Revision Notes on Gaseous State
Parameters of Gases
The characteristics of gases are described in terms of following four parameters
 Mass
 Volume
 Pressure
 Temperature
1. Mass (m):
The mass of the gas is related to the number of moles as
n = w/M
Where n = number of moles
w = mass of gas in grams
M = molecular mass of the gas
2. Volume (V):
Since gases occupy the entire space available to them, therefore the gas volume means the volume of the container in which the gas is enclosed.
Units of Volume: Volume is generally expressed in litre (L), cm3 & dm3
3. Pressure:
Pressure of the gas is due to its collisions with walls of its container i.e. the force exerted by the gas per unit area on the walls of the container is equal to its pressure.
Pressure is exerted by a gas due to kinetic energy of its molecules.
As temperature increases, the kinetic energy of molecules increases, which results in increase in pressure of the gas. So, pressure of any gas is directly proportional to its temperature.
Units of Pressure:
The pressure of a gas is expressed in atm, Pa, Nm–2, bar and lb/In2 (psi).
3. Temperature (T):
Temperature is defined as the degree of hotness. The SI unit of temperature is Kelvin. ^{o}C and ^{o}F are the two other units used for measuring temperature. On the Celsius scale water freezes at 0°C and boils at 100°C where as in the Kelvin scale water freezes at 273 K and boils at 373 K.
K = ^{o}C + 273.5
F = (9/5) ^{o}C + 32
Gas Laws:
1. Boyle’s Law:
”At constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume”.
Graphical Representation of Boyle’s Law :
 A plot of P versus 1/V at constant temperature for a fixed mass of gas would be a straight line passing through the origin.
 A plot of P versus V at constant temperature for a fixed mass of a gas would be a rectangular hyperbola.
 A plot of P (or V ) versus PV at constant temperature for a fixed mass of a gas is a straight line parallel to the PV axis.
2. Charles’ Law:
”At constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature”
or
Graphical Representation of Charles’s Law :
1. For a definite mass of the gas a plot of V vs T (^{o}K) at constant pressure is a straight line passing through the origin.
2. A plot of V vs t (^{o}C) at constant pressure is a straight line cutting the temperature axis at 273 ^{o}C
3. Combined Gas Law:
This law states that “at constant volume, the pressure of a given mass of a gas is directly proportional to its absolute temperature”.
the combination of Boyle’s Law and Charles’ Law:
4. Gay Lussac’s Law:
Where,
P = Pressure of Gas
T= Absolute Temperature
If the pressure and temperature of a gas changes from P_{1} & T_{1} to P_{2} & T_{2 }, volume remaining constant , we have
where,
P_{t} = Pressure of gas at t ^{o}C
Po = Pressure of gas at 0 ^{o}C
t = Temperature in ^{o}C.
Graphical Representation of GayLussac’s Law
5. Avogadro Law:
“Samples of different gases which contain the same number of molecules (any complexity, size, shape) occupy the same volume at the same temperature and pressure”.
It follows from Avogadro’s hypothesis that (when T and P are constant).
Mathematically
6. Ideal Gas Equation:
Ideal gas obey all the three laws i.e. Boyle’s, Charles’s, and Avogadro‘s law strictly.
pv = nRT
Where,
where R is the constant of proportionality or universal gas constant
The value of R was found out to be
R = 8.314 J mol^{–1} K^{–1}
R = 0.0821 litre atm K^{–1} mol^{–1}
R = 2 cal K^{–1} mol^{–1}
Ideal gas equation is also known as equation ofstate.
7. Dalton’s law of partial pressures:
The total pressure of mixture of nonreactive gases at constant temperature and pressure is equal to the sum of the individual partial pressures of the gases.
p_{total }= p_{1} +p_{2}+p_{3}+p_{4}…
p_{1} = x_{1 }p_{total}
p_{2} = x_{2 }p_{total}
p_{3} = x_{3 }p_{total}
Aqueous tension:
Pressure exerted by saturated water vapour.
p_{dry gas} = p_{Total} –Aqueous Tension
Gas Eudiometry:
Gas  Absorbing Reagent used: 
O_{3}  Turpentine oil

O_{2}  Alkaline pyrogallol

NO  FeSO_{4} solution

CO_{2},SO_{2}  Alkali solution (NaOH, KOH, Ca(OH)_{2}, HOCH_{2}CH_{2}NH_{2}, etc.)

