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 NO₂, CO₂ 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 non-ideal. 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 50⁰C.

Therefore following are gases:

air (NBP= -194⁰C),

nitrogen (NBP = -183⁰C),

oxygen (NBP = -196⁰C),

argon (NBP = – 185.6⁰C),

hydrogen (NBP = – 253⁰C)

helium (NBP= – 269⁰C)

These are permanent gases at atmospheric conditions. Because these are far above their saturation temperatures.

Properties of gases

1. It is easy to compress or expand a gas.

2. These occupy far more space than the solids or liquids.

3. Gas has no fixed shape and no fixed volume.

4. Ir-respective 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. Inter-molecular attraction is weakest in gases whereas

    h. inter-molecular 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,

• Bert-helot equation,

• Dietetic equation,

• Benedict-Webb-Rubin equation,

• Wohl equation,

• Redlich-Kwong equation

• Virial equation.

GAS LAWS

1. Boyle’s Law-—pV= constant or p₁V₁ = p₂V₂

During an isothermal process ,product of absolute pressure and volume of a given mass of a gas is constant.

1. (a). First Charles’s Law——– V/T = constant or V₁/T₁ = 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 p₁/T₁ = p₂/T₂

During an isochoric process, pressure of a given mass of a gas varies directly as its absolute temperature).

3. 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

• p₁v₁ = p₂v₂

4. Dalton’s Law

5. 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.

5. 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.

6. 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.

7. 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 m³/kg mole

IT IS TO BE OBSERVED THAT  IT IS NOT 22.41 m³/kg.

For example, for hydrogen, the mass of 1 mole is 2 kg

Therefore for hydrogen it is 22.41 m³/2 kg

( NOTE CAREFULLY THAT   22.41 m³/kg for hydrogen is wrong)

Mathematically Avogadro law is M₁v₁=M₂v₂

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 iso-thermal process is W = p₁V₁ ln V₂/V₁

(ii) Work done in an reversible adiabatic process is W = (p₁V₁-p₂V₂)/(γ—1)

(iii) Work done in an irreversible adiabatic process is

W = (γ-n)/(γ—1) (p₁V₁-p₂V₂)/(γ—1)

Van der Waal equation of state

For a real gas, Van der Waal equation is used which given below:

p = R_uT/(v-b) –a/v²

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/ν² 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:

1. Shape factors

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

2. 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.

3. Inter-molecular forces

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

3. 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) Non-permanent: Electrical moments arise for short duration during electrons collisions

5. Hydrogen Bonding

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

6. 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

1. Mixture component

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

2. 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

3. 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

4. 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

5. Partial Pressure ‘p_A’

 Pressure of a component ‘A’ in the mixture when alone present in the entire volume of the mixture.