Lesson Notes By Weeks and Term v3 - Senior Secondary 2
Gas Laws
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Gas Laws
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: Physics
Class: Senior Secondary 2
Term: 1st Term
Week: 7
Theme: Conservation Principles
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Students should be able:to explain, using the ideas of the kinetictheory of gases.the variation of volume with temperature of agas when the pressure is keptconstant.the variation of pressure with volume of a gaswhen temperature is kept constant. Explain Charles' and Boyle's laws of gases. deduce the generalgas law from a givenmass of gas whichobeys Charles' law. solve simpleproblems in volvingthe gas laws. identify and useinstruments for measuring pressure.
= constant (k)
For changes between two states: P1/T1 = P2/T2 Explanation using Kinetic Theory: When the temperature of a gas in a rigid container (constant volume) is increased, the average kinetic energy and speed of the molecules increase. The faster-moving molecules collide with the container walls more frequently and with greater force. Since the volume is constant, this leads to an increase in the total force exerted on the walls per unit area, hence an increase in pressure.
P-T Graph: A graph of pressure versus absolute temperature (K) for a fixed mass of gas at constant volume is a straight line passing through the origin. 2.
6. General Gas Law (Combined Gas Law)
Deduction (Performance Objective 3): The General Gas Law combines Boyle's Law and Charles' Law into a single relationship for a fixed mass of gas.
1. From Boyle's Law: At constant T, V ∝ 1/P.
2. From Charles' Law: At constant P, V ∝
T. Combining these two proportionalities, we get: V ∝ T/P This can be written as: PV/T = constant (k)
Mathematical Expression: For changes between two states of a fixed mass of gas: P1V1/T1 = P2V2/T2 Standard Temperature and Pressure (STP): Often used as reference conditions for comparing gases.
Standard Temperature: 0 °C (273 K)
Standard Pressure: 1 atm (101325 Pa or 760 mmHg)
Worked Example (General Gas Law): A gas in a sealed container has a volume of 300 cm3 at 27 °C and a pressure of 750 mmHg. What will be its volume if the temperature is changed to 77 °C and the pressure to 800 mmHg?
Solution: Given: V1 = 300 cm3 T1 = 27 °C = 27 + 273 = 300 K P1 = 750 mmHg T2 = 77 °C = 77 + 273 = 350 K P2 = 800 mmHg V2 = ?
Using the General Gas Law: P1V1/T1 = P2V2/T2 (750 mmHg 300 cm3) / 300 K = (800 mmHg V2) / 350 K (750 300 / 300) = (800 V2) / 350 750 = (800 V2) / 350 V2 = (750 350) / 800 V2 = 262500 / 800 V2 = 328.125 cm3
Commentary: Notice the careful conversion of temperatures to Kelvin. The final volume accounts for both pressure and temperature changes. --- molecules have less space to move. This means they will collide more frequently with the container walls. Since the temperature is constant, the average kinetic energy (and thus the speed) of the molecules remains unchanged. The increased frequency of collisions over a smaller area results in a greater average force per unit area, hence an increase in pressure. Conversely, increasing the volume gives molecules more space, leading to fewer collisions with the walls and thus lower pressure.
P-V Graph: A graph of pressure versus volume for a fixed mass of gas at constant temperature is a hyperbola. A graph of pressure versus 1/volume is a straight line passing through the origin.
Worked Example (Boyle's Law): A gas occupies a volume of 500 cm3 at a pressure of 1.5 atm. If the temperature is kept constant, what will be its volume if the pressure is increased to 3.0 atm?
Solution: Given: P1 = 1.5 atm V1 = 500 cm3 P2 = 3.0 atm V2 = ?
Using Boyle's Law: P1V1 = P2V2 1.5 atm 500 cm3 = 3.0 atm V2 750 atm cm3 = 3.0 atm V2 V2 = 750 atm cm3 / 3.0 atm V2 = 250 cm3
Commentary: The volume decreased as the pressure increased, consistent with Boyle's Law. 2.
4. Charles' Law (Volume-Temperature Relationship)
Statement: For a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature (in Kelvin).
Mathematical Expression: V ∝ T (when P is constant) V/T = constant (k)
For changes between two states: V1/T1 = V2/T2 Explanation using Kinetic Theory (Performance Objective 1 - variation of volume with temperature): When the temperature of a gas is increased (at constant pressure), the average kinetic energy of the molecules increases, meaning they move faster. To keep the pressure constant (i.e., the rate and force of collisions with the container walls), the molecules must have more space to travel before colliding with the walls.
Therefore, the gas expands, and its volume increases. If the container is rigid, the pressure would increase instead. Conversely, decreasing the temperature causes molecules to move slower, requiring a smaller volume to maintain the same collision rate and thus constant pressure.
