GASES AND GAS MIXTURES
GASES AND GAS MIXTURES
Gas is one of four fundamental states of matter among a
solid, liquid, gas and plasma. A pure gas contains only one
type of atoms like oxygen gas. Rather it may consist of more
than one type of atoms like NO_{2}, CO_{2} and air. The molecules
in a gas are far apart than that in solids and liquids. Use of a
gas and mixture of gases is
quiet common. Gas mixture can be
ideal or nonideal. Partial pressures
of components of a gas mixture are
governed by Dalton’s Law.
Gases
A gas is a vapor with degree of super heat greater than 50^{0}C.
Therefore following are gases:
air (NBP= 194^{0}C),
nitrogen (NBP = 183^{0}C),
oxygen (NBP = 196^{0}C),
argon (NBP = – 185.6^{0}C),
hydrogen (NBP = – 253^{0}C)
helium (NBP= – 269^{0}C)
These are permanent gases at atmospheric conditions. Because these are far above their saturation temperatures.
Properties of gases

It is easy to compress or expand a gas.

These occupy far more space than the solids or liquids.

Gas has no fixed shape and no fixed volume.

Irrespective its quantity, these fill the container in whichthese are put.
e. It acquires the shape of the container.
f. Gases have lower density than solids and liquids.
g. Intermolecular attraction is weakest in gases whereas
h. intermolecular separation is largest.
i. A gas is in constant, rapid, random motion which is
called a ‘Brownian’ motion.
j. The particles in a gas are constantly undergoing
collisions with each other.
k. There is no surface of its own as gas molecules escape
from an open container.
l. These can diffuse into another gas easily.
m. Gases are not rigid substances.
n. Velocity of the molecules of a gas is very fast. Hence
diffusion is fast.
o. A gas, when cooled,+ changes into liquid state. Further
if cooling is continued, it will change into a solid.
p. These gases flow in all directions. Thus, these need a
container to contain the gas.
Four properties namely pressure, temperature, volume and
number of moles define completely the physical state of a
gas. It is assumed to be an ideal gas.
GAS EQUATIONS

Ideal gas—Which obeys all the gas laws

Boyle’s Law, Charles’s Law, Dalton’s Law are gas laws.

Combination of Boyle’s and Charles’s Law in the form of PERFECT GAS EQUATION.

Real gas Which does not follow gas laws.

There are number of modified equations of state for the real gases,

Some of these modified equations of state are as follows:

Van der Waal equation

Clausius equation,

Bettie Bridgman equation,

Berthelot equation,

Dietetic equation,

BenedictWebbRubin equation,

Wohl equation,

RedlichKwong equation

Virial equation.
GAS LAWS

Boyle’s Law—pV= constant or p_{1}V_{1} = p_{2}V_{2}
During an isothermal process ,product of absolute pressure and volume of a given mass of a gas is constant.

(a). First Charles’s Law——– V/T = constant or V_{1}/T_{1} = V2/T2
During an isobaric process, volume of a given mass of a gas varies directly as its absolute temperature.
2.(b) Second Charles’s Law——– p/T = constant or p_{1}/T_{1} = p_{2}/T_{2 }
During an isochoric process, pressure of a given mass of a gas varies directly as its absolute temperature).

Combination of Boyle’s and Charles’s Laws
Perfect gas equation. There are four mathematical forms of perfect gas equation.

p V =R _{u }T, here R_{u} is universal constant =8.3143 kJ/mole K

For 1 kg of gas, p v =R _{g }T , here R _{g} is gas constant = R_{u}/M_{g}, M_{g} is the molecular mass of the gas (OR R_{u} = M_{g} R _{g})

For m kg of gas, p V = m R _{g }T

p_{1}v_{1} = p_{2}v_{2}

Dalton’s Law

It states that pressure exerted by a mixture of gases in a fixed volume is equal to the sum of the pressures that would be exerted by each gas alone in the same volume
OR
It states that pressure exerted by a mixture of gases in a fixed volume is equal to the sum of the partial pressures of all the gases.
NOTE: PARTIAL PRESSURE OF A GAS–The pressure exerted by a single gas in a mixture of gases is called its partial pressure.

Joule’s Law–When a gas expands without doing any work with no heat gain or no heat loss (during throttling),the internal energy of a gas depends only on temperature i.e. if temperature increases, its internal energy increases and vice versa.

