Boyle’s Law: The Pressure-Volume Relationship in Gases
Boyle’s Law: The Pressure-Volume Relationship in Gases
Definition
Boyle’s Law states that the volume of a fixed amount of gas is inversely proportional to its pressure when temperature is held constant.
Mathematical Expression
P ∝ 1/V
PV = k (where k is a constant)
or
P₁V₁ = P₂V₂ = k
Conditions
- Temperature (T) must remain constant
- The amount of gas (n) must not change
- Applies to ideal gases (no intermolecular forces, negligible particle volume)
Experimental Verification
Robert Boyle verified this law using a J-shaped tube with mercury. Modern verification uses a cylinder with a movable piston:
| Pressure (atm) | Volume (dm³) | P × V (dm³·atm) | Observation |
|---|---|---|---|
| 2.0 | 1.0 | 2.0 | Initial state |
| 4.0 | 0.5 | 2.0 | Pressure doubled → volume halved |
| 6.0 | 0.33 | 2.0 | Pressure tripled → volume reduced to 1/3 |
Conclusion: The product PV remains constant (k = 2.0 dm³·atm in this experiment), verifying Boyle’s Law.
Example Calculation
Problem: A gas occupies 10.0 dm³ at 2.5 atm and 0°C. What is its volume at 2.0 atm (temperature constant)?
Solution
Given:
- P₁ = 2.5 atm
- V₁ = 10.0 dm³
- P₂ = 2.0 atm
- T = constant (0°C = 273 K)
Apply Boyle’s Law:
P₁V₁ = P₂V₂
V₂ = (P₁V₁)/P₂ = (2.5 atm × 10.0 dm³)/2.0 atm = 12.5 dm³
Answer: The new volume is 12.5 dm³.
Graphical Representation
A graph with pressure on the x-axis and volume on the y-axis creates a curve called an isotherm, where “iso” means the same and “therm” means heat.
When the gas temperature is increased and held constant while varying pressure and volume, the isotherm moves away from both axes due to the increase in gas volume with higher temperatures. Further temperature increases will result in additional isotherms that are positioned even further from the axes.
Kinetic Molecular Theory Explanation
Boyle’s Law can be explained at the molecular level:
- Gas particles are in constant random motion, colliding with container walls (creating pressure).
- When volume decreases (compression):
- Particles are confined to a smaller space
- Collisions with walls become more frequent
- Result: Higher pressure
- When volume increases (expansion):
- Particles spread out
- Collisions with walls become less frequent
- Result: Lower pressure
- Temperature remains constant: Average kinetic energy of particles doesn’t change
Practical Applications
- Syringes:
- Pulling the plunger increases volume → decreases pressure → draws fluid in
- Pushing the plunger decreases volume → increases pressure → expels fluid
- Scuba Diving Tanks:
- Air is compressed to a high pressure (small volume) for storage
- As a diver uses air, pressure decreases, and volume remains constant
- Breathing:
- Diaphragm expands chest cavity (↑V) → ↓P in lungs → air flows in
- Diaphragm contracts (↓V) → ↑P in lungs → air flows out
Limitations of Boyle’s Law
Boyle’s Law applies perfectly only to ideal gases. Real gases show deviations:
- At high pressures:
-
- Gas particles occupy a significant volume
- Intermolecular forces become noticeable
- The actual volume is greater than predicted
-
- At low temperatures:
- Intermolecular attractions become significant
- Actual pressure is less than predicted
- Near condensation points:
- Gas begins to liquefy
- The law completely breaks down
These deviations are accounted for in the van der Waals equation.
Historical Context
Robert Boyle (1627-1691) first published this law in 1662 after experiments with air trapped in a J-shaped glass tube sealed with mercury. By adding mercury to increase pressure, he observed volume changes, establishing the inverse relationship.