V-T Graph: A graph of volume versus absolute temperature (K) for a fixed mass of gas at constant pressure is a straight line passing through the origin. If plotted against Celsius temperature, the straight line extrapolates to -273.15 °C (absolute zero) at zero volume.
Worked Example (Charles' Law): A balloon contains 2.0 L of air at 27 °C. If the pressure remains constant, what will be its volume if the temperature is increased to 127 °C?
Solution: Given: V1 = 2.0 L T1 = 27 °C = 27 + 273 = 300 K T2 = 127 °C = 127 + 273 = 400 K V2 = ?
Using Charles' Law: V1/T1 = V2/T2 2.0 L / 300 K = V2 / 400 K V2 = (2.0 L 400 K) / 300 K V2 = 800 / 300 L V2 = 2.67 L (approximately)
Commentary: The volume increased as the temperature increased, consistent with Charles' Law. Note the essential conversion of temperature to Kelvin. 2.
5. Pressure Law (Gay-Lussac's Law - Pressure-Temperature Relationship)
Statement: For a fixed mass of gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature (in Kelvin).
Mathematical Expression: P ∝ T (when V is constant) P/T = constant (k)
For changes between two states: P1/T1 = P2/T2 Explanation using Kinetic Theory: When the temperature of a gas in a rigid container (constant volume) is increased, the average kinetic energy and speed of the molecules increase. The faster-moving molecules collide with the container walls more frequently and with greater force. Since the volume is constant, this leads to an increase in the total force exerted on the walls per unit area, hence an increase in pressure. * P-T Graph: A graph of pressure versus This section provides a detailed explanation of the core concepts, definitions, and laws related to the behaviour of gases, suitable for teacher reference. 2.
1. Introduction to Gases and the Kinetic Theory of Gases Gases are one of the states of matter characterized by particles that are far apart, in constant random motion, and possess weak intermolecular forces. Their behaviour can be explained by the Kinetic Theory of Gases, which postulates:
1. Random Motion: Gas molecules are in continuous, rapid, random motion, colliding with each other and the walls of their container.
2. Negligible Volume: The actual volume occupied by the gas molecules themselves is negligible compared to the total volume of the container.
3. Elastic Collisions: Collisions between molecules and with the container walls are perfectly elastic, meaning no kinetic energy is lost during collisions.
4. No Intermolecular Forces: There are no attractive or repulsive forces between gas molecules.
5. Kinetic Energy and Temperature: The average kinetic energy of the gas molecules is directly proportional to the absolute temperature (Kelvin) of the gas. These postulates help explain macroscopic properties like pressure, volume, and temperature. 2.
2. Fundamental Gas Variables The state of a given mass of gas is defined by three primary variables: Pressure (P): Definition: Pressure is the force exerted perpendicularly per unit area (P = F/A). In gases, it results from the incessant collisions of gas molecules with the walls of the container. The more frequent and forceful these collisions, the higher the pressure.
Units: The SI unit is Pascal (Pa) or N/m
2. Other common units include atmospheres (atm), millimetres of mercury (mmHg) or torr, and pounds per square inch (psi).
Conversion: 1 atm ≈ 101325 Pa ≈ 760 mmHg.
Instruments: Barometer: Used to measure atmospheric pressure. A simple mercury barometer uses the height of a mercury column supported by atmospheric pressure.
Manometer: Used to measure the pressure of a gas in a container relative to atmospheric pressure. It typically consists of a U-shaped tube containing a liquid (often mercury), with one end open to the atmosphere and the other connected to the gas source. The difference in liquid levels indicates the pressure difference.
Volume (V): Definition: The volume of a gas is the space it occupies. Gas molecules spread out to fill their container entirely.
Units: The SI unit is cubic metre (m3). Other common units include cubic decimetre (dm3) or litre (L), and cubic centimetre (cm3) or millilitre (mL).
Conversion: 1 m3 = 1000 dm3 = 1000 L = 1,000,000 cm3 = 1,000,000 m
L. Temperature (T): Definition: Temperature is a measure of the average kinetic energy of the gas molecules. Higher temperature means molecules move faster on average.
Units: The SI unit is Kelvin (K). Celsius (°C) is also commonly used. For all gas law calculations, temperature must be in Kelvin (absolute temperature).
Conversion: T(K) = T(°C) + 273.15 (often approximated as 273 for simplicity in SSCE-level problems).
Absolute Zero: The theoretical temperature at which gas molecules would have minimum kinetic energy and exert no pressure, approximately -273.15 °C or 0 K. 2.
3. Boyle's Law (Pressure-Volume Relationship)
Statement: For a fixed mass of gas at constant temperature, the volume of the gas is inversely proportional to its pressure.
