kinetic energy for a given mole of a gas

 but ρ= m/v

pv=

but from PV =RT

 = =RT

or

 kinetic energy of gram mole  of the gas is given by

K.E =

thus

DENSITY OF AN IDEAL GAS

density of an ideal gas is the sum of the masS of individual molecules divided by the volume occupied by the gas.

PV=RT

n= m/M

PV=

note replace small letter p in the above equation with rho,ρ

derivation for the equations of gas law

THE PRESSURE OF AN IDEAL GAS THUS

PV=nRT

BOYLE’S LAW

boyle’s law state that at constant temperature , the volume of a gas is directly proportional to pressure.

pv=nRT, at constant temperature  and for a mole of a gas RT =constant.

PV =constant , P1V1=P2V2 OR P1/P2=V2/V1

charle’s law

at constant pressure  the volume of fixed mass of a gas is inversely proportional to its temperature.

PV=nRT

 for a mole of a gas

AVOGAGROS LAW

when two gases combine they do so in a volume which bear a simple ratio to one another and to the volume of the product if gaseous provided temperature and pressure remain constant.

from PV=n RT

For a gas with pressue P, TEMPERATURE T, VOLUME V1 AND NUMBER OF MOLES N

for another gas at the same condition of volume of gas V2 and number of moles n2

IF V1=V2 THEN

THUS

n1=n2ρ

equal volume of all gases at same same temperature and pressure contain the same number of molecules.

Daltons law of partial of partial pressure

The total pressure of a given mixture of a gas is equal to the sum of the individual partial pressures.

from p=1/3 ρĆ2

 for a gas with partial pressure  p1=1/3 ρ1Ć12

with another with partial pressure  p2 =1/3 ρ2Ć22

total pressure , P = p1 +p2

GRAHAM’S LAW OF DIFFUSION

the graham’s law of diffusion states that the rate of diffusion of a gas at constant temperature is inversely proportional to the square root of its density.

for a gas with density p1, mean velocity D1 and pressure P

and another gas of density p2,mean vel. D2