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or, , xK.E., , x kT, , Mu2, , 2, , T or K.E. = k7], , and k are constants, , [K.E. «, , [K.E.= Mu1, , 1, , [M=m N= wt of one mole ofa gas = Mol. wt], , (kinetic gas equation), , PV= a constant at constant T., , constant temperature, 7T, , 3, , PV mNu 2, , P, , 1. Derivation of Boyle's Law., , constant at, , Mathematically., We know, , P=a

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Gaseous State, , 113, , This is Bojyle s Lav. According to this law *TemnerauIre romainina constant, the volume of given mass oy d, , inversely proporlonal, , gas is, , to the, , 2. Derivation of Charle's Law., Mathematically., , pressure, , applied", V, , VxT, , or, , T, , a constant at constant P, , PVmNu, , W'e know, , [kinetic gas equation]), , xmMu? =x Mi?, , [, , M=mN, , =, , wt., , ofone, , moleof gas=Mol. wt], , [K.E.Mu'], , xK.E., , PV-x, 3 kT, , K.E.«Tor K.E. =kT], , andand k, , a constant at constant pressure P, , is, 's law., According to this law "pressure remaining constant, the volume, gas is directly proportional to its absolute temperature"., , This Charle, , are, , constants, , ofa given mass of a, , 3. Derivation of Avogadro's Law., Consider two gases A and B. From combined gas equation, we know that, , When temperature is keptconstant, then T, , =T2;, , PV=P2V2, , 1, , () Forgas A: PVim N1us, i) For gas B: A, P, , f, , [kinetic gas equation], , m> Nauá [kinetic gas equation, P2 and V= V2 then () PVi =P2V2, , m Nuf, , (6), , -, , axmM-x, , M, , mN2, , ..), , Ifthe temperature of gas A and B is the same, then their kinetic energies will be same., Kinetic energy of gas A = Kinetic energy of gas B, , ma, , Dividing the relation () by (i),, , we, , KEK.E.mu*|, , .ii), , m>u, get, , N, N, , = N, , = No. of molecules of gas A, , N2, , No. of molecules of gas E|, , This is the Avogadro's law. According to this law,"Equal volumes of all gases under similar conditions of, contain equal number ofmolecules.", Iemperature and pressure, 4. Derivation of Gas equation (Combined gas laws). A gas equation tells the simultaneous effect ofthe, on the, , volume, , chunge of temperature and pressure, written as:, Combined gasequation can be, , T, , of a given mass of a, , P2 V2 or P - Constant, T, T2, , gas.

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We kno, , kinetic gas cquation, , Pl' mNu, 3, , PV=, , xmNu, , P, , K.E., , mNu, .K.E. xT'K.E., , T, , PV, , ifk, , kT] where k isconstant, , 3, , -A'T or, ., , K.E., , k, , K'Constant, , k' T. It is combined gas, , k', another constant, , equation., , R (gas constant), then P, , RT(for one mole of a gas) or Pl= nRT(for n moles ofa gas), , 5. Derivation of Grahm's law of diffusion. This law states that "under similar conditions of temperature and, pressure, the rate of diffusion of gases is inversely proportional to the square root of their densities"., , raN, , Mathematically,, , According to kinetic gus equation,, , or, , Pl', , Mu, , ., , M, , mN, , Mol., , wt., , of gas]l, , 3P, , u23PV, , M, , Por, , P, , 3P, , u, , At constant pressure, P, , mNu, , PV, , u, , Butr, , *, , u, , r, , This is the Grahm's law of diffusion, , of gases., , 6. Derivation of Dalton's Law of Partial Pressure, , According to kinetic gas equation., , PV-mnu? or PV x, , Again, , mnu-K.E., , K.E.-PV, PVmn u? mu (nt n t... .), mn uf +, , mn^ u +, , K.EK.E2, K.E, , PV pV+pPzV t.., P, , Pit P2, , t, , Ps., , PV, , Pitp2t...)V, ', , This is Dalton's Law of partial pressure., According to this law "when two or more chenically inert gases are enclosed in, a vessel, the, exerted by these gases will be equal to the sum of partial, total pressure, pressure exerted by each gas if, occupy the total volume, separately.

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Molecular Speeds, , a, , Different types of molecular speeds are described as under, () Root mean square speed (u). It is the square root ofthe average ot, particular, , the squares of the different velocities of the gas molecules at, , temperature., , of the molecules present in a, , at a, , the, , largest, , It is the arithmetic mean of the different, given sample of gas at a particular, , Mathematically u = 3RT, VM, (6) Average speed ()., velocities, , temperature., , TM, , gas, , Mathematically, + = 8RT, Most, , a, , probable speed (a): It is the velocity possessed by, particular temperature, , of the molecules of, , (c), , fraction, , Mathematically, a = 2RT, V M, , REMEMBER, , speed. Due, , on, , to, , It is important to note that so long as, the temperature of the gas is constant, the fraction of the molecules (AN/N), having most probable speed remains, the same. The individual molecules do, , not have the same, , keep, , collisions, the molecules, , having, , molecules with, , colliding with one another and, exchange their speed. In tact,, same speed are, , molecules, , replaced by new set of, the same speed.