constant pressure

Apply the combined gas law and ideal gas equation (PV = nRT) to calculate pressure, volume, temperature or moles

Gas laws

Revision Notes

Concise lesson notes for Gas laws, written to the KCSE Chemistry marking standard. Read the first lesson free below.

Understanding Boyle's Law

Boyle's Law states that at constant temperature, the pressure (P) of a gas is inversely proportional to its volume (V). This relationship can be expressed mathematically as P₁V₁ = P₂V₂, where:

  • P₁ and V₁ are the initial pressure and volume,
  • P₂ and V₂ are the final pressure and volume.

To apply Boyle's Law, follow these steps:

  1. Identify the initial and final states of the gas.
  2. Ensure the temperature remains constant.
  3. Rearrange the equation to solve for the unknown variable.

Example Problem: A gas occupies a volume of 4.0 L at a pressure of 2.0 atm. What will be the volume when the pressure is increased to 4.0 atm?

Solution:

  • Given: P₁ = 2.0 atm, V₁ = 4.0 L, P₂ = 4.0 atm.
  • Using Boyle's Law: P₁V₁ = P₂V₂
  • Rearranging gives: V₂ = (P₁V₁) / P₂ = (2.0 atm * 4.0 L) / 4.0 atm = 2.0 L.

Thus, the final volume is 2.0 L.

Key points to remember

  • Boyle's Law relates pressure and volume at constant temperature.
  • Use the formula P₁V₁ = P₂V₂ for calculations.
  • Inversely proportional means increased pressure decreases volume.
  • Always ensure temperature remains constant during application.

Worked example

A gas has a volume of 5.0 L at 1.0 atm. What is the volume at 2.0 atm? Answer: V₂ = (P₁V₁) / P₂ = (1.0 atm * 5.0 L) / 2.0 atm = 2.5 L.

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Lesson 2: Understanding Charles's Law

Objective: State and apply Charles's law (V₁/T₁ = V₂/T₂) to solve problems at constant pressure

Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure. This can be mathematically expressed as:

V₁/T₁ = V₂/T₂

Where:

  • V₁ = initial volume
  • T₁ = initial temperature (in Kelvin)
  • V₂ = final volume
  • T₂ = final temperature (in Kelvin)

To apply Charles's Law, convert temperatures from Celsius to Kelvin by adding 273.15. Follow these steps:

  1. Identify initial and final conditions (V₁, T₁, V₂, T₂).
  2. Rearrange the formula to find the unknown variable.
  3. Substitute the known values and solve.

Example:
A gas occupies a volume of 300 mL at 27°C. What will its volume be at 77°C?

  • Convert temperatures: T₁ = 27 + 273.15 = 300.15 K, T₂ = 77 + 273.15 = 350.15 K.
  • Use Charles's Law: V₁/T₁ = V₂/T₂
  • Rearranging gives V₂ = V₁ × (T₂/T₁)
  • V₂ = 300 mL × (350.15 K / 300.15 K) ≈ 349.5 mL.
  • Volume and temperature are directly proportional at constant pressure.
  • Convert Celsius to Kelvin for calculations.
  • Rearrange the formula to find unknowns.
  • Use consistent units when applying the law.
  • Practice with real-life gas scenarios.

A gas has a volume of 400 mL at 20°C. What is its volume at 60°C?

  • T₁ = 20 + 273.15 = 293.15 K, T₂ = 60 + 273.15 = 333.15 K.
  • V₂ = 400 mL × (333.15 K / 293.15 K) ≈ 455.2 mL.
Lesson 3: Understanding Gas Laws and Their Applications

Objective: Apply the combined gas law and ideal gas equation (PV = nRT) to calculate pressure, volume, temperature or moles

The combined gas law relates pressure (P), volume (V), and temperature (T) of a gas. It is expressed as:

P1V1/T1 = P2V2/T2
This equation shows how changes in one variable affect the others when the amount of gas remains constant.

The ideal gas equation is:

PV = nRT
Where:

  • n = number of moles of gas
  • R = ideal gas constant (8.31 J/(mol·K))
  • T = temperature in Kelvin

To apply these equations, ensure all units are consistent. For example, pressure in pascals (Pa), volume in cubic meters (m³), and temperature in Kelvin (K).

Example:
Calculate the pressure of 2 moles of gas occupying a volume of 0.5 m³ at a temperature of 300 K.

