Boyle's Law

Boyle's Law states that pressure and volume are inversely proportional at constant temperature. When you compress a gas (decrease volume), its pressure increases proportionally.

Boyle's Law

P₁V₁ = P₂V₂

Initial pressure × initial volume = Final pressure × final volume

The Inverse Relationship

P ∝ 1/V (at constant T and n)

  • Double the pressure → volume cuts in half
  • Halve the pressure → volume doubles
  • Compress a gas → pressure rises
  • Expand a gas → pressure drops

Variable Definitions

P₁ = Initial Pressure

Common Units: atm, mmHg, torr, kPa, Pa, bar, psi

Pressure before the change

V₁ = Initial Volume

Common Units: L, mL, cm³, m³

Volume before the change

P₂ = Final Pressure

Units: Same as P₁

Pressure after the change

V₂ = Final Volume

Units: Same as V₁

Volume after the change

⚠️ Constant Conditions

Temperature (T) must remain constant
Amount of gas (n) must remain constant
No gas can enter or leave the system

Rearranged Forms

Find P₂:

P₂ = P₁V₁ / V₂

Find V₂:

V₂ = P₁V₁ / P₂

Find P₁:

P₁ = P₂V₂ / V₁

Find V₁:

V₁ = P₂V₂ / P₁

Step-by-Step Example

Problem: A gas at 1.50 atm occupies 6.00 L. If compressed to 2.00 L at constant temperature, what is the new pressure?

Given:

  • P₁ = 1.50 atm
  • V₁ = 6.00 L
  • V₂ = 2.00 L
  • Find: P₂

Step 1: Write Boyle's Law

P₁V₁ = P₂V₂

Step 2: Rearrange to solve for P₂

P₂ = P₁V₁ / V₂

Step 3: Substitute values

P₂ = (1.50 atm)(6.00 L) / (2.00 L)

Step 4: Calculate

P₂ = 9.00 atm·L / 2.00 L = 4.50 atm

Answer: P₂ = 4.50 atm

✅ Makes sense: Volume decreased by 1/3, so pressure increased by 3×

Real-World Applications

🫁 Breathing

Diaphragm expands lungs → volume increases → pressure drops → air rushes in

💉 Syringes

Pull plunger → volume increases → pressure drops → liquid drawn in

🎈 Balloons

Squeeze balloon → volume decreases → internal pressure increases

🤿 Scuba Diving

Ascend from depth → external pressure decreases → air in lungs expands (must exhale!)

Common Mistakes

❌ Temperature not constant

Boyle's Law ONLY works when temperature is constant. If T changes, use the Combined Gas Law instead.

❌ Unit mismatches

P₁ and P₂ must be in the same units. V₁ and V₂ must be in the same units. Convert before calculating!

❌ Flipping the relationship

It's P₁V₁ = P₂V₂, NOT P₁V₂ = P₂V₁. Initial with initial, final with final.

❌ Not checking your answer

If volume decreases, pressure MUST increase. If volume increases, pressure MUST decrease. Verify your answer makes physical sense!

Related Calculators

Frequently Asked Questions

What is Boyle's Law?

P₁V₁ = P₂V₂ at constant temperature. Pressure and volume are inversely proportional - when one goes up, the other goes down.

Why does this happen?

Gas molecules collide with container walls. Smaller volume = more collisions per area = higher pressure. Same number of molecules, less space!

When does Boyle's Law NOT work?

At very high pressures (molecules too close), very low temperatures (gas liquefies), or when temperature changes during compression.

Can I use any pressure units?

Yes, as long as P₁ and P₂ use the SAME units. atm, kPa, mmHg, psi - all work! Same rule for volume units.

How is this different from the Ideal Gas Law?

Boyle's Law is a special case of PV=nRT when n and T are constant. It's simpler when you only care about P and V changes.