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Boyle's Law — Definition, Formula & Examples

Boyle's Law is a rule about gases. It says that if you squeeze a gas into a smaller space without changing its temperature, its pressure goes up by the same factor that its volume goes down.

For a fixed amount of an ideal gas held at constant temperature, pressure PP varies inversely with volume VV. That is, PV=kPV = k for some positive constant kk, or equivalently P=kVP = \dfrac{k}{V}.

Key Formula

P1V1=P2V2P_1V_1 = P_2V_2
Where:
  • P1P_1 = Starting pressure of the gas (for example, in kPa)
  • V1V_1 = Starting volume of the gas (for example, in L)
  • P2P_2 = New pressure, measured in the same unit as P_1
  • V2V_2 = New volume, measured in the same unit as V_1

How It Works

Because the product PVPV never changes, you can compare any two states of the same gas with the equation P1V1=P2V2P_1V_1 = P_2V_2. If you know three of the four values, solve for the fourth. A quick check is that halving the volume doubles the pressure, and tripling the volume cuts the pressure to one third. On a graph of PP against VV, the points lie on a curve called a hyperbola, not on a straight line.

Worked Example

Problem: A sample of gas occupies 6 L at a pressure of 100 kPa. A piston compresses it to 2 L, and the temperature stays the same. What is the new pressure?
Step 1: Find the constant product kk from the starting state.
k=P1V1=(100)(6)=600 kPa⋅Lk = P_1V_1 = (100)(6) = 600 \ \text{kPa}\cdot\text{L}
Step 2: Set the new product equal to the same constant.
P2(2)=600P_2(2) = 600
Step 3: Divide both sides by 2 to solve for P2P_2.
P2=6002=300 kPaP_2 = \frac{600}{2} = 300 \ \text{kPa}
Answer: The new pressure is 300 kPa. The volume dropped to one third, so the pressure tripled.

Another Example

Problem: A weather balloon holds 4 L of gas at 100 kPa. It rises to a height where the pressure is 80 kPa. Assuming the temperature stays constant, what is its new volume?
Step 1: Write Boyle's Law with the known values.
(100)(4)=(80)V2(100)(4) = (80)V_2
Step 2: Multiply on the left, then divide by 80.
V2=40080=5 LV_2 = \frac{400}{80} = 5 \ \text{L}
Answer: The balloon expands to 5 L. Lower pressure means a larger volume.

Visualization

Why It Matters

Boyle's Law is one of the first real-world examples of inverse variation in Algebra 2. It also appears again in chemistry class as part of the combined and ideal gas laws. Scuba divers rely on it to understand why air in their lungs expands as they rise, and engineers use it to design syringes, air compressors, and car engines.

Common Mistakes

Mistake: Writing P1V1=P2V2\dfrac{P_1}{V_1} = \dfrac{P_2}{V_2}, which treats pressure and volume as varying directly.
Correction: Pressure and volume move in opposite directions, so their product stays constant, not their ratio. Always multiply: P1V1=P2V2P_1V_1 = P_2V_2. Then check that a smaller volume gives a larger pressure.
Mistake: Applying Boyle's Law when the temperature or the amount of gas changes.
Correction: The law only holds for a fixed amount of gas at constant temperature. If the temperature changes, use the combined gas law P1V1T1=P2V2T2\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2} instead.

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