156
2
100
%
0.033333
atm·L/K
0.066667
atm·L/K
156
2
100
%
0.033333
atm·L/K
0.066667
atm·L/K
The Combined Gas Law Calculator solves for the final pressure, volume, or temperature of a gas when conditions change, using the relationship P₁V₁/T₁ = P₂V₂/T₂. This equation combines Boyle's law, Charles's law, and Gay-Lussac's law into a single powerful formula that handles simultaneous changes in multiple gas properties.
This tool is essential for solving gas problems where more than one condition changes simultaneously — for example, a gas being compressed and heated at the same time. It applies to a fixed amount of an ideal gas and is one of the most practical equations in chemistry and physics.
The combined gas law states that for a fixed amount of ideal gas:
$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
Rearranging to solve for each final variable:
$$P_2 = \frac{P_1 V_1 T_2}{T_1 V_2}$$
$$V_2 = \frac{P_1 V_1 T_2}{T_1 P_2}$$
$$T_2 = \frac{P_2 V_2 T_1}{P_1 V_1}$$
This equation reduces to special cases when one variable is held constant: if T is constant, it becomes Boyle's law (P₁V₁ = P₂V₂); if P is constant, it becomes Charles's law (V₁/T₁ = V₂/T₂); if V is constant, it becomes Gay-Lussac's law (P₁/T₁ = P₂/T₂). All temperatures must be in Kelvin. The change ratio shows how much the solved variable changed relative to its initial value.
The calculated value gives the final state of the gas property you selected. The change ratio indicates the factor by which it changed: a ratio greater than 1 means an increase, less than 1 means a decrease. For example, if you solve for V₂ and get a ratio of 0.5, the volume halved. Remember that this equation only applies to a fixed amount of gas — if gas is added or removed, use the ideal gas law instead.
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Results
A gas at 1 atm, 10 L, 300 K is compressed to 3 atm and heated to 450 K. The final volume is 5 L. Despite heating (which would expand the gas), the tripling of pressure dominates, reducing volume to half.
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Results
A gas expands from 5 L to 15 L while pressure drops from 2 atm to 1 atm. The final temperature is 600 K — the gas cooled less than expected because the expansion was accompanied by a pressure drop.
The combined gas law (P₁V₁/T₁ = P₂V₂/T₂) describes how pressure, volume, and temperature of a fixed amount of ideal gas are related when conditions change. It combines Boyle's, Charles's, and Gay-Lussac's laws into one equation.
The ideal gas law (PV = nRT) describes the state of a gas at a single set of conditions and requires knowing the number of moles. The combined gas law compares two states of the same gas sample and doesn't require knowing the number of moles, as n and R cancel out.
Temperature must be in Kelvin because the gas laws are based on proportionality relationships. A gas at 200 K has twice the volume of the same gas at 100 K. This proportionality fails with Celsius because 0°C doesn't represent zero molecular motion. Convert using T(K) = T(°C) + 273.15.
When temperature is constant: P₁V₁ = P₂V₂ (Boyle's law). When pressure is constant: V₁/T₁ = V₂/T₂ (Charles's law). When volume is constant: P₁/T₁ = P₂/T₂ (Gay-Lussac's law). The combined gas law contains all three as special cases.
Yes, as long as you use the same units for both initial and final values. If P₁ is in atm, P₂ must also be in atm. If V₁ is in liters, V₂ must be in liters. The units cancel in the ratios, so consistency is what matters.
Weather balloons are a classic example. As a balloon rises, atmospheric pressure decreases and temperature changes. The combined gas law predicts how the balloon expands. Scuba diving is another: divers must account for pressure-volume-temperature changes as they ascend and descend.
The combined gas law works well for real gases at moderate temperatures and pressures where ideal gas behavior is a good approximation. At high pressures or low temperatures, real gas effects (intermolecular forces, molecular volume) cause deviations and equations like van der Waals should be used.
Always convert Celsius to Kelvin before using the combined gas law: T(K) = T(°C) + 273.15. A common error is using Celsius directly, which gives incorrect results because the ratios T₂/T₁ would be wrong.
Yes, the equation is symmetric. To find P₁, V₁, or T₁, simply rearrange: P₁ = P₂V₂T₁/(T₂V₁) — but this requires knowing T₁ already. In practice, you can relabel initial and final states as needed.
It assumes: (1) the gas behaves ideally, (2) the amount of gas remains constant (no gas added or removed), and (3) the gas undergoes a quasi-static process between states. It does not require the process to be reversible or follow any particular path.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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