Overview

Gas Law Summary Table

Law	Variables	Constant	Formula	Graph
Boyle's	P and V	T, n	$PV = k$	P vs V: hyperbola ↓
Charles's	V and T	P, n	$V/T = k$	V vs T(K): line ↑
Gay-Lussac's	P and T	V, n	$P/T = k$	P vs T(K): line ↑
Avogadro's	V and n	T, P	$V \propto n$	V vs n: line ↑
Ideal Gas	All	—	$PV = nRT$	—

Molecular Speed Comparison

Speed	Formula	Coefficient	Relative Magnitude
Most probable ( $v_{mp}$ )	$\sqrt{2RT/M}$	$\sqrt{2} \approx 1.414$	Smallest
Average ( $v_{avg}$ )	$\sqrt{8RT/\pi M}$	$\sqrt{8/\pi} \approx 1.596$	Middle
RMS ( $v_{rms}$ )	$\sqrt{3RT/M}$	$\sqrt{3} \approx 1.732$	Largest

All speeds ↑ with temperature (T ↑), ↓ with molar mass (M ↑).

Real Gas Behavior: Z vs P Trends

Gas	Behavior at Low P	Behavior at High P	Reason
Most real gases ( $CO_{2}$ , $N_{2}$ , $CH_{4}$ )	Z < 1 (attraction dominates) ↓	Z > 1 (repulsion dominates) ↑	Both $a$ and $b$ significant
$H_{2}$ , He	Z > 1 at all pressures ↑	Z > 1 (stronger) ↑	$a \approx 0$ , volume effect always wins
Ideal gas	Z = 1 (flat)	Z = 1 (flat)	Neither correction applies

Liquid State Properties vs. Temperature

Property	Effect of Temperature ↑	Reason
Vapour pressure	↑ increases	More molecules have enough KE to escape
Surface tension	↓ decreases	Cohesive intermolecular forces weaken
Viscosity (liquid)	↓ decreases	KE overcomes resistance to flow
Boiling point	Lower at reduced external P	BP = T where $P_{vap} = P_{ext}$

Liquefaction Condition (Mermaid Flowchart)

Key Numerical Values for NEET

$R = 0.0821\ \text{L·atm/(mol·K)}$ $T(\text{K}) = T(°C) + 273$ $\text{Molar volume at STP} = 22.4\ \text{L/mol}$ $T_c(\text{CO}_2) = 31.1°C = 304.25\ \text{K}$