Chemistry · Lesson

Pressure, gas laws and the ideal gas model

Connect gas pressure, volume, amount and temperature with an explicit model. Work with kelvin, absolute pressure and matching units rather than memorizing an unexplained molar volume.

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By the end, you can

Identify the variables held fixed in a gas-law comparison.
Use PV = nRT with coherent pressure and volume units.
Distinguish absolute pressure from pressure measured relative to the surroundings.

Pressure comes from momentum transfer

A gas presses on a container because particles transfer momentum when they collide with its walls. Pressure is force per area. In an equilibrium description it depends on particle motion, how many particles are present and the space available to them.

In the ideal model, at fixed gas amount n and absolute temperature T, reducing volume V raises pressure P. At fixed n and V, raising T raises P. Each comparison needs its stated fixed variables: a leaking container or a chemical reaction can change n.

Put the variables together

The ideal gas equation is PV = nRT. Here P is absolute pressure, V is gas volume, n is amount of specified gas entities, T is temperature in kelvin, and R is the molar gas constant. Ideal behaviour is an approximation, generally better at low density and sufficiently far from condensation.

R is approximately 8.31446 kPa L mol⁻¹ K⁻¹, which is numerically equivalent to the same value in J mol⁻¹ K⁻¹ because 1 kPa L = 1 J. Use a matching form of R for your pressure and volume units. The exact SI definition of R does not make measured variables or an approximate gas model exact.

Watch the inverse relationship

For the same ideal gas amount at fixed temperature, PV is constant. An original illustrative case has PV = 200 kPa L. Volumes 1.00, 2.00 and 4.00 L then correspond to absolute pressures 200, 100 and 50.0 kPa. Doubling V halves P; the relation is not a straight line on ordinary P-versus-V axes.

The plotted curve is the ideal prediction P = 200/V for this stated model case. It does not show measurements or promise that a real gas follows it exactly. The positive-volume domain also matters: the expression does not assign a usable gas state at V = 0.

Halving volume doubles ideal-model pressure

Absolute pressure P / kPa

Volume V / L

Calculated ideal states
— Ideal relation: P = 200/V

Underlying data

Volume V / L	Absolute pressure P / kPa
1	200 · Calculated ideal states
2	100 · Calculated ideal states
4	50 · Calculated ideal states

Original model case, fixed n and T: PV = 200 kPa L. Circular markers are selected calculated states; the dashed curve is P = 200/V over 1–4 L. There are no measured data here.

Name the temperature and pressure convention

Temperature ratios in gas laws use kelvin. Heating from 20 °C to 40 °C does not double absolute temperature: the corresponding values are about 293 K and 313 K. A gauge that reads zero relative to surrounding air also does not imply zero absolute pressure.

Likewise, “standard conditions” need their numerical temperature and pressure. At 273.15 K, an ideal mole occupies about 22.71 L at 100 kPa and 22.41 L at 101.325 kPa. A familiar 22.4 L mol⁻¹ value is an approximate prediction at one named convention, not the volume of every gas mole under all conditions.

Worked examples

Find the volume with matching units

An approximately ideal gas has n = 0.100 mol, T = 298.15 K and absolute P = 100.0 kPa. What volume does the model predict?

Rearrange PV = nRT to V = nRT/P.
Choose R = 8.314462618… kPa L mol⁻¹ K⁻¹.
Substitute: V = (0.100 × 8.314462618… × 298.15)/100.0 L = 2.478957… L.
Report three significant figures, limited here by the stated amount.

V = 2.48 L. This is an ideal-model prediction with the given approximate inputs.

Try it yourself

In the plotted model, what pressure corresponds to V = 4.00 L?
Show the answer and reasoning
50.0 kPa.
At fixed n and T, P = 200/4.00 kPa.
Which two variables must remain fixed for the plotted inverse P–V comparison?
Show the answer and reasoning
Gas amount and temperature.
The equation PV = constant applies to the same amount at fixed absolute temperature.
Does 20 °C to 40 °C double T in PV = nRT?
Show the answer and reasoning
No.
Use kelvin: the approximate ratio is 313/293, rather than 40/20.
Is 22.4 L mol⁻¹ a universal gas molar volume?
Show the answer and reasoning
No.
Gas volume depends on pressure, temperature and how accurately the ideal model applies.

What to carry forward

State fixed variables before using a gas-law ratio.
Use absolute pressure and temperature in kelvin.
Choose R with matching units.
Name numerical reference conditions and the model’s limits.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.