Renault’s Law—Two specifics of a gas namely C_{p }(specific heat at constant pressure) and C_{v }(Specific heat at constant volume) remain constant with change of temperature and pressure.

Avogadro’s Law–It states that equal volumes of different ideal (perfect) gases contain same number of molecules at the same temperature and pressure.
Molar volume of each gas at N.T.P. is 22.41 m^{3}/kg mole
IT IS TO BE OBSERVED THAT IT IS NOT 22.41 m^{3}/kg.
For example, for hydrogen, the mass of 1 mole is 2 kg
Therefore for hydrogen it is 22.41 m^{3}/2 kg
( NOTE CAREFULLY THAT 22.41 m^{3}/kg for hydrogen is wrong)
Mathematically Avogadro law is M_{1}v_{1}=M_{2}v_{2}
Universal and individual gas constant
There is an universal gas constant R_{u}= 8.3143 kJ/kg K
R_{u}=M R_{g}
Where M is the molecular mass of a gas and R_{g} is the individual gas constant
Work done
(i) Work done in an isothermal process is W = p_{1}V_{1} ln V_{2}/V_{1}
(ii) Work done in an reversible adiabatic process is W = (p_{1}V_{1}p_{2}V_{2})/(γ—1)
(iii) Work done in an irreversible adiabatic process is
W = (γn)/(γ—1) (p_{1}V_{1}p_{2}V_{2})/(γ—1)
Van der Waal equation of state
For a real gas, Van der Waal equation is used which given below:
p = R_{u}T/(vb) –a/v^{2}
where a and b are van der Waal constants. These are different for different gases.
b is a correction for the volume occupied by a gas in a container. It considers the volume occupied by a gas = volume of the container volume of the gas molecules. a/ν^{2} is also another correction which accounts for the attraction forces existing between gas molecules. According to this correction, there is decrease in pressure against the vessel walls. It is because of molecular between the molecules near the wall of the container. Constants a and b are found empirically from the experimental data.
DEVIATIONS OF REAL GASES FROM IDEAL GAS
Ideal gases obey gas laws whereas real gases do not because of certain deviations. These deviations are as given below:

Shape factors
Molecules are point masses in ideal gas. Actually different molecules have different shapes. Thus there is a deviation.

Compressibility factor (pv/RT =Z)
Volume occupied by molecules of an ideal gas is negligible as compared to the total volume occupied by a gas. The volume occupied by molecules of gases is significant at high pressures. Hence this becomes a deviation. Z =1 for an ideal gas.

Intermolecular forces
There are no intermolecular forces between molecules of an ideal gas. There are inter molecular forces between the molecules of real gases. Hence a deviation.

Electrical forces
Electrical forces are zero in an ideal gas. But actually there are two types of electrical forces present.
(i) Permanent: these are found only in polar molecules.
(ii) Nonpermanent: Electrical moments arise for short duration during electrons collisions

Hydrogen Bonding
There are hydrogen bonds in polar molecules which are neglected in an ideal gas. Hence it becomes a deviation.

Quantum effects
These are neglected in an ideal gas. It is the energy due to translation motion of molecules. These are found in molecules of hydrogen, helium and neon at low temperatures.
TERMS RELATED TO IDEAL GAS MIXTURES
These terms are number of important terms which are used in the analysis of mixture of gases. These are

Mixture component
The individual gases ( gas A, Gas B and Gas C—) in the mixture is called the component of the mixture.

Mole fraction ‘x’
It is the ratio of the moles of a certain component to the total number of moles in the mixture.
x_{A }= n_{A}/n_{t}
Where
x_{A }is the mole fraction
n_{A} is the number of molecules of gas A in the mixture
n_{t} is the total number of molecules in the mixture

Mass fraction ‘y_{A}’
It is the ratio of the mass of a certain component to the total mass of the mixture.
y_{A }= m_{A}/m_{t}
Where
y_{A }is the mass fraction
m_{A} is the mass of gas A in the mixture
m_{t} is the total mass of the mixture

Volume fraction ‘z_{A}’
Ratio of volume occupied by a certain component to the total volume of the mixture.
z_{A }= V_{A}/V_{t}
Where
z_{A }is the volume fraction
V_{A} is the volume occupied by gas A in the mixture
V_{t} is the total volume of the mixture

Partial Pressure ‘p_{A}’