Properties of Gas
Pressure: When a gas particle collides with the walls of its container it causes pressure. Pressure is measured in pascals, Pa. (1 Pa = 1 Nm-2)
Temperature: It is the measure of internal energy of the gas and it is equal to the average K.E. of its particles. It is measured in Kelvin, K.
Volume: It is the space occupied by the particle that makes up the gas. It is measured in meters cubed, m3.
Mass: It is considered the amount of gas. It is measured in mole.
Avogadro and the Mole
One mole of a material is the amount of that substance which contains the same number of particles as there are in 0,012 kg of carbon-12.
One mole of any substance contains Na particles.
Na = 6.02 × 1023 mol-1
Boyle’s Law
The pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature of gas remains constant.
P α 1/v for constant T
So, P1V1 = P2V2
Charles’s Law
The volume occupied by gas at constant pressure is directly proportional to its thermodynamic temperature.
V1/T1 = V2/T2ussac’s L
Pressure Law
P1/T1 = P2/T2
Ideal Gas
We know from the three gas laws that pV/T = constant
Ideal gases all behave in the same way so we can keep R as constant,
PV/T = R
If the volume and temperature of a gas are kept constant then the pressure depends on R and the number of particles in the container. We must take account to this by bring number of moles, n:
pV/T = nR
PV = nRT
Which is the ideal gas equation for n moles.
Using the Avogadro’s equation for n;
pV = nRT
pV = N/NART
pV =N (R/NA) T
Boltzmann Constant
It provides evidence for the fast, random movement of molecules in gas. The Boltzmann constant is represented by k and is given as;
R/NA=k
Kinetic Theory of Gases
It is the theory which links these microscopic properties of particles to the macroscopic properties of a gas. The assumptions of the kinetic theory of an ideal gas are:
Time of collision negligible compared to time between collisions.
No intermolecular forces except during collision.
Consider a collision in which a single molecule with mass m is moving with speed c parallel to one side of the box. Collision in side ABCD is elastically rebounded, so momentum from single collision is:
Change in momentum = -mc – (+mc)
= -mc – mc = 2mc
Between the consecutive collisions with side ABCD, molecule travels distance 2l at speed c.
Time = 2l/c
Force =2mc/(2l/c) =mc2/l
Pressure is given by,
Pressure = mc2/l3
For large number N of molecule,
P = Nm <c2>/l3
P = 1/3 Nm <c2>/l3
P = 1/3 Nm/V <c2>
PV = 1/3 Nm <c2>
Since the average K.E. of molecule is;
Ek = ½ m <c2> = 3/2 kT