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 = (PV_real/nRT) (i) of gas shows

Ideal behavior then PV_ideal = nRT i.e. V_ideal = nRT/P

So from equation (i) Z = V_real/V_ideal

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 Waal’s 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 Waal’s 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.