Notes on Kinetic Theory of Gases
Kinetic Theory of Matter:-
(a) Solids:- It is the type of matter which has got fixed shape and volume. The force of attraction between any two molecules of a solid is very large.
(b) Liquids:- It is the type of matter which has got fixed volume but no fixed shape. Force of attraction between any two molecules is not that large as in case od solids.
(c) Gases:- It is the type of matter does not have any fixed shape or any fixed volume.
Ideal Gas:- A ideal gas is one which has a zero size of molecule and zero force of interaction between its molecules.
Ideal Gas Equation:- A relation between the pressure, volume and temperature of an ideal gas is called ideal gas equation.
PV/T = Constant or PV = nRT
Here, n is the number of moles and R is the universal gas constant.
Gas Constant:-
(a) Universal gas constant (R):-
R= P0 V0/T0
=8.311 J mol-1K-1
(b) Specific gas constant (r):-
PV= (R/M) T = rT,
Here, r = R/M
Real Gas:-The gases which show deviation from the ideal gas behavior are called real gas.
✅Vander wall’s equation of state for a real gas:-
[P+(na/V)2?][V-nb] = nRT
Here n is the number of moles of gas.
Avogadro’s number (N):- Avogadro’s number (N), is the number of carbon atoms contained in 12 gram of carbon-12.
N = 6.023×10^23
(a) To calculate the mass of an atom/molecule:-
Mass of one atom = atomic weight (in gram)/N
Mass of one molecule = molecular weight (in gram)/N
(b) To calculate the number of atoms/molecules in a certain amount of substance:-
Number of atoms in m gram = (N/atomic weight)×m
Number of molecules in m gram = (N/molecular weight)×m
(c) Size of an atom:-
Volume of the atom, V = (4/3)πr3
Mass of the atom, m = A/N
Here, A is the atomic weight and N is the Avogadro’s number.
Radius, r =[3A/4πNρ]1/3\
Here ρ is the density.
✅Gas laws:-
Graph Between Pressure and Volume for Boyle's Law(a)
Boyle’s law:- It states that the volume of a given amount of gas varies inversely as its pressure, provided its temperature is kept constant.
PV = Constant
(b) Charles law or Gey Lussac’s law:- It states that volume of a given mass of a gas varies directly as its absolute temperature, provided its pressure is kept constant.
Graph Between Volume and Temperature for Charles LawV/T= Constant
V–V0/V0t = 1/273 = γp
Here γp (=1/273) is called volume coefficient of gas at constant pressure.
Volume coefficient of a gas, at constant pressure, is defined as the change in volume per unit volume per degree centigrade rise of temperature.
(c) Gay Lussac’s law of pressure:- It states that pressure of a given mass of a gas varies directly as its absolute temperature provided the volume of the gas is kept constant.
P/T = P0/T0 or P – P0/P0t = 1/273 = γp
Here γp (=1/273) is called pressure coefficient of the gas at constant volume.
Pressure coefficient of a gas, at constant volume, is defined as the change in pressure per unit pressure per degree centigrade rise of temperature.
(d) Dalton’s law of partial pressures:-
Partial pressure of a gas or of saturated vapours is the pressure which it would exert if contained alone in the entire confined given space.
P= p1+p2+p3+……..
nRT/V = p1+p2+p3+……..
(e) Grahm’s law of diffusion:- Grahm’s law of diffusion states that the rate of diffusion of gases varies inversely as the square root of the density of gases.
R∝1/√ρ or R1/R2 =√ρ2/ ρ1
So, a lighter gas gets diffused quickly.
(f) Avogadro’s law:- It states that under similar conditions of pressure and temperature, equal volume of all gases contain equal number of molecules.
For m gram of gas, PV/T = nR = (m/M) R