4.4 Gas Laws
Learn the relationships between gas pressure, temperature, and volume through Kinetic Theory, Boyle's Law, Charles' Law, and Gay-Lussac's Law.
Learning Objectives
- Explain gas pressure, temperature, and volume in terms of the behaviour of gas molecules based on the Kinetic Theory of Gas.
- State Boyle's Law, Charles' Law, and Gay-Lussac's Law.
- Determine the relationships between pressure, temperature, and volume of a fixed mass of gas through experiments and graphical analysis.
- Define absolute zero and convert temperatures between Celsius (°C) and Kelvin (K).
- Solve numerical problems involving pressure, temperature, and volume of a fixed mass of gas using gas law formulae.
The Gas Laws at a Glance: Graphs, Formulae, and Molecular Behaviour
Compare Boyle's Law, Charles' Law, and Gay-Lussac's Law in terms of constant variables, mathematical equations, characteristic graphs, and molecular kinetic behaviour.
Short Explanation
Pressure, Temperature, and Volume
Gas molecules move randomly. When they collide with the container wall and rebound, a force is exerted on the wall. Force per unit area is the gas pressure. The average kinetic energy of gas molecules increases with temperature. Gas molecules move freely and fill the entire space of the container, so the volume of the gas equals the volume of its container.
Boyle's Law
Pressure is inversely proportional to volume for a fixed mass of gas at constant temperature. \(P_1V_1 = P_2V_2\)
Charles' Law
Volume is directly proportional to absolute temperature for a fixed mass of gas at constant pressure. \(\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}\)
Gay-Lussac's Law
Pressure is directly proportional to absolute temperature of a fixed mass of gas at constant volume. \(\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}\)
| Quantity | Symbol | S.I. Unit | Other Units |
|---|---|---|---|
| Pressure | P | pascal (Pa) | cm Hg, kPa |
| Temperature | T | kelvin (K) | °C, °F |
| Volume | V | (metre)³ (m³) | mm³, cm³, mℓ |
Experiments to Determine the Gas Laws
Laboratory methods for the three relationships between pressure, temperature and volume.
Experiment 4.4: Boyle's Law
Inference: The volume of a gas influences the pressure of the gas. Hypothesis: The smaller the volume of the gas, the higher the gas pressure.
Variables: manipulated — volume, \(V\); responding — pressure, \(P\); constant — temperature and mass of air.
Apparatus: \(100\text{ ml}\) syringe, rubber tube, pressure gauge and retort stand.
Procedure: Adjust the piston so the air in the syringe is \(100\text{ ml}\), then connect the syringe to the pressure gauge and record the initial volume and pressure. Push the piston slowly until the volume becomes \(90\text{ ml}\) and record the pressure. Repeat for \(80\text{ ml}\), \(70\text{ ml}\) and \(60\text{ ml}\). Pushing slowly keeps the temperature constant.
Analysis: Plot \(P\) against \(V\) and \(P\) against \(\dfrac{1}{V}\). The graph of \(P\) against \(V\) falls as volume increases, while the graph of \(P\) against \(\dfrac{1}{V}\) is a straight line through the origin, showing \(P \propto \dfrac{1}{V}\).
Experiment 4.5: Charles' Law
Inference: The temperature of a gas influences the volume of the gas. Hypothesis: The higher the temperature, the larger the volume of the gas.
Variables: manipulated — temperature, \(\theta\); responding — volume, \(V\), represented by the length of the air column, \(L\), in the capillary tube; constant — pressure and mass of air.
Apparatus: Capillary tube containing air trapped by a column of concentrated sulphuric acid, \(500\text{ ml}\) beaker, thermometer, ruler, Bunsen burner, tripod stand, wire gauze, stirrer and retort stand.
Analysis: Plot \(L\) against \(\theta\) over the range \(0\ ^\circ C\) to \(100\ ^\circ C\). Then plot \(L\) against \(\theta\) again with the \(\theta\)-axis covering \(-300\ ^\circ C\) to \(100\ ^\circ C\) and extrapolate the line until \(L = 0\), which occurs at \(-273\ ^\circ C\).
Experiment 4.6: Gay-Lussac's Law
Inference: The temperature of a gas influences the pressure of the gas. Hypothesis: The higher the temperature, the higher the gas pressure.