Using the ideal gas equation:

  • P = nRT/V
  • P = (2 mol)(8.31 J/(mol·K))(300 K) / 0.5 m³
  • P = 4986 Pa

Thus, the pressure is 4986 Pa.

  • Understand the relationship between pressure, volume, and temperature.
  • Use consistent units for calculations in gas laws.
  • Apply the combined gas law for changing conditions.
  • Utilize the ideal gas equation for pressure, volume, or moles.

Calculate the volume of 1 mole of gas at 1 atm and 273 K.
Using PV = nRT:

  • V = nRT/P
  • V = (1 mol)(0.0821 L·atm/(mol·K))(273 K) / 1 atm
  • V = 22.4 L
Lesson 4: Understanding Gas Laws

Objective: Gas laws

Gas laws describe the behavior of gases under various conditions. The main gas laws include Boyle's Law, Charles's Law, and Avogadro's Law.

  • Boyle's Law states that at constant temperature, the pressure of a gas is inversely proportional to its volume. Mathematically, this is expressed as P1V1 = P2V2.
  • Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). This can be written as V1/T1 = V2/T2.
  • Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present. This is expressed as V1/n1 = V2/n2.

Understanding these laws helps predict how gases will respond to changes in pressure, volume, and temperature. Always remember to use absolute temperature in Kelvin for calculations involving Charles's Law.

  • Boyle's Law: P1V1 = P2V2 at constant temperature.
  • Charles's Law: V1/T1 = V2/T2 at constant pressure.
  • Avogadro's Law: V1/n1 = V2/n2 at constant temperature and pressure.

A gas occupies 2.0 L at 1.0 atm. What will be the volume at 2.0 atm? Using Boyle's Law: P1V1 = P2V2, we have 1.0 atm * 2.0 L = 2.0 atm * V2. Thus, V2 = 1.0 L.

Sample Questions

Read 3 questions and answers free. Sign up to access all 78 questions with full KNEC-style marking schemes and a personalised study plan.

1
easySHORT ANSWER3 marks

A balloon filled with helium gas has a volume of 3 litres at a pressure of 1.5 atm and a temperature of 20°C. If the pressure is decreased to 1 atm while the temperature remains constant, what will be the new volume of the gas in litres? (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Use Boyle's Law: P1V1 = P2V2 (1 mk)
Substitute values: 1.5 × 3 = 1 × V2 (1 mk)
Solve for V2: V2 = (1.5 × 3)/1 = 4.5 litres (1 mk)
2
easySHORT ANSWER4 marks

A gas sample at 25°C occupies a volume of 5 dm³ and exerts a pressure of 1.2 atm. If the gas is heated to 75°C while maintaining the pressure constant, what will be the new volume of the gas? (4 marks)

Answer & marking scheme

Part (a) — 4 marks
Convert temperatures to Kelvin: 25°C = 298 K; 75°C = 348 K (1 mk)
Apply Charles's Law: V1/T1 = V2/T2 (1 mk)
Rearrange to find V2: V2 = V1 × (T2/T1) (1 mk)
Substitute values: V2 = 5 × (348/298) = 5.83 dm³ (or appropriate unit) (1 mk)
3
easySHORT ANSWER3 marks

Calculate the pressure exerted by 2 moles of carbon dioxide gas occupying a volume of 10 dm³ at a temperature of 300 K using the ideal gas equation. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Use the ideal gas equation PV = nRT (1 mk)
Substitute values: P = (nRT)/V = (2 × 8.31 × 300)/10 (1 mk)
Calculate pressure P = 49.86 atm (or appropriate unit) (1 mk)
4

A balloon filled with gas has a volume of 2.0 litres at a temperature of 20°C. If the temperature is decreased to 0°C at constant pressure, what will be the new volume of the gas? (4 marks)

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Frequently asked questions

What does the KCSE Chemistry topic "Gas laws" cover?

Gas laws covers State and apply Boyle's law (P₁V₁ = P₂V₂) to solve problems at constant temperature; State and apply Charles's law (V₁/T₁ = V₂/T₂) to solve problems at constant pressure; Apply the combined gas law and ideal gas equation (PV = nRT) to calculate pressure, volume, temperature or moles, and more, all aligned to the official KNEC KCSE Chemistry syllabus.

How many practice questions are available for Gas laws?

HighMarks has 78 Gas laws practice questions for KCSE Chemistry, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Chemistry syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Gas laws for the KCSE exam?

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