Combined Gas Law: formula
Enter the initial pressure, initial volume, initial temperature in kelvin, final pressure and final temperature. Pressures can be in any unit as long as both use the same one. Temperatures must be in kelvin, so add 273.15 to Celsius values.
The law states that pressure times volume divided by temperature is constant for a fixed amount of gas, so the final volume follows from the other five values.
Combined Gas Law: worked example
| Initial pressure (any unit) | 1 |
|---|---|
| Initial volume (L) | 10 |
| Initial temperature (K) | 300 |
| Final pressure (same unit) | 2 |
| Final temperature (K) | 350 |
| Final volume (L) | 5.8 |
| P × V ÷ T (constant) | 0.0333 |
It applies to an ideal gas with a fixed amount, and real gases deviate at high pressure or low temperature. Gas leaking or added changes the amount. Using Celsius instead of kelvin is the most common mistake.
Phase changes such as condensation break the law.
Combined Gas Law: changing Initial pressure (any unit)
| Initial pressure (any unit) | Final volume (L) | P × V ÷ T (constant) |
|---|---|---|
| 0.8 | 4.7 | 0.0267 |
| 0.9 | 5.3 | 0.0300 |
| 1 (example) | 5.8 | 0.0333 |
| 1.1 | 6.4 | 0.0367 |
| 1.2 | 7 | 0.0400 |
Combined Gas Law: compare input ranges
| Input | Tested from | To | Final volume (L): low input | Final volume (L): high input | Swing |
|---|---|---|---|---|---|
| Initial temperature (K) | 270 | 330 | 6.5 | 5.3 | 1.2 (20%) |
| Final pressure (same unit) | 1.8 | 2.2 | 6.5 | 5.3 | 1.2 (20%) |
| Initial pressure (any unit) | 0.9 | 1.1 | 5.3 | 6.4 | 1.2 (20%) |
| Initial volume (L) | 9 | 11 | 5.3 | 6.4 | 1.2 (20%) |
| Final temperature (K) | 315 | 385 | 5.3 | 6.4 | 1.2 (20%) |
Combined Gas Law: individual input comparisons
| Input | Value | Final volume (L) | P × V ÷ T (constant) |
|---|---|---|---|
| Initial pressure (any unit) | 0.8 | 4.7 | 0.0267 |
| 0.9 | 5.3 | 0.0300 | |
| 1 | 5.8 | 0.0333 | |
| 1.1 | 6.4 | 0.0367 | |
| 1.2 | 7 | 0.0400 | |
| Initial volume (L) | 8 | 4.7 | 0.0267 |
| 9 | 5.3 | 0.0300 | |
| 10 | 5.8 | 0.0333 | |
| 11 | 6.4 | 0.0367 | |
| 12 | 7 | 0.0400 | |
| Initial temperature (K) | 240 | 7.3 | 0.0417 |
| 270 | 6.5 | 0.0370 | |
| 300 | 5.8 | 0.0333 | |
| 330 | 5.3 | 0.0303 | |
| 360 | 4.9 | 0.0278 | |
| Final pressure (same unit) | 1.6 | 7.3 | 0.0333 |
| 1.8 | 6.5 | 0.0333 | |
| 2 | 5.8 | 0.0333 | |
| 2.2 | 5.3 | 0.0333 | |
| 2.4 | 4.9 | 0.0333 | |
| Final temperature (K) | 280 | 4.7 | 0.0333 |
| 315 | 5.3 | 0.0333 | |
| 350 | 5.8 | 0.0333 | |
| 385 | 6.4 | 0.0333 | |
| 420 | 7 | 0.0333 |
Combined Gas Law: combined input changes
| Initial pressure (any unit) / Initial volume (L) | 8 | 10 | 12 |
|---|---|---|---|
| 0.8 | 3.7 | 4.7 | 5.6 |
| 0.9 | 4.2 | 5.3 | 6.3 |
| 1 | 4.7 | 5.8 | 7 |
| 1.1 | 5.1 | 6.4 | 7.7 |
| 1.2 | 5.6 | 7 | 8.4 |
Combined Gas Law: which assumptions move the result?
Combined Gas Law: values and definitions
| Quantity and definition | Value used |
|---|---|
| Initial pressure (any unit) | 1 |
| Initial volume (L) | 10 |
| Initial temperature (K) — Kelvin: add 273.15 to a Celsius reading. | 300 |
| Final pressure (same unit) | 2 |
| Final temperature (K) | 350 |
| Final volume (L) | 5.8 |
| P × V ÷ T (constant) | 0.0333 |
Combined Gas Law: half and double Initial temperature (K)
| Initial temperature (K) | Final volume (L) |
|---|---|
| 150 | 11.7 |
| 300 | 5.8 |
| 600 | 2.9 |
Common error: Applying it when gas is added or leaks out. The law holds only for a fixed amount of gas, and a changing amount needs the ideal gas law instead.
Science & Electronics calculators: Percent Yield Calculator, PPM Concentration Calculator, Ohm's Law Calculator, Density Calculator, Molarity Calculator, Voltage Drop Calculator.
The combined gas law joins Boyle's, Charles's and Gay-Lussac's laws: pressure times volume divided by temperature stays constant for a fixed amount of gas. Raise the pressure from 1 to 2 and the temperature from 300 to 350 kelvin, and 10 liters shrink to about 5.83. Pressure pushes the volume down, and the temperature pushes it up, and the two effects multiply.
Use kelvin for both temperatures and the same pressure unit on both sides. A Celsius reading in the formula gives a result that is far off.
Convert temperatures on the temperature converter, pressures on the pressure converter, and volumes on the volume converter. The density and molarity calculators cover related lab quantities, and the percent yield and dilution pages support chemistry work.
Why must temperature be in kelvin?
Because the gas laws are proportional to absolute temperature, and Celsius and Fahrenheit have zero points that do not correspond to zero energy.
Does it work for real gases?
Approximately, at moderate pressures and temperatures. At high pressure or near condensation, real gases deviate from ideal behavior.
What is the combined gas law?
It says that pressure times volume divided by temperature stays constant for a fixed amount of gas, combining Boyle's, Charles's and Gay-Lussac's laws.