Edexcel A Level (IAL) Physics-5.6 Ideal Gas Equation- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -5.6 Ideal Gas Equation- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -5.6 Ideal Gas Equation- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- be able to use the equation pV = NkT for an ideal gas
Using the Ideal Gas Equation \( pV = NkT \)
The ideal gas equation relates the macroscopic properties of a gas (pressure and volume) to the microscopic behaviour of its molecules.
The Ideal Gas Equation
The equation for an ideal gas is:
\( pV = NkT \)
- \( p \) = pressure of the gas (Pa)
- \( V \) = volume of the gas (m³)
- \( N \) = number of molecules
- \( k \) = Boltzmann constant \( (1.38\times10^{-23}\ \mathrm{J\,K^{-1}}) \)
- \( T \) = absolute temperature (K)
Important: Temperature must always be in kelvin.
Meaning of the Equation
- Gas pressure is caused by molecules colliding with the container walls.
- Higher temperature → molecules move faster → greater pressure.
- More molecules → more collisions → greater pressure.
- Larger volume → fewer collisions per unit area → lower pressure.
This equation links molecular motion to observable gas behaviour.
When the Equation Applies
- Gas molecules have negligible volume.
- No intermolecular forces between molecules.
- Molecules move randomly and collide elastically.
- Gas is dilute and at relatively low pressure.
Under these conditions, a gas behaves as an ideal gas.
Rearranging the Equation
The equation can be rearranged to find different quantities:
- \( p = \dfrac{NkT}{V} \)
- \( V = \dfrac{NkT}{p} \)
- \( T = \dfrac{pV}{Nk} \)
- \( N = \dfrac{pV}{kT} \)
Relation to \( pV = nRT \)
The macroscopic ideal gas equation is:
\( pV = nRT \)
- \( n \) = number of moles
- \( R \) = molar gas constant
These two equations are related by:
\( R = N_A k \)
where \( N_A \) is the Avogadro constant.
Example (Easy)
A gas contains \( 2.0\times10^{22} \) molecules at a temperature of \( 300\,\mathrm{K} \). Calculate the pressure if the volume is \( 0.010\,\mathrm{m^3} \).
▶️ Answer / Explanation
Use \( p = \dfrac{NkT}{V} \):
\( p = \dfrac{(2.0\times10^{22})(1.38\times10^{-23})(300)}{0.010} \)
\( p = \dfrac{82.8}{0.010} = 8.28\times10^{3}\ \mathrm{Pa} \)
Example (Medium)
A container holds gas at pressure \( 1.0\times10^{5}\ \mathrm{Pa} \) and temperature \( 300\,\mathrm{K} \). If the volume is \( 0.025\,\mathrm{m^3} \), find the number of molecules.
▶️ Answer / Explanation
Use \( N = \dfrac{pV}{kT} \):
\( N = \dfrac{(1.0\times10^{5})(0.025)}{(1.38\times10^{-23})(300)} \)
\( N \approx 6.0\times10^{23} \)
Example (Hard)
A gas at constant volume has its absolute temperature doubled. Explain how the pressure changes using the ideal gas equation.
▶️ Answer / Explanation
- From \( pV = NkT \), at constant \( V \) and \( N \): \( p \propto T \).
- If \( T \) doubles, pressure doubles.
- This is because molecules move faster and collide more frequently.