Intuition The ONE core ideaA real gas is just an ideal gas that lies about two things : its molecules secretly take up space and secretly pull on each other. Every symbol on the parent page (P V m Z a b T B measure how big those two lies are and which one is winning .
Before you can read the parent note, you must be able to look at each symbol and instantly see a picture . This page builds all of them from nothing, in the order they depend on each other. Nothing here is used before it is defined.
P Pressure is the total shove per unit area from all those hits added up.
Picture: a wall being drummed on by a hailstorm of balls.
Unit here: the atmosphere (atm
V L
T speed score : hotter gas = faster balls = harder, more frequent wall hits. We always measure it in kelvin (K
Why kelvin and not Celsius? Because formulas like P V = n R T T T
These three come from Kinetic Theory of Gases — the model that says pressure and temperature are just the bookkeeping of bouncing balls.
Definition Amount of substancen mole is just a giant fixed count (6.022 × 1 0 23 n
Definition The gas constantR R fixed number of nature that makes the units on the left of P V = n R T R = 0.0821 L⋅atm⋅mol − 1 K − 1
This is the pretend rulebook — see Ideal Gas Law . It assumes two fantasies:
Each ball is a point with zero size.
Balls never attract each other — they only collide and fly apart.
The whole parent topic is about what happens when both fantasies fail .
V m per mole
V m = n V V n V m
Picture: a pizza V n V m
Why bother? Because deviations depend on how crowded each molecule is, not on how big your tank happens to be. Dividing out n
When V m large , molecules are far apart (uncrowded). When V m small , they are packed.
Definition Compressibility factorZ Z = R T P V m what you actually measured (P V m what the ideal contract promised (R T
Z = 1 Z < 1 Z > 1
ratio and not a difference?
A ratio is dimensionless — it comes out as a pure number with no units, so Z Z P V m − R T
These are the two knobs that fix the two fantasies. They come from Intermolecular Forces (the pull) and the finite size of molecules (the shove).
b hard balls , not points. Two balls cannot overlap, so around every molecule there is a shell of space no other centre can enter. Summed over a mole, this stolen space is b L⋅mol − 1
Picture: bumper cars — even in an "empty" rink, each car's rubber ring means the usable floor is smaller than the total floor.
Effect: available room becomes ( V m − b ) less than V m harder to squeeze → pushes Z
a pull on each other (weak forces described in Intermolecular Forces ). A molecule flying toward the wall gets tugged backward by the crowd behind it, so it hits the wall softer than ideal. a atm⋅L 2 mol − 2
Picture: a runner about to slam a wall, but friends grab their shirt from behind — the impact is gentler.
Effect: measured pressure drops → gas seems easier to squeeze → pushes Z down .
Intuition Why the attraction correction isa / V m 2 arriving at the wall AND molecules behind it doing the pulling. Each of those crowd-densities is proportional to 1/ V m V m 1/ V m 2 squared — it is a two-body effect.
Definition Boyle temperatureT B b a / R T exactly cancel at low pressure, so the gas mimics ideal behaviour over a range of low pressures.
T B = R b a Boyle Temperature .
Above T B Z > 1
Below T B Z
When attraction wins hard enough, a gas can collapse into a liquid . The border conditions for that are the critical constants — the topic of Critical Constants and Liquefaction . You don't need them to read the parent page, but know that the same a b Z
Kinetic theory bouncing balls
Temperature T speed score
Gas constant R exchange rate
Molar volume Vm room per mole
Compressibility factor Z lie score
Real gases and Z deviations
Test yourself — reveal only after answering aloud.
What does pressure P Total wall-shove per unit area from all molecular collisions.
Why must temperature be in kelvin, not Celsius? Formulas multiply by T
What is a mole and what symbol counts it? A fixed bundle of 6.022 × 1 0 23 n
What role does R P V = n R T A fixed exchange rate making the units of n T P V
Define molar volume and why we use it. V m = V / n
Write Z Z = P V m / R T = 1 < 1 > 1
Why is Z A ratio is dimensionless, so all gases plot on one comparable scale.
What does b Z Finite molecular size (excluded volume); pushes Z
What does a Z Intermolecular attraction; pushes Z
Why is the attraction correction squared (a / V m 2 It needs both an arriving molecule and a pulling crowd — two densities, each ∝ 1/ V m
Define T B The temperature where the size and attraction corrections cancel at low pressure, so the gas acts ideal.
Recall One-line summary of every symbolP V T n R V m Z b a T B
