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Free Combined Gas Law Calculator

The combined gas law relates the pressure, volume, and absolute temperature of a fixed amount of gas between two states. It states that the quantity PV/T stays constant when the amount of gas does not change, which is written P1·V1/T1 = P2·V2/T2. Enter any five of the six values (two pressures, two volumes, two temperatures) and this calculator solves for the sixth. Temperatures must be entered on the Kelvin (absolute) scale; a value in Celsius is converted with K = °C + 273.15. Pressure and volume may use any units, provided you use the same unit for both states.

Volume 2 (V₂)
1

P₁V₁/T₁ = P₂V₂/T₂. Pressures and volumes use any consistent units; temperatures must be in kelvin. Contains Boyle's law (T constant), Charles's law (P constant), and Gay-Lussac's law (V constant).

Quick answer

The combined gas law states that P1·V1/T1 = P2·V2/T2 for a fixed amount of gas, where temperature is measured in Kelvin. To solve for an unknown, rearrange the equation: for example, V2 = P1·V1·T2 / (T1·P2). The same units must be used for both pressure values and for both volume values, and both temperatures must be on the absolute (Kelvin) scale.

Formula & method

P₁V₁ / T₁ = P₂V₂ / T₂

Contains Boyle's law (T constant), Charles's law (P constant), and Gay-Lussac's law (V constant). Temperatures must be in KELVIN.

Examples

Example 1: Boyle's law special case (temperature constant)
Input
A gas occupies 4.0 L at 1.0 atm. It is compressed to 2.0 atm at constant temperature. Find the new volume.
Result
V2 = 2.0 L
Why
When temperature is held constant, T1 = T2 cancels and the combined gas law reduces to Boyle's law: P1·V1 = P2·V2. Solving, V2 = P1·V1/P2 = (1.0 atm × 4.0 L) / 2.0 atm = 2.0 L. Doubling the pressure halves the volume, the inverse relationship Boyle observed.
Example 2: Charles's law special case (pressure constant)
Input
A balloon holds 2.0 L at 300 K. It is warmed to 450 K at constant pressure. Find the new volume.
Result
V2 = 3.0 L
Why
When pressure is held constant, P1 = P2 cancels and the combined gas law reduces to Charles's law: V1/T1 = V2/T2. Solving, V2 = V1·T2/T1 = 2.0 L × (450 K / 300 K) = 3.0 L. Volume is directly proportional to absolute temperature, so a 1.5x rise in Kelvin gives a 1.5x rise in volume.
Example 3: Gay-Lussac's law special case (volume constant)
Input
A sealed rigid cylinder reads 2.0 atm at 300 K. It is heated to 360 K. Find the new pressure.
Result
P2 = 2.4 atm
Why
When volume is held constant, V1 = V2 cancels and the combined gas law reduces to Gay-Lussac's law: P1/T1 = P2/T2. Solving, P2 = P1·T2/T1 = 2.0 atm × (360 K / 300 K) = 2.4 atm. Pressure is directly proportional to absolute temperature in a fixed, rigid volume.
Example 4: Full combined gas law (all three variables change)
Input
A gas occupies 5.0 L at 1.0 atm and 300 K. It is changed to 2.0 atm and 330 K. Find the new volume.
Result
V2 = 2.75 L
Why
With all three properties changing, rearrange the full law for V2: V2 = (P1·V1·T2) / (T1·P2) = (1.0 atm × 5.0 L × 330 K) / (300 K × 2.0 atm) = 1650 / 600 = 2.75 L. The pressure increase shrinks the volume while the temperature increase partly offsets it.

When to use this tool

  • Finding how a gas's volume, pressure, or temperature changes between two states when the amount of gas is fixed.
  • Working chemistry or physics homework that involves a before-and-after gas change with two or three properties varying at once.
  • Quickly checking a Boyle's, Charles's, or Gay-Lussac's law problem, since each is a special case obtained by holding one variable constant.
  • Estimating how a sealed container's pressure responds to heating or cooling, or how a balloon's volume responds to altitude or temperature shifts.
  • Teaching or learning how the three classical gas laws unify into a single relationship before introducing the ideal gas law (PV = nRT).

Common mistakes

  • Using Celsius or Fahrenheit instead of Kelvin. The law depends on absolute temperature; always convert first with K = °C + 273.15. Using a scale with negative or arbitrary-zero values gives wrong (or even negative) results.
  • Mixing units between the two states. The pressure unit must match for P1 and P2, and the volume unit must match for V1 and V2. The actual unit (atm, kPa, L, mL) does not matter as long as it is the same on both sides; only temperature is locked to Kelvin.
  • Forgetting that the amount of gas (moles) and its identity must stay fixed. The combined gas law applies only when no gas is added, removed, or leaks between the two states.
  • Inverting a ratio when rearranging. A reliable approach is to cross-multiply P1·V1·T2 = P2·V2·T1 first, then isolate the unknown, rather than guessing whether a ratio should be flipped.
  • Assuming the law is exact for real gases under all conditions. It models an ideal gas; accuracy drops at very high pressure or very low temperature, where intermolecular forces and molecular volume become significant.

Frequently asked questions

Why must temperature be in Kelvin?

The combined gas law is built on absolute temperature, which is measured in Kelvin. Kelvin starts at absolute zero, the point where molecular motion theoretically stops, so a Kelvin value is directly proportional to the average kinetic energy of the gas particles. Celsius and Fahrenheit place their zero at arbitrary points and can be negative, which would produce meaningless or negative results in the ratios. Convert with K = °C + 273.15 before calculating.

How does the combined gas law relate to Boyle's, Charles's, and Gay-Lussac's laws?

Each of the three classical laws is a special case of the combined gas law obtained by holding one variable constant. Hold temperature constant and it becomes Boyle's law (P1·V1 = P2·V2). Hold pressure constant and it becomes Charles's law (V1/T1 = V2/T2). Hold volume constant and it becomes Gay-Lussac's law (P1/T1 = P2/T2). The combined gas law simply lets all three properties change at once.

Do pressure and volume need specific units?

No. You may use any pressure unit (atm, kPa, mmHg, psi) and any volume unit (L, mL, m^3), as long as you use the same unit for both states. Because the units appear on both sides of the equation, they cancel. Temperature is the exception: it must be on the Kelvin scale. If you ever need an absolute pressure-volume product, choose consistent units throughout.

What is the difference between the combined gas law and the ideal gas law?

The combined gas law (P1·V1/T1 = P2·V2/T2) compares two states of the same fixed amount of gas, so the number of moles never appears. The ideal gas law (PV = nRT) describes a single state and includes the amount of gas n and the gas constant R. The combined gas law is effectively the ideal gas law applied to two states with n held constant, so nR cancels out.

Does this law work for real gases?

It is an idealisation. It models an ideal gas accurately at moderate temperatures and pressures, conditions common in everyday and classroom problems. At very high pressures or very low temperatures, real gases deviate because intermolecular attractions and the finite size of molecules become significant, and more advanced equations of state (such as the van der Waals equation) give better results.

How do I rearrange the equation to solve for a different variable?

Start from the cross-multiplied form P1·V1·T2 = P2·V2·T1, then isolate the unknown. For example, V2 = (P1·V1·T2) / (T1·P2), P2 = (P1·V1·T2) / (T1·V2), or T2 = (P2·V2·T1) / (P1·V1). This calculator does the rearrangement automatically once you leave one field blank.

Sources & references

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