Combined Gas Law Calculator

Free Combined Gas Law Calculator - calculate combined gas law for chemistry problems. Accurate results using standard formulas.

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What the combined gas law calculator does and when to use it

The combined gas law links the pressure, volume and temperature of a fixed amount of gas. If a gas sample changes from one state to another and no gas enters or leaves, the quantity pressure times volume divided by temperature stays the same. This calculator takes your starting pressure, volume and temperature, then any two of the three final values, and solves for whichever one you leave blank. It also reports the number of moles of gas, calculated from the ideal gas law.

It is the tool to reach for in chemistry and physics problems such as a balloon rising into thinner air, a syringe being compressed, or a sealed container being heated. Because the law merges Boyle's, Charles's and Gay-Lussac's laws, you can also use it when only one property changes: keep the other two the same in both states and the corresponding single-variable law falls out. It assumes ideal-gas behavior, so it is most accurate at moderate pressures and temperatures well above the gas's condensation point.

Formula and variables

The calculator uses P1V1 / T1 = P2V2 / T2, rearranged for the blank value.

  • P is pressure in atmospheres, V is volume in litres, and T is absolute temperature in kelvin (K = °C + 273.15). Subscript 1 is the starting state and 2 is the final state.
  • P2 = P1V1T2 / (T1V2); V2 = P1V1T2 / (T1P2); T2 = P2V2T1 / (P1V1).
  • Moles n = P1V1 / (R T1) with R = 0.082057 L·atm/(mol·K).

Pressure and volume units cancel in the ratio, so any consistent units work for the combined law itself, but the mole calculation needs atm and litres.

Worked example: heating and compressing a gas

A gas starts at P1 = 1 atm, V1 = 2 L and T1 = 300 K. It is compressed to P2 = 2 atm and heated to T2 = 350 K. Leave V2 blank.

  • P1V1/T1 = (1 × 2) / 300 = 0.006667 atm·L/K.
  • V2 = 0.006667 × 350 / 2 = 1.1667 L.
  • Check: P2V2/T2 = (2 × 1.1667) / 350 = 0.006667, matching the start.
  • Moles: n = (1 × 2) / (0.082057 × 300) = 0.0812 mol.

The doubling of pressure would halve the volume to 1 L, and the temperature increase from 300 K to 350 K stretches it by a factor of 1.1667, which gives the same answer.

Common mistakes and how to interpret the result

  • Using Celsius. Temperatures must be in kelvin. Using 25 instead of 298.15 gives wildly wrong answers and can even give negative values.
  • Filling in all three final values or only one. Exactly one of P2, V2, T2 must be blank.
  • Letting gas escape. The law only applies to a fixed amount of gas; a leaking balloon or open container breaks the assumption.
  • Ignoring real-gas effects. At very high pressure or near condensation, real gases deviate from ideal behavior and the answer becomes approximate.

Frequently Asked Questions

What is the difference between the combined and ideal gas laws?
The combined gas law compares two states of the same gas sample and needs no knowledge of how much gas there is. The ideal gas law, PV = nRT, describes one state and includes the amount n. This calculator uses the first for your answer and the second for the mole count.
Why must temperature be in kelvin?
Kelvin is an absolute scale where zero means no thermal motion in the ideal model. The law relies on temperature being proportional to average molecular energy, which is not true for Celsius or Fahrenheit.
Can I use other pressure or volume units?
For the combined-law ratio, yes, as long as you use the same units in both states. The mole count assumes atmospheres and litres.
What if I only know two of the three starting values?
Then the problem has too few knowns. You need the complete starting state and two of the three final values, or use the ideal gas calculator if the amount of gas is known.

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