Variables: manipulated — temperature, \(\theta\); responding — pressure, \(P\); constant — volume and mass of air.
Apparatus: Round-bottom flask, large beaker, thermometer, pressure gauge, Bunsen burner, wire gauze, tripod stand, stirrer, retort stand and wooden block.
Analysis: Plot \(P\) against \(\theta\) and extrapolate the line until \(P = 0\), which again occurs at \(-273\ ^\circ C\).
Reading the Extrapolated Graphs
For both Charles' Law and Gay-Lussac's Law the measured line does not pass through the origin of the \(\theta\) axis: at \(0\ ^\circ C\) the gas still has volume and still exerts pressure. Extrapolating the line backwards until \(V = 0\) or \(P = 0\) gives \(-273\ ^\circ C\), which is absolute zero. Replotting against absolute temperature in kelvin gives a straight line through the origin, which is why \(T\) must be in kelvin in \(\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}\) and \(\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}\).
Try to Answer First
Answer in your mind, then press "Check Answer".
Air in a closed syringe has an initial volume of 60 cm³ and a pressure of 108 kPa. If the piston is pushed slowly to compress the air to 48 cm³ at constant temperature, what is the new pressure?
Check Answer
An air bubble trapped under water has a volume of 1.2 cm³ at a temperature of 27 °C. Find its volume if the temperature increases to 47 °C at constant pressure.
Check Answer
A sealed steel cylinder contains gas at a pressure of 180 kPa and a temperature of 25 °C. What is the pressure inside the cylinder if it is heated to 52 °C?
Check Answer
Common Mistakes
- Using Celsius (°C) directly in Charles' Law and Gay-Lussac's Law calculations instead of converting to kelvin (K).
- Forgetting to convert the final calculated absolute temperature back into Celsius when the question explicitly requests the answer in °C.
- Pushing the syringe piston too rapidly during the Boyle's Law experiment, which causes temperature to change and invalidates the condition of constant temperature.
- Assuming that volume becomes zero at 0 °C rather than at absolute zero (-273 °C or 0 K).
- Mixing up the responding and manipulated variables on the graph axes, for example plotting V on the y-axis instead of P when investigating Boyle's Law.
Concept Misunderstandings
At 0 °C, gas molecules stop moving and exert zero pressure.
At 0 °C, gas molecules are still moving randomly and exert pressure. Molecules only theoretically stop moving and exert zero pressure at absolute zero (-273 °C or 0 K).
Gas pressure is caused by gas molecules colliding with each other.
Gas pressure is the force per unit area exerted when gas molecules collide with and rebound from the walls of the container.
The volume of a gas is simply the sum of the volumes of the individual molecules.
Gas molecules move freely and fill the entire container; the volume of the gas is taken as the total volume of the container enclosing it.
Summary
- Kinetic Theory of Gas: Molecules move randomly; pressure is force per unit area on container walls; temperature reflects average kinetic energy; volume equals the volume of the container.
- Boyle's Law: \(P \propto \dfrac{1}{V}\) or \(P_1V_1 = P_2V_2\) at constant T and mass. Graph of P against 1/V is a straight line through the origin.
- Charles' Law: \(V \propto T\) or \(\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}\) at constant P and mass. Graph of V against T (K) is a straight line through the origin; graph of V against θ (°C) intercepts the axis at -273 °C.
- Gay-Lussac's Law: \(P \propto T\) or \(\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}\) at constant V and mass. Graph of P against T (K) is a straight line through the origin; graph of P against θ (°C) intercepts the axis at -273 °C.
- Absolute Zero: -273 °C = 0 K. Temperature conversion: \(T = \theta + 273\).
Short Activity
Objective: Identify gas laws, absolute zero, and the relationships between pressure, volume, and temperature.
A. Objective Quiz
1 Which physical quantity is kept constant for a fixed mass of gas in Gay-Lussac's Law?
2 What happens to the air molecules inside a rigid, sealed container when the gas is heated?
B. Fill in the Blanks
3 The lowest possible temperature where gas molecules theoretically cease to move and gas volume becomes zero is called .
4 According to Boyle's Law, when the volume of a fixed mass of gas decreases at constant temperature, gas pressure because the rate of collisions with the walls increases.
C. Matching / Drag and Drop
Match each gas law or concept with its correct characteristic formula or defining relationship. If using a phone, tap the answer first, then tap the matching box.
