Combined Gas Law Calculator
Calculate initial and final pressure, volume, and temperature of a gas system using the Combined Gas Law (P1V1/T1 = P2V2/T2) with automatic Kelvin conversion.
Calcady™ · Calculation Report Chemistry: Combined Gas Law Calculator calcady.com Gas SettingsInitial State (1)Final State (2)Calculated ValueFinal Volume (V₂)1.3333L |
Quick Answer: What is the Combined Gas Law?
The Combined Gas Law merges Boyle's, Charles's, and Gay-Lussac's Laws into one equation: (P1 x V1) / T1 = (P2 x V2) / T2. It predicts how a fixed amount of gas behaves when pressure, volume, and temperature all change simultaneously. If you hold one variable constant, the equation reduces to eachindividual law. Temperature must always be in Kelvin for the math to work correctly.
How It Reduces to Individual Gas Laws
The Combined Gas Law is the parent equation. When you lock one variable, it simplifies to a named law:
| Hold Constant | Reduces To | Formula | Real-World Example |
|---|---|---|---|
| Temperature | Boyle's Law | P1V1 = P2V2 | Squeezing a syringe (isothermal compression) |
| Pressure | Charles's Law | V1/T1 = V2/T2 | Hot air balloon expanding as air is heated |
| Volume | Gay-Lussac's Law | P1/T1 = P2/T2 | Pressure cooker heating in a rigid container |
| None | Combined Gas Law | P1V1/T1 = P2V2/T2 | Weather balloon rising (P drops, T drops, V changes) |
Pro Tips & Common Chemistry Mistakes
Do This
- ✓Always convert to Kelvin before plugging in. K = C + 273.15. A gas at 25C is 298.15 K. Plugging 25 into the formula instead of 298 produces an answer off by a factor of ~12. This calculator auto-converts, but understanding the why is essential for exams and lab work.
- ✓Match pressure and volume units on both sides. If P1 is in atm, P2 must also be in atm. If V1 is in liters, V2 must be in liters. The law does not convert units for you.
Avoid This
- ✗Do not apply when gas is added or removed. The Combined Gas Law assumes a fixed quantity (moles) of gas. If you are filling a tire (adding gas) or a balloon is leaking, you need the full Ideal Gas Law (PV = nRT) which accounts for changing n.
- ✗Do not use near phase transitions. If a gas is being cooled toward its condensation point (e.g., water vapor near 100C), it stops behaving ideally. The volume collapses as gas liquefies, and the Combined Gas Law no longer applies.
Frequently Asked Questions
When should I use the Combined Gas Law vs. the Ideal Gas Law?
Use the Combined Gas Law when you have a fixed amount of gas changing between two known states (before and after). Use PV = nRT when you need to calculate the number of moles, or when gas is being added or removed from the system. The Combined Gas Law is derived from PV = nRT by setting n and R as constants and comparing two states.
Can I use different temperature units for T1 and T2?
Yes, this calculator supports independent temperature unit selection for T1 and T2. You can enter T1 in Celsius and T2 in Fahrenheit if desired. The calculator converts both to Kelvin internally before performing the calculation. The key requirement is that the math is always done in Kelvin. Both sides of the equation must use the same absolute scale.
Why does this calculator let me solve for any of the 6 variables?
The Combined Gas Law has 6 variables (P1, V1, T1, P2, V2, T2). If you know any 5, the 6th is algebraically determined. In real-world problems, the unknown variable differs by scenario: a chemist might know initial conditions and final P/T but need V2 (balloon problem); an engineer might know both volumes and temperatures but need the final pressure (piston design).
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Calculation Provenance & Validation Record
Physics and physical sciences calculations derived from canonical mechanics, electromagnetism, and thermodynamics.