NH_{3}  Acid solution or CuSO_{4} solution

Equation for combustion of hydrocarbons:
C_{x}H_{y} + (x + y/4) O_{2} ——> xCO_{2} + y/2 H_{2}O
Kinetic molecular theory of gases:
 Gases are made of large number of identical particles (atoms or molecules), which are very small and perfectly hard spheres.
 The actual volume of the molecules is negligible as compare to the space between them and hence they are considered as the point masses.
 Interaction between the particles is negligible.
 Particles of a gas are always in constant and random motion and the collision between them is perfectly elastic.
 The average kinetic energy of the particles of a gas is directly proportional to the absolute temperature.
 Pressure of the gas is due to the collision between gas molecules and walls of the container.
The Kinetic Equation
Velocities of gas molecules
 Average Velocity
Average velocity =
 Root Mean Square Velocity:
Maxwell proposed the term U_{rms} as the square root of means of square of all such velocities.
also
 Most probable velocity:
It is the velocity which is possessed by maximum no. of molecules.
Furthermore
Kinetic Energy of Gas
As per kinetic equation
For 1 mole m × n = Molecular Mass (M)
Also
Where k is the Boltzmann constant (k = R / N)
Graham’s Law of Diffusion/Effusion:
1. Diffusion: ability of a gas to spread and occupy the whole available volume irrespective of other gases present in the container
2. Effusion: process by which a gas escapes from one chamber of a vessel through a small opening or an orifice
r ∝ 1 / √d
where r is the rate of diffusion and d is the density of the gas.
Now, if there are two gases A and B having r_{1} and r_{2} as their rates of diffusion and d_{1} and d_{2} their densities respectively. Then
r_{1} ∝ _{1}
and
r_{2} ∝
or
,
The rate of diffusion (r) of a gas at constant temperature is directly preoperational to its pressure
Deviation from ideal gas behavior:
For ideal gas,
Compressibility factor i.e. Z = PV/nRT =1
For nonIdeal gas, Z ≠1
Thus for nonideal gas,Z can be < 1 or > 1
When Z < 1, it is a negative deviation. It shows that the gas is more compressible than expected from ideal behaviour.
When Z > 1, it is a positive deviation. It shows that the gas is less compressible than expected from ideal behaviour.
1. Causes of deviation from ideal behaviour:
The volume occupied by gas molecules is negligibly small as compared to the volume occupied by the gas.
The forces of attraction between gas molecules are negligible.
2. Van der waals Equation:
Where,
a and b are van der waals constants.
At low pressures:
PV = RT – a/V
or
PV < RT
This accounts for the dip in PV vs P isotherm at low pressure
At fairly high pressures
a/V^{2} may be neglected in comparison with P. The Vander Waals equation becomes
PV = RT + Pb
or
PV > RT
This accounts for the rising parts of the PV vs P isotherm at high pressures
Boyle’s Temperature (T_{b}) :temperature at which real gas obeys the gas laws over a wide range of pressure.
T_{b} = a / Rb = 1/2 T_{1}
Liquefaction of gases:
 Critical temperature (Tc): temperature at which a gas liquefies. T_{c} = 8a / 27Rb
 Critical Volume: (V_{c}) : volume of one mole of a gas at critical temperature.V_{c} = 3b
 Critical pressure (pc): pressure of A gas at its critical temperature. P_{c} = a/27b^{2}
 Molar heat capacity of ideal gases:the amount of heat required to raise the temperature of 1 mole of a gas trough 1^{0}C.
C_{P} C_{V} = R &
Poisson’s ratio (γ) = C_{P}/C_{V}
For monatomic gas C_{p} = 5 cal and C_{v} =3 cal
γ = 5/3 = 1.67
For diatomic gas C_{p} = 7 cal and C_{v} = 5 cal
γ =7/5 = 1.4
For polyatomic gas C_{p} = 8 cal and C_{v}= cal
γ = 8/6 = 1.33
Also C_{p} = C_{p}m,
Where, C_{p} and C_{v} are specific heat and m, is molecular weight.