Ideal Gas vs Real Gas

Ideal gas vs real gas comes down to one question: when is $PV = nRT$ a good approximation? An ideal gas is a model in which particles have negligible volume and no intermolecular forces except during collisions. A real gas is an actual gas, so its molecules have finite size and can attract or repel one another.

That is why

$$PV = nRT$$

works well only under the right conditions. In general, gases behave more ideally at relatively low pressure and higher temperature, where molecules are farther apart and less likely to condense.

Ideal Gas vs Real Gas: The Core Difference

The ideal-gas model removes two real-world complications.

First, it treats gas particles as if they take up essentially no space compared with the container volume. Second, it ignores intermolecular attractions and repulsions except for perfectly elastic collisions.

Those assumptions make the math simple. They are not exactly true for real molecules, but they are often close enough for introductory chemistry and many everyday gas calculations.

Why Real Gases Deviate From The Ideal Gas Law

Real gases deviate because molecules are not points and they do interact.

If attractive forces matter, molecules pull on one another and can hit the container walls a little less forcefully. Under those conditions, the measured pressure can be lower than the ideal-gas prediction for the same $n$, $V$, and $T$.

If the gas is compressed strongly enough, the finite size of the molecules starts to matter more. Then the gas may resist compression more than the ideal model suggests. Which effect dominates depends on the gas and the condition, so the direction of deviation is not always the same.

One Worked Example Using The Compressibility Factor

A practical way to check ideality is the compressibility factor:

$$Z = \frac{PV}{nRT}$$

For an ideal gas, $Z = 1$. For a real gas, $Z$ can be above or below $1$.

Suppose $1.00\ \mathrm{mol}$ of a gas is held at $300\ \mathrm{K}$ in a $1.00\ \mathrm{L}$ container, and the measured pressure is $24.0\ \mathrm{atm}$.

If the gas were ideal, the pressure would be

$$P_{\text{ideal}} = \frac{nRT}{V} = \frac{(1.00)(0.0821)(300)}{1.00} \approx 24.6\ \mathrm{atm}$$

Now compare the measured state with ideal behavior:

$$Z = \frac{(24.0)(1.00)}{(1.00)(0.0821)(300)} \approx 0.97$$

Since $Z < 1$, this sample shows a small negative deviation from ideal behavior under these conditions. That usually means attractive forces are lowering the pressure slightly compared with the ideal prediction.

Common Mistakes When Comparing Ideal And Real Gases

Thinking The Ideal Gas Law Is Useless For Real Gases

The ideal gas law is a model, not an exact law for every gas in every condition. Many real gases still follow it closely enough for ordinary calculations.

Assuming Deviation Happens Only At High Pressure

High pressure is one common cause, but low temperature matters too. As a gas gets closer to condensation, intermolecular attractions become more important.

Assuming Deviation Always Goes In One Direction

It does not. If attractions dominate, a real gas often gives $Z < 1$. If finite molecular size and short-range repulsion dominate, it often gives $Z > 1$.

Forgetting That The Condition Matters

The same gas can behave nearly ideally in one range and noticeably non-ideally in another. You cannot label a gas as "ideal" or "real" without also thinking about pressure and temperature.

When The Ideal Gas Model Works Well

The ideal gas model usually works best when pressure is relatively low and the gas is far from condensation. Under those conditions, the molecules are far enough apart that their size and attractions matter less.

It matters less as a rough estimate in simple textbook problems, but it matters much more in high-pressure systems, low-temperature gas behavior, liquefaction problems, and any situation where accuracy matters.

When You Should Think About Real-Gas Behavior

Start being more careful when pressure is high, temperature is low, or the gas is near a phase change. Those are the conditions where the assumptions behind the ideal model are most likely to break down.

In chemistry courses, the ideal model is still the right starting point because it connects pressure, volume, temperature, and moles cleanly. Real-gas behavior explains when that first model needs correction.

Try A Similar Problem

Try your own version with the same $n$, $V$, and $T$, but use a measured pressure of $26.0\ \mathrm{atm}$. Compute $Z$ and ask what it suggests about how that sample is deviating from ideal behavior.

If you want the next step after this comparison, the ideal gas law is the natural follow-up because it shows how the simplified model is used in actual calculations.