States of Matter (Class 11): Gas Laws and Kinetic Molecular Theory

The gas laws, and what each one holds constant

The ideal gas equation

Combining the laws gives the equation of state for an ideal gas:

where n is the amount in moles and R is the gas constant. R takes different numerical values depending on units, and picking the wrong one is the other frequent numerical error. Using 8.314 J K−¹ mol−¹ requires pressure in pascals and volume in cubic metres; using 0.0821 L atm K−¹ mol−¹ requires atmospheres and litres. Decide which set you are working in before substituting anything.

Since n = mass/molar mass, the equation also gives a route to molar mass from measured P, V, T and mass — a standard numerical.

Dalton's law of partial pressures

In a mixture of non-reacting gases, each exerts the pressure it would exert alone, and the total is their sum:

where x_i is the mole fraction. Questions on gas collected over water use this: the measured pressure includes water vapour, so the vapour pressure must be subtracted to get the dry gas pressure.

Kinetic molecular theory

The theory explains the gas laws from a small set of assumptions:

• Gases consist of a large number of particles in constant random motion.
• The particles' own volume is negligible compared with the container volume.
• There are no intermolecular forces between them.
• Collisions are perfectly elastic — no kinetic energy is lost.
• The average kinetic energy is directly proportional to absolute temperature.

That last point is the important one conceptually: temperature is a measure of average molecular kinetic energy. Two different gases at the same temperature have the same average kinetic energy, so the lighter one must move faster.

Three molecular speeds

Their order is always most probable < average < root mean square, and being asked to state that order is a routine question.

Why real gases deviate

Real gases obey the ideal equation well at low pressure and high temperature. They deviate where the assumptions break down — and each deviation traces to a specific assumption:

• At high pressure, molecules are close together and their own volume is no longer negligible.
• At low temperature, molecules move slowly enough that intermolecular attractions matter.

The van der Waals equation corrects both:

Here a corrects for intermolecular attraction and b for the volume occupied by the molecules themselves. Being able to say which constant fixes which assumption is worth more than reciting the equation.

Frequently asked questions

Why does the Charles law graph pass through −273.15 °C?

Extrapolating the volume of any gas to zero gives the same intercept, which defines absolute zero. It is an extrapolation, not an observation — every real gas liquefies well before reaching it.

Which gas deviates least from ideal behaviour?

Gases with weak intermolecular forces and small molecular size, such as hydrogen and helium, come closest. Gases that are easily liquefied deviate most, since strong attractions are exactly what the ideal model ignores.

Does the kinetic theory apply to liquids and solids?

The idea of particles in constant motion does. The specific assumptions — negligible particle volume and no intermolecular forces — do not, which is precisely what makes liquids and solids condensed phases.

What is the compressibility factor?

Z = PV/nRT. It equals 1 for an ideal gas. Z above 1 indicates that repulsion or molecular volume dominates; Z below 1 indicates attraction dominates. Reading a Z-against-P plot is a standard higher-order question.

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