Mathematical Expression: V ∝ 1/P (when T is constant) PV = constant (k)
For changes between two states: P1V1 = P2V2 Explanation using Kinetic Theory (Performance Objective 1 - variation of pressure with volume): When the volume of a gas is reduced (at constant temperature), the molecules have less space to move. This means they will collide more frequently with the container walls. Since the temperature is constant, the average kinetic energy (and thus the speed) of the molecules remains unchanged. The increased frequency of collisions over a smaller area results in a greater average force per unit area, hence an increase in pressure. Conversely, increasing the volume gives molecules more space, leading to fewer collisions with the walls and thus lower pressure. * P-V Graph: A graph of pressure versus volume for a fixed observations. Write down Charles' Law statement and formula. Engage in the kinetic theory explanation. Copy the worked example and confirm the Kelvin conversion.
D. The General Gas Law (5 minutes)
Teacher Activity: Guide students to deduce the General Gas Law from Boyle's (V ∝ 1/P) and Charles' (V ∝ T) laws, showing the combination to V ∝ T/P, hence PV/T = constant. Present the combined formula P1V1/T1 = P2V2/T
2. Explain its utility when all three variables change.
Student Activity: Follow the deduction process and understand how the laws are combined. Write down the General Gas Law formula. 3.
3. Guided Practice and Problem Solving (15 minutes)
Teacher Activity: Present a mix of 2-3 problems (Boyle's, Charles', General Gas Law) on the board or projector. Guide students through the problem-solving process, emphasizing:
1. Identifying the knowns and unknowns.
2. Determining which law applies (constant T, P, V, or all changing).
3. Converting units, especially temperature to Kelvin.
4. Substituting values into the correct formula.
5. Solving for the unknown and stating the final unit. Encourage students to work in pairs and discuss their approaches.
Student Activity: Work collaboratively or individually on the practice problems. Show all steps, including unit conversions. Ask questions when stuck or to clarify understanding. Present their solutions for discussion and correction. 3.
4. Conclusion (5 minutes)
Teacher Activity: Summarize the main gas laws (Boyle's, Charles', General). Reiterate the importance of using absolute temperature (Kelvin). Briefly connect back to the real-life applications discussed at the beginning. Assign independent practice questions as homework.
Student Activity: Participate in the summary. * Note down homework assignment. ---
Understanding Gas Laws is not merely an academic exercise; it has profound implications for various aspects of daily life, industry, and the environment in Nigeria. Vehicle Tyres and Road Safety (Boyle's and Charles' Laws): Application: Tyres for cars, buses, motorcycles ("okada"), and lorries across Nigeria must be properly inflated.
Explanation: On a hot day or after a long journey (especially on rough Nigerian roads), the temperature of the air inside the tyres increases significantly (Charles' Law). If the volume of the tyre is relatively constant, this leads to an increase in pressure (Pressure Law). Over-inflated tyres can burst, leading to accidents. Conversely, under-inflated tyres heat up faster and wear out quickly. Motorists need to check tyre pressure when cool. When inflating a tyre, compressing air into the tyre increases its pressure (Boyle's Law).
Local Context: Nigeria's often hot climate and prevalence of motor vehicle travel make this a highly relevant safety issue. Tyre vendors and mechanics often adjust tyre pressures based on ambient temperature or expected journey conditions. Cooking Gas (LPG) Cylinders and Safety (Boyle's and Pressure Laws): Application: Liquefied Petroleum Gas (LPG) is a common cooking fuel in Nigerian homes and restaurants. It is stored under high pressure in cylinders.
Explanation: The gas inside the cylinder is under very high pressure to keep it in liquid form. If the cylinder is exposed to high temperatures (e.g., left in direct sunlight or near a heat source), the temperature of the gas increases. Since the volume of the cylinder is constant, the pressure of the gas rises dramatically (Pressure Law). This can exceed the cylinder's structural limits, leading to leaks, rupture, or explosion, posing a serious safety hazard.
Local Context: Reports of cooking gas explosions due to improper handling or storage are not uncommon in Nigeria. Understanding these gas laws informs safe practices, such as storing cylinders in cool, well-ventilated areas away from direct sunlight and heat sources. Weather Forecasting and Atmospheric Phenomena (Charles' and General Gas Laws): Application: Predicting local weather patterns, understanding atmospheric pressure changes, and the formation of winds.
Explanation: Differences in temperature at various altitudes and locations cause variations in the volume and density of air. For instance, warmer air is less dense (expands by Charles' Law), creating low-pressure zones that rise. Cooler, denser air creates high-pressure zones that sink. This movement of air masses drives wind patterns and influences local weather conditions, including rainfall and humidity important for Nigerian agriculture.
Local Context: Farmers, fishermen, and aviators in Nigeria rely on weather forecasts based on these principles to plan their activities, from planting and harvesting to safe navigation. The Harmattan season, with its dry, dusty, and often cooler air, provides a contrasting example of atmospheric gas behaviour compared to the humid rainy season. ---