Experimental Gas Laws

This lesson covers: 

  1. Boyle's Law relating pressure and volume
  2. Charles' Law relating volume and temperature
  3. The Pressure Law relating pressure and temperature
  4. Graphical representations of each gas law
  5. An experiment to demonstrate Boyle's Law
  6. An experiment to estimate absolute zero based on the Pressure Law

The Three Gas Laws

These three fundamental gas laws describe how gases behave under various conditions of pressure, volume, and temperature:

  1. Boyle's Law: This law states that at a constant temperature, the pressure (p) and volume (V) of a gas are inversely proportional to each other.
  2. Charles' Law: Here, at a constant pressure, the volume (V) of a gas changes in direct proportion to its absolute temperature (T).
  3. The Pressure Law: This law indicates that at a constant volume, the pressure (p) of a gas is directly proportional to its absolute temperature (T).


An ideal gas perfectly follows these three laws under all conditions.

Boyle's Law - Pressure and Volume Relationship

Graph showing the inverse relationship between pressure and volume according to Boyle's Law.

Boyle's Law asserts that for a given amount of gas at a constant temperature:


p V = constant


Where:

  • p = pressure (Pa)
  • V = volume (m3)


This implies that if the volume increases, the pressure decreases, and vice versa. This inverse relationship is represented graphically as a hyperbola.

Boyle's law experiment

Diagram showing Boyle's Law experiment setup with a tube, air, oil, pressure gauge, and pump.

To demonstrate Boyle's Law, you can:

  1. Confine air in a tube filled with oil.
  2. Record the initial volume and pressure.
  3. Calculate the initial product of pressure and volume.
  4. Use a pump to increase the pressure inside this tube.
  5. Record the new values for pressure and volume.
  6. Calculate the new product of pressure and volume. 
  7. If the product calculated initially is equal to the final product, the gas is obeying Boyle's law.

Worked example - Demonstrating Boyle's law with a syringe

Air in a syringe is compressed from 20 cm³ to 10 cm³. The initial pressure is 101 kPa. Calculate the final pressure of the gas after it is compressed.


Step 1: Boyle's law formula

p1​V1​ = p2​V2​


Step 2: Substitution and correct evaluation

p2​=V2​p1​V1​​=10101,000×20​=202 kPa


The pressure law - pressure and temperature relationship

Graph showing the relationship between pressure and temperature with a direct proportionality starting from -273 degrees Celsius.

The Pressure Law establishes a direct relationship between the pressure (p) and absolute temperature (T) of a gas when the volume is constant:


Tp​ = constant


Where:

  • p = pressure (Pa)
  • T = absolute temperature (K)


This indicates a direct proportionality between temperature and pressure under constant volume conditions.

Pressure law experiment

Diagram showing the setup of a pressure law experiment with a flask in a water bath, thermometer, pressure gauge, and Bunsen burner.

To experimentally verify the pressure law:

  1. Place an air-filled flask in a temperature-controlled water bath.
  2. Record the initial temperature and pressure.
  3. Heat or cool the water, while recording the pressure and temperature changes.
  4. Plot these changes on a graph of pressure vs. temperature.
  5. Extrapolate the line to find where it intersects the x-axis, which provides an experimental value for absolute zero.

Worked example - Applying the pressure law in a tyre

A car tyre has a pressure of 202 kPa at 15°C. Calculate the pressure in the tyre if the temperature increases to 35°C.


Step 1: Pressure law formula

T1​p1​​=T2​p2​​


Step 2: Convert celsius to kelvin

to convert from °C to K, add 273.15

T1​ = 288.15 K

T2​ = 308.15 K


Step 3: Substitution and correct evaluation

p2​=p1​×T1​T2​​ = 202,000 ×288.15308.15​=216 kPa

Charles' law - Volume and temperature relationship

Graph showing the direct proportional relationship between volume and temperature according to Charles' Law.

Charles' Law proposes that at a constant pressure, the volume (V) and the absolute temperature (T) of a gas are directly proportional:


TV​ = constant


Where:

V = volume (m3)

T = temperature (K)

Worked example - Applying Charles' law in a balloon

A helium balloon contains

A helium-filled balloon has a volume of 1 x 10-3 m3 at 20°C.

Calculate the volume of the helium when the temperature is increased to 50°C.


Step 1: Charles' law formula

T1​V1​​=T2​V2​​


Step 2: Convert celsius to kelvin

to convert form °C to K, add 273.15

20°C = 293.15 K

50°C = 323.15 K


Step 3: Substitution and correct evaluation

V2​ = T1​V1​T2​​

V2​ = 293.151×10−3×323.15​ = 1.1 x 10−3 m3

Worked example - Applying Charles' law in a balloon

A helium-filled balloon has a volume of 1 x 10-3 m3 at 20°C.

Calculate the volume of the helium when the temperature is increased to 50°C.


Step 1: Charles' law formula

T1​V1​​=T2​V2​​


Step 2: Convert celsius to kelvin

to convert form °C to K, add 273.15

20°C = 293.15 K

50°C = 323.15 K


Step 3: Rearrangement

V2​ = T1​V1​T2​​


Step 4: Substitution and correct evaluation

V2​ = 293.151×10−3×323.15​ = 1.1 x 10−3 m3