Deduce a Charles, law b. Graham's law of diffusion from kinetic gas equation.

Explanation

a. Charles. law: According to kinetic theory, the average K.E. of gas moleculs is directly proportional to the absolute temperature.
(i.e. ) `K.E prop T ` But `K.E . =1/2mnc^(2)`
`:.1/2mnc^(2)prop T ` (or) `=1/2mnc^(2)=KT`
According to kinetic gas equation
`PV=1/3mnc^(2)`
(or) `PV=2/3xx1/2mnc^(2)` (or) `PV=2/3xxKT` (or) `V=2/3(KT)/P`
If P is kept constant than V
`=` constant `xxT` (or) `V prop T`(P constant)
At constant pressure , the volume of a given mass of gas is directly proportional to its absolute temperature. This is Charles. law.
b. Graham.s law: According to kinetic gas equation
`PV=1/2mnc^(2)`
(or) `PV=1/3mc^(2)` (or) `c^(2)=(3PV)/m` But `V/m=1/d`
`:.c^(2)=(3P)/d` (or) `c=sqrt((3P)/d)`
At constant pressure
`c=` constant `xx1/(sqrt(d))` (or) `c prop 1/(sqrt(d))`
In the case of gases r.m.s velcoity (c) is directly proportiona to rate of diffusion (r)
`:. r prop 1/(sqrt(d))` (At constant T and P)
i.e., At constant temperature and pressure the rateof diffusion of a gas is inverely proportional to the square root of its density. This is Graham.s law.