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# Behavior of Real Gases

Behavior of Real gases (Deviation from ideal behavior)

Ideal gas is that which obeys ideal gas equation PV = nRT under all conditions of temperature and pressure.

No gas is ideal. All gases are real and show deviation from ideal gas behavior

Study of deviation → As PV = const. (Boyle’s law) so graph bet PV (v/s) P should be straight line parallel to x-axis. But real gases don’t show such a behavior.

The extent to which a real gas deviates from ideal behavior is studied is terms of compressibility factor ‘Z’ & Z = PV/nRT

For ideal gases, PV = nRT & Z = 1

For real gases, PV ≠ nRT so

(i) Of Z < 1 (ep. CH4, CO2 etc) the gas shows negative deviation i.e. gas is more compressive than expected from ideal behavior.

(ii) Of Z > 1 (ep. H2, He etc) the gas shows positive deviation i.e. gas is less compressive than expected from ideal behavior.

The curve of Z (v/s) P for N2 at different temperatures indicate that at high temperature & low pressure the value of Z approaches = 1. i.e. behavior ideally

Boyle temperature or Boyle point → It’s the temperature at which a real gas behaves like an ideal gas over an appreciable range of pressure.

Significance of Z → Z = (PVreal/nRT) (i) of gas shows

Ideal behavior then PVideal = nRT i.e. Videal = nRT/P

So from equation (i) Z = Vreal/Videal

Cause of deviation from ideal behavior:- At low temperature and low pressure. The gases behave ideally & at low temperature & high pressure ideal behavior.

(i) The volume occupied by gas molecules is negligible in compassion to total volume of gas.

(ii) The force of attraction & or repulsion between gas molecules is negligible.

At low T & high P → (i) The actual mol of gas is not negligible in compassion to total volume.

(ii) The force of attraction or repulsion is not negligible.

Equation of state for the real gases (Vander Waals equation) → (in 1873)

(P + a/V2) (V – b) = RT for 1 mol of gas

(P + an2/V2) (V – nb) = nRT (for n moles of gas)

Deviation of Vander Waals equation

Correction for volume

Suppose volume of gas molecule = v

Effective volume = b = 4 x v (excluded volume)

So volume of gas = V – b (for 1 mol)

V – nb (for n moles)

Correction for pressure → The molecule colliding with the half of container is attracted by other molecules so it exerts lessee pressure.

So corrected pressure = P + þ

Þ ∝ (density)2 but d ∝ (1/V) or d ∝ (n/V)

(1 mol)     (n moles)

So Þ ∝ (1/V2) (1 mole)

Þ = a/V2

Þ ∝ (n2/V2) (for n moles)

Þ = (an2/V2)

Where a → constant

In Vander Waal’s equation,

(P + an2/V2) (V – nb) = nRT

‘a’, & ‘b’, are Vander Waal’s constant their significance is

‘a’ → Greater the value of ‘a’ for a gas greater is the magnificence of attractive forces between gas molecules. & more easily the gas is liquefiable.

‘b’ → It is a measure of effective size of gas molecule greater the value of ‘b’ higher is the size of gas molecules.

Units of a As P = (an2/V2) or a = (PV2/n2) = atm. L2 mol-2 or bar dm6 mol-2

Units of b As v = nb or b = v/n = L mol-1 or dm3 mol-1

Explanation of behavior of real gases by V.W equation

(i) At very low pressure → V is very large, (a/V2) = small

b → neglected so PV = RT the gas behaves ideally.

(ii) At Moderate pressure → V = small (a/V2) = large

V → still larger than b so

(P + a/V2) (V) = RT or PV + (a/V) = RT

Or PV = RT – (a/V)

Or (PV/RT) = 1 – (a/RTV)

Or Z = 1 – (a/RTV) i.e. Z < 1

(iii) At Greater P → V → very small, (a/V2) large but P is more

So (a/V2) neglected, but ‘b’ can’t be neglected

So P(V – b) = RT or PV – Pb = RT

Or PV = RT + Pb or (PV/RT) = 1 + Pb i.e. Z > 1

Is negligible i.e. a → very = 2 small (a/V2) = negligible

So P(V – b) = RT or Z > 1 & increases with increases is value of P at constant P.

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