Ideal Gas Law — PV = nRT Explained with Examples

The ideal gas law is the equation

$$PV = nRT$$

It connects four quantities in one model: pressure $P$, volume $V$, amount of gas $n$ in moles, and absolute temperature $T$. If you know three of them, you can usually solve for the fourth.

That is the fast intuition. More gas means a larger $n$, hotter gas means a larger $T$, and both effects tend to increase pressure or volume unless one of those is being held fixed.

What $PV = nRT$ Actually Means

The equation is not saying every gas behaves perfectly in every condition. It is a model for an ideal gas, which means the particles are treated as having negligible volume and negligible intermolecular forces except during collisions.

For many introductory chemistry problems, that model works well enough to be useful. It usually works better at lower pressure and higher temperature. Real gases often deviate more at high pressure or near condensation conditions.

One more condition matters in every calculation: temperature must be in Kelvin. If you use Celsius directly, the ratio and the final answer will be wrong.

How To Read Each Symbol

• $P$ is pressure
• $V$ is volume
• $n$ is the amount of gas in moles
• $R$ is the gas constant
• $T$ is temperature in Kelvin

The value of $R$ depends on the units you choose. A common chemistry version is:

$$R = 0.08206\ \mathrm{L \cdot atm \cdot mol^{-1} \cdot K^{-1}}$$

If pressure is in atm and volume is in liters, this value is convenient. If you use different units, use a matching value of $R$.

A Simple Way To Think About It

Imagine a sealed container of gas.

If you heat it while keeping the same amount of gas and the same volume, the pressure rises. If you let the gas expand while keeping pressure about the same, the volume rises instead. The ideal gas law keeps those relationships in one place instead of making you switch between separate gas laws.

That is why the equation is so common. It combines the ideas behind Boyle's law, Charles's law, and Avogadro's law into one expression.

Worked Example: Solving For Volume

Suppose a gas sample has:

• $n = 0.50\ \mathrm{mol}$
• $T = 300\ \mathrm{K}$
• $P = 1.20\ \mathrm{atm}$

Find the volume using $R = 0.08206\ \mathrm{L \cdot atm \cdot mol^{-1} \cdot K^{-1}}$.

Start by rearranging the equation:

$$V = \frac{nRT}{P}$$

Substitute the values:

$$V = \frac{(0.50)(0.08206)(300)}{1.20}$$

Now simplify:

$$V = \frac{12.309}{1.20} \approx 10.26\ \mathrm{L}$$

So the gas volume is about $10.3\ \mathrm{L}$.

This example is worth remembering because it shows the full workflow clearly: choose a matching value of $R$, keep temperature in Kelvin, rearrange once, then check whether the answer is reasonable. A half mole of gas at room temperature taking up several liters at around $1\ \mathrm{atm}$ is plausible, so the result passes a quick sanity check.

Common Mistakes

Using Celsius Instead Of Kelvin

The ideal gas law uses absolute temperature. If a problem gives $27^\circ\mathrm{C}$, convert it to $300\ \mathrm{K}$ before substituting.

Mixing Units Without Changing $R$

If pressure is in atm and volume is in liters, use an $R$ value consistent with those units. If pressure is in Pa and volume is in $\mathrm{m^3}$, you need a different matching constant.

Treating The Law As Exact For Every Gas

$PV = nRT$ is an approximation. It is often very good for simple problems, but it is not equally accurate for every gas under every condition.

Forgetting What Is Being Held Fixed

Students often memorize "higher temperature means higher pressure" without stating the condition. That statement is only directly true if volume and amount of gas stay constant.

When The Ideal Gas Law Is Used

The ideal gas law appears in introductory chemistry, thermodynamics, gas collection problems, laboratory calculations, and engineering approximations. It is especially useful when you need one equation that relates pressure, volume, temperature, and moles at the same time.

It is also a practical bridge concept. Once this equation feels natural, it becomes easier to understand molar volume, real-gas deviations, and why separate gas laws are really special cases of the same model.

A Practical Next Step

Try your own version by changing just one value in the worked example, such as doubling $n$ or lowering $P$, and predict the effect before calculating. If you want to test another set of numbers or units, explore a similar case in GPAI Solver.