gaseous state

1. Formulae of Gaseous State for JEE (Main)-NEET
By SUPRATIM DAS DURGAPUR-WESTBENGAL #9434008713
■ Boyle’s law, pressure-volume relationship,
(At constant temperature),
■ Charle’s law, volume-temperature relationship,
Charles law can be represented mathematically as: Temperature α Volume,
Temperature = Constant x Volume
In other words the relation can also be expressed as, Volume = Constant x Temperature
Volume and temperature can also be related as, Volume/Temperature = Constant
Kelvin Scale of Temperature: T(K) = t(o
C) + 273.15
■ Gay-Lussac’s law, pressure-temperature relationship,
Temperature α Pressure, P/T= Constant ( also called Amonton’s Law)
■ Avogadro’s law, volume-moles relationship,
Volume α number of molecules (N), Volume α number of moles (n)
■ Ideal Gas equation, combination of Boyel’s law, Charle’s law & Avogadro’s law,
PV= nRT, P= dRT/M,
■ Dalton’s Law, on partial pressures,
Partial pressure = Mole fraction X Total pressure
■ Graham’s law, diffusion or effusion of gases, rate of diffusion-density relationship,
Rate of Diffusion α 1/√d, Rate of Diffusion α 1/√M, Rate of Diffusion α P, so Rate of Diffusion α P/√M
■ Kinetic gas equation; based on kinetic molecular theory,
, m = mass of gas molecules, n = total number of molecules, u = r.m.s

2. Average Kinetic Energy of Gas: KE per mole = 3/2 RT, KE per molecule = 3/2 kT (k =
Boltzmann Constant, R/No)
■ Root mean square velocity;
Urms = √3RT/M = √3PV/M
■ Average velocity;
,
Average Speed = 0.921 X R.M.S
■ Most probable velocity
, Most Probable Speed = 0.817 X R.M.S
Most Probable Speed: Average Speed : Root Mean Square Speed = 1.0 : 1.128 : 1.224
■ Van der Waals equation, for Real Gases
■ Critical Constant and Vander Waal's Constant
The relationship between critical constants of the gases and their Van der Waal constants is as follows:
(i) Vc = 3b (ii) Pc = a/27b2
(iii) Tc = 8a/27Rb (iv) The critical compressibility factor Zc is given by,
■ Liquefaction of Gases :
Boyle’s Temperature (Tb )= a/Rb ( at which real gases behave like ideal gas)
Inversion Temperature (Ti )= 2a/Rb ( at which no Joule-Thomson effect)
Ratio of Molar Heat Capacity:
(a) Cp/ Cv = γ = 1.66 for Monoatomic gas
(b) Cp/ Cv = γ = 1.40 for Diatomic gas
c) Cp/ Cv = γ = 1.33 for Triatomic gas