Combined Gas Law Calculator
Solve for pressure, volume, or temperature changes simultaneously ($(P_1V_1)/T_1 = (P_2V_2)/T_2$).
Initial State (1)
Final State (2)
Unified State Visualizer
The Grand Unification
The Combined Gas Law is the "Swiss Army Knife" of thermodynamics. It merges three famous laws into one master equation, allowing you to predict the behavior of any gas in a closed system.
The Master Equation
Pressure × Volume ÷ Temperature = Constant (k)
Deriving the Law
This law isn't a "new" discovery but a mathematical synthesis. By holding one variable constant, this single formula transforms into the others:
- Constant T→Boyle's Law
- Constant P→Charles's Law
- Constant V→Gay-Lussac's Law
Proportionality
The relationships are intuitive if you think about them logically:
Cloud Formation
As warm air rises, pressure drops (P↓). According to the law, this expansion causes the temperature to drop (T↓). When T drops below the dew point, clouds form.
Diesel Engines
Diesel engines compress air rapidly (V↓↓, P↑↑). This massive compression causes the temperature to skyrocket (T↑↑) enough to spontaneously ignite the fuel without a spark plug.
Scientific Balloons
Weather balloons are launched only 10% full. Why? Because at 100,000 feet, the pressure is so low that the gas expands 100x. If filled completely, they would pop instantly.
Explore More Chemistry Tools
Frequently Asked Questions
What is the Combined Gas Law?
It is a gas law that combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single formula. It describes how Pressure (P), Volume (V), and Temperature (T) interact when the amount of gas remains constant.
What is the formula?
The formula is (P1V1) / T1 = (P2V2) / T2. This equation shows that the ratio of the product of pressure and volume to temperature is constant.
When should I use it?
Use this law when all three variables (Pressure, Volume, Temp) are changing simultaneously, or when you are given 5 values and need to calculate the 6th. It is the most versatile choice for 'closed system' problems.
Do I have to use Kelvin?
Yes. Using Celsius or Fahrenheit is a critical mistake. Calculations involving gas laws must use an absolute temperature scale (Kelvin) to avoid dividing by zero or getting negative volumes.
What if one variable stays constant?
If a variable is constant (e.g., T1 = T2), you can simply cancel it out from the equation. This automatically reverts the formula back to a simpler law (e.g., Boyle's Law P1V1 = P2V2).
Do pressure and volume units matter?
As long as the units are consistent (e.g., liters on both sides, atm on both sides), the math works out. You don't necessarily need to convert to standard units like Pascals or Cubic Meters unless asked.
What is STP?
STP stands for Standard Temperature and Pressure. It is defined as 0°C (273.15 K) and 1 atm (101.325 kPa). Many problems ask you to find the volume of a gas at STP.
How is it related to the Ideal Gas Law?
The Ideal Gas Law is PV = nRT. Since 'n' (moles) and 'R' (gas constant) are static for a closed container, we can rearrange it to say PV/T = k (constant). This proves that the initial state must equal the final state.
Why does the balloon expand when it rises?
Two forces are at work. The drop in external pressure tries to expand the balloon. The drop in temperature tries to shrink it. Because pressure drops exponentially with altitude, the expansion effect usually wins.
Does this law work for liquids?
No. Liquids are generally incompressible (volume doesn't change much with pressure). This law applies specifically to gases which have large spaces between molecules.
Who discovered this law?
There is no single discoverer. It is a mathematical unification of the earlier works of Robert Boyle (1662), Jacques Charles (1787), and Joseph Louis Gay-Lussac (1808).
What is absolute zero?
0 Kelvin (-273.15°C). It is the theoretical temperature where all molecular motion stops. In the Combined Gas Law, if T reached zero, the volume would theoretically collapse to zero.
Can I solve for Temperature (T2)?
Yes, but be careful with algebra. To isolate T2, the formula becomes: T2 = (P2V2T1) / (P1V1).
What are common mistakes?
The most common errors are: 1) Forgetting to convert Celsius to Kelvin. 2) Using mismatched units (e.g., mL on one side and L on the other). 3) Algebra mistakes when rearranging variables.
Is density related?
Yes. Since Density = Mass/Volume, and Mass is constant, Density is inversely proportional to Volume. You can rewrite the law as P1/(D1T1) = P2/(D2T2).