Boyle’s Law Calculator (P₁V₁ = P₂V₂)
Solve pressure–volume problems fast. Enter any three of P₁, V₁, P₂, V₂ and the calculator will compute the fourth using Boyle’s Law (constant temperature & moles).
Background
Boyle’s Law describes an inverse relationship between pressure and volume for a fixed amount of gas at constant temperature: when pressure increases, volume decreases proportionally, and vice versa. Mathematically, P₁V₁ = P₂V₂. This calculator supports common pressure/volume units and shows the steps.
How to use this calculator
1) Choose which variable to solve for (default P₂).
2) Enter the other three values and their units.
3) Click Calculate. You’ll see unit conversions, the Boyle’s Law setup, and the answer.
Key Points
- Boyle’s Law: P₁V₁ = P₂V₂ (constant T and n).
- Keep units consistent—this tool converts pressure to atm and volume to L internally.
- Typical assumptions: ideal gas behavior, no temperature change.
Formula & Rearrangements
P₁V₁ = P₂V₂
- Solve for P₂: P₂ = (P₁V₁) / V₂
- Solve for V₂: V₂ = (P₁V₁) / P₂
- Solve for P₁: P₁ = (P₂V₂) / V₁
- Solve for V₁: V₁ = (P₂V₂) / P₁
Example Problems & Step-by-Step Solutions
Example 1
A gas at P₁ = 1.00 atm, V₁ = 2.50 L is compressed to V₂ = 1.00 L. Find P₂.
- Use P₁V₁ = P₂V₂ → P₂ = (P₁V₁)/V₂
- P₂ = (1.00 atm × 2.50 L) / 1.00 L = 2.50 atm
Example 2
A gas at P₁ = 760 mmHg, V₁ = 500 mL expands to P₂ = 380 mmHg. Find V₂.
- Convert: 760 mmHg = 1.00 atm; 380 mmHg = 0.500 atm; 500 mL = 0.500 L.
- V₂ = (P₁V₁)/P₂ = (1.00 atm × 0.500 L) / 0.500 atm = 1.00 L.
Frequently Asked Questions
Q: When can I use Boyle’s Law?
When temperature and the amount of gas are constant (isothermal, closed system).
Q: Which units are supported?
Pressures: atm, kPa, mmHg (torr), Pa. Volumes: L, mL, cm³. All values are converted internally.
Q: Does this consider non-ideal gases?
This uses the ideal gas assumption, which is usually fine for typical general-chem problems.
