Introduction
The gaseous state is the simplest state of matter where molecular forces of attraction between particles are minimum. Gases show great uniformity in behavior and have several characteristic properties.
Gaseous State is characterized by minimum intermolecular forces, infinite expansibility, high compressibility, and random molecular motion with high kinetic energy.
Characteristics of Gases
Measurable Properties of Gases
Gases are described by four measurable properties: Volume (V), Pressure (P), Temperature (T), and Amount (mass or moles).
Pressure Units Conversion
| Unit | Symbol | Value in Pa |
|---|---|---|
| Bar | bar | 1 bar = 10⁵ Pa |
| Atmosphere | atm | 1 atm = 1.01325 × 10⁵ Pa |
| Torr | Torr | 1 Torr = 133.322 Pa |
| mm of Hg | mm Hg | 1 mm Hg = 133.322 Pa |
Gas Laws
At constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure.
Graph between P and V at constant temperature is an isotherm (rectangular hyperbola).
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.
Volume coefficient: αᵥ = 1/273.15 = 3.661 × 10⁻³ °C⁻¹
At constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature.
Pressure coefficient: αₚ = 1/273.15 = 3.661 × 10⁻³ °C⁻¹
Equal volumes of all gases at the same temperature and pressure contain equal number of molecules.
Molar volume at STP = 22.414 L mol⁻¹
Ideal Gas Equation
Ideal Gas Equation combines Boyle's, Charles', and Avogadro's laws: PV = nRT
Gas Constant (R) Values
Boltzmann Constant
Gas Density Calculations
Dalton's Law of Partial Pressures
Dalton's Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.
Applications
Graham's Law of Diffusion
Graham's Law states that at constant temperature and pressure, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its density or molar mass.
Diffusion vs Effusion
Rate of Diffusion
Kinetic Theory of Gases
Kinetic Theory explains gas behavior in terms of molecular motion. It's based on several postulates about gas molecules.
Postulates of Kinetic Theory
Kinetic Gas Equation
Where m = mass of molecule, n = number of molecules, u = root mean square velocity
Kinetic Energy Calculation
Molecular Speeds
Gas molecules have different speeds described by Maxwell-Boltzmann distribution.
Relationship Between Velocities
Real Gases and Deviations
Real gases deviate from ideal behavior due to intermolecular forces and molecular volume. These deviations increase at high pressures and low temperatures.
Compressibility Factor (Z)
Van der Waals Equation
Van der Waals equation modifies the ideal gas equation to account for molecular volume and intermolecular attractions.
Van der Waals Constants
Critical Constants
Important Points to Remember
Key Points for JEE Main
- Ideal gases obey PV = nRT at all temperatures and pressures
- Real gases show deviations at high pressures and low temperatures
- RMS velocity is the highest, most probable velocity is the lowest
- Average kinetic energy depends only on temperature, not on nature of gas
- Van der Waals equation accounts for molecular size and attractions
- Critical temperature is the temperature above which gas cannot be liquefied
- Diffusion rate is inversely proportional to square root of molar mass
Do's
Don'ts
JEE Main Weightage
This chapter typically carries 2-3 questions in JEE Main, making it a high-weightage chapter. Questions often focus on gas laws, kinetic theory, molecular speeds, and real gas behavior.