Reading Time: 2 minutesPressure (
Kinetic Theory: Understanding the Behavior of Gases in A-Level Science
What Is Kinetic Theory?
Kinetic theory explains the behavior of gases based on the motion of their particles, providing a microscopic understanding of pressure, temperature, and volume.
Assumptions of Kinetic Theory
- Gas particles are in constant, random motion
- Collisions between particles are elastic (no energy loss)
- The volume of individual particles is negligible compared to the gas volume
- No intermolecular forces act between particles
Key Formulas in Kinetic Theory
Pressure (
)
)Pressure arises from collisions of particles with container walls:
![\[ P = \frac{1}{3} \frac{Nm}{V} \langle v^2 \rangle \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-6157b38b578a3c594c4467b81e46f3a6_l3.png "Rendered by QuickLaTeX.com")
Where:
: Number of particles
: Mass of one particle- : Volume (m³)
: Mean square speed
: Number of particles
: Mass of one particle
: Volume (m³)
: Mean square speedIdeal Gas Law
![\[ PV = nRT \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-8e00f9e216b40376ab3da95300c27166_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Pressure (Pa)
- : Volume (m³)
: Number of moles
: Universal gas constant
: Temperature (K)
: Number of moles
: Universal gas constant
: Temperature (K)Applications of Kinetic Theory
Weather Prediction
Understanding atmospheric pressure and temperature helps forecast weather.
Engineering
Kinetic theory is applied in designing engines and refrigeration systems.
Medicine
Used in oxygen and anesthetic gas storage.
Example Problem
A gas occupies 
at 
and a pressure of 
. Find the number of moles.
- Formula:
![\[ PV = nRT \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4OSIgaGVpZ2h0PSIxMiIgdmlld0JveD0iMCAwIDg5IDEyIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg== "Rendered by QuickLaTeX.com")
- Rearrange for :
![\[ n = \frac{PV}{RT} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NSIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDY1IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg== "Rendered by QuickLaTeX.com")
- Substitute Values:
![\[ n = \frac{100,000 \times 0.02}{8.31 \times 300} \approx 0.8 \, \text{moles} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNDYiIGhlaWdodD0iMzYiIHZpZXdCb3g9IjAgMCAyNDYgMzYiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
![\[ n = \frac{PV}{RT} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-d79ffd1b2c24af29e097f8b14a291067_l3.png "Rendered by QuickLaTeX.com")
![\[ n = \frac{100,000 \times 0.02}{8.31 \times 300} \approx 0.8 \, \text{moles} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-a0b375d0aa1aaa333699a473a1e247b1_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes in Kinetic Theory Problems
- Forgetting to convert temperature to Kelvin
- Using incorrect units for pressure or volume
- Mixing up molar mass and mass of a gas sample
Practice Questions
- A gas has a volume of
at 
and a pressure of 
. Calculate the number of moles. - Explain how kinetic theory relates to Boyle’s Law.
- Describe one application of the ideal gas law in engineering.
at 
and a pressure of 
. Calculate the number of moles.