The Ideal Gas Law Explained

Why does a sealed bag of chips puff up on a plane, then shrink back on the ground? One formula explains it: the ideal gas law. It links pressure, volume, moles, and temperature in a single equation, PV = nRT, so you can predict how a gas reacts when one of those values shifts. Once you know what each letter stands for, the formula turns into a simple, reliable tool instead of a string of symbols.

What the Ideal Gas Law Says

The ideal gas law is written as PV = nRT. In plain words, pressure times volume equals moles times the gas constant times temperature. It is one of the most useful formulas in chemistry because it connects four measurable properties of any gas into one relationship.

The formula works as a package deal that grew out of three older, narrower gas laws. Rather than learning several separate rules, you can use PV = nRT to handle almost any basic gas problem in one step.

A gas that obeys this formula exactly is called an “ideal gas.” Real gases like air, oxygen, and nitrogen follow it closely enough under everyday conditions to make it genuinely useful, not just a classroom exercise.

Breaking Down Each Letter in Pv = Nrt

Each letter in the formula stands for a specific, measurable property of a gas. Knowing what each one means, and its usual unit, is the first step to using the formula correctly.

The amount of gas, n, is measured in moles, a counting unit for particles. If moles and Avogadro’s number are new to you, our guide on moles and Avogadro’s number explained covers that piece on its own.

What Makes a Gas Ideal

The word “ideal” describes a simplified model, not a judgment about the gas. An ideal gas is one that follows three simplifying assumptions perfectly.

• Its particles take up no space of their own; they are treated as tiny points.
• Its particles do not attract or repel each other at a distance.
• Its particles bounce off each other and the container walls without losing energy.

No real gas follows these assumptions perfectly, because real molecules do have a tiny size and do feel weak forces between them. Even so, gases like air behave very close to ideal at normal room temperature and everyday pressure. That closeness is exactly why PV = nRT is so widely used in real chemistry and engineering problems.

Getting to Know the Gas Constant R

R is the one part of the formula that never changes for a given set of units. It is the fixed number that makes the two sides of the equation balance correctly.

The value you use depends on the units for pressure and volume in your problem. The two most common versions are:

• R = 8.314 J/(mol*K), used when pressure is in pascals and volume is in cubic meters (SI units).
• R = 0.0821 L*atm/(mol*K), used when pressure is in atmospheres and volume is in liters.

Picking the wrong version of R for your units is the single most common mistake in ideal gas law problems. Always check that your pressure and volume units match the R value you choose before you calculate.

Why Temperature Must Be in Kelvin

Kelvin is an absolute temperature scale, meaning it starts at absolute zero, the coldest possible temperature. Celsius and Fahrenheit do not start at zero energy, so they can show negative or zero readings that have nothing to do with a gas having no energy.

If you plugged 0 degrees Celsius directly into PV = nRT as if it were zero, the math would say the gas has no pressure or volume at all, which is false. Zero degrees Celsius is actually 273.15 Kelvin, a perfectly normal temperature for a gas.

To convert, add 273.15 to any Celsius reading. Always convert temperature to Kelvin first, before you touch any other part of the ideal gas law formula.

How the Four Variables Affect Each Other

Because PV always equals nRT, the four variables are locked together. Change one, hold two others steady, and the fourth must shift to keep both sides equal.

• Hold moles and temperature steady: pressure and volume move opposite to each other. Squeeze the volume down and pressure rises.
• Hold moles and pressure steady: volume and temperature rise and fall together. Heat the gas and it expands.
• Hold volume and temperature steady: pressure and moles rise and fall together. Pump in more gas and pressure climbs.
• Hold pressure and temperature steady: volume and moles rise and fall together. Add more gas and it needs more room.

You do not need to memorize each pairing separately. Once you understand PV = nRT as a whole, every one of these patterns falls directly out of the same formula.

Worked Example: Finding the Volume of a Gas

Numbers make the formula click faster than theory alone. Here is one full example, solved step by step.

Problem: You have 1 mole of gas at a temperature of 273.15 K (0 degrees Celsius) and a pressure of 1 atm. What volume does it fill?

Step 1: Start with the formula. PV = nRT.

Step 2: Solve for V. Divide both sides by P, so V = nRT / P.

Step 3: Pick the right R. Since pressure is in atm and we want volume in liters, use R = 0.0821 L*atm/(mol*K).

Step 4: Plug in the numbers. V = (1 mol) x (0.0821 L*atm/(mol*K)) x (273.15 K) / (1 atm).

Step 5: Do the math. 0.0821 x 273.15 = 22.42 (rounded). Divide by 1, and V is about 22.4 liters.

You can check any similar problem, or skip the manual steps entirely, with our Ideal Gas Law Calculator. It solves for whichever variable you are missing once you enter the other three.

Comparing a Gas at Low and High Temperature and Pressure

Picture the same sealed, rigid container holding the same amount of gas in both cases, so only temperature and pressure change.

At low temperature and low pressure, gas particles move slowly and hit the container walls gently and less often. The push they create on the walls, the pressure, stays low.

At high temperature and high pressure, the same particles move fast and slam into the walls harder and more often. That stronger, more frequent bombardment is what higher pressure actually means at the particle level.

This is the ideal gas law in action: with volume and moles fixed, pressure and temperature rise and fall together, exactly as PV = nRT predicts.

When the Ideal Gas Law Is Not Enough

The ideal gas law is remarkably accurate for everyday conditions, like room temperature and normal atmospheric pressure. It starts to lose accuracy at very high pressure or very low temperature.

Under those extreme conditions, real particle size and real attractive forces finally matter enough to throw off the simple math. Chemists then reach for more advanced formulas built for those edge cases, but for the vast majority of classroom and lab problems, PV = nRT is the right tool.

Related Chemistry Concepts to Explore

The ideal gas law connects naturally to a few other core chemistry topics that this article does not cover in depth.

The n in PV = nRT is measured in moles, which is built on Avogadro’s number. For that foundation, see our guide on moles and Avogadro’s number explained.

If you are working with gases dissolved in or reacting with solutions, our guide on how to calculate molarity explains that related, but separate, concept.

Frequently Asked Questions About the Ideal Gas Law

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This article is for general education only. Formulas and examples use standard chemistry conventions and ideal conditions, so real-world lab results can vary with technique, purity, and equipment. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 13, 2026.