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The Deviation Of Real Gas From Ideal Gas Behavior - Practice Questions & MCQ

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Behaviour of Real Gases: Deviation from Ideal Gas Behaviour is considered one of the most asked concept.
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The states of hybridisation of boron and oxygen atoms in boric acid $\mathrm{(H_{3}BO_{3})}$ are respectively

$\mathrm{s p^{2} \text { and } s p^{2}}$

$\mathrm{s p^{2} \text { and } s p^{3}}$

$\mathrm{s p^{3} \text { and } s p^{2}}$

$\mathrm{s p^{3} \text { and } s p^{3}}$

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In a hydrogen-oxygen fuel cell, combustion of hydrogen occurs to

generate heat

create potential difference between the two electrodes

produce high purity water

remove adsorbed oxygen from electrode surface.

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Behaviour of Real Gases: Deviation from Ideal Gas Behaviour

Ideal Gas:
These gases obey gas laws under all the conditions of temperature and pressure,

No gas is ideal in reality (hypothetical).
No force of attraction is present between molecules In them.
Volume of molecules is negligible to the total volume of the gas (container).

Real Gas:
These gases obey gas laws only at high temperature and low pressure.

All the gases are real.
Here the force of attraction between molecules cannot be neglected at high pressure and low temperature.
Here volume occupied by gas molecule is not negligible specially at high pressure and low temperature.

Behaviour of Real Gases: Deviation from Ideal Gas Behaviour and Compressibility factor Z

The extent of deviation of a real gas from ideal gas behaviour is expressed in terms of compressibility factor Z. It is an empirical correction for the non-ideal behaviour of real gases which allows the simple form of the combined gas law to be retained It is given as:
$\mathrm{Z=\frac{P V}{n R T}}$
When Z = 1 (ideal gas behaviour)

When Z < 1 (negative deviations)

When Z > 1 (positive deviations)

When Z < 1 gas is more compressible

When Z > 1 gas is less compressible

For He and H₂ , Z > 1 as PV>RT [as a/V² = 0 ] that is, positive deviations.
At very Low Pressure: PV RT (as a/V² and b are neglected) that is, Z 1 so nearly ideal gas behaviour.
At Low Pressure: PV<RT that is, Z < 1 so negative deviation
At Moderate Pressure : PV = RT i.e, Z = 1 so ideal gas behaviour
At High Pressure: PV > RT (as b can not be neglected). that is, Z > I so positive deviation.
An increase in temperature shows a decrease in deviation from ideal gas behaviour.

Plot of pV vs p for real gas and ideal gas

Plot of pressure vs volume for real gas and ideal gas

Van der Waal’s Equation
Van der waal's equation is a modification of the ideal gas equation that takes into account the non-ideal behaviour of real gases Van der Waal 's equation modified kinetic theory of gases by considering these two points of kinetic theory of gases not to be fully correct or are not followed by real gases.
The force of attraction between gaseous molecules is negligible. The volume of gaseous molecules is negligible to the total volume of the gas.
He made following two corrections :

Volume Correction
According to him, at high pressure the volume of the gas becomes lower so volume of molecules can not be ignored Hence the actual space available inside the vessel for the movement of gas molecules is not the real volume of the gas, actually it is given as:
V_{real gas} = V - b
Here V is the volume of the container while b is the volume occupied by gas molecules and it is called co-volume or excluded volume.
The excluded volume for 'n' molecules of a gas = 4nV_m or (4 x 4/3?r³)
Here V_m = Volume of one molecule (4/3?r³
Thus, the ideal gas equation can be written as:
P(V-nb) = nRT
Pressure Correction
According to him, at high pressure the gaseous molecules are closer so attraction forces cannot be ignored hence, pressure of the real gas is given as:
Pressure of the Real gas = pressure developed due to collisions (P) + pressure loss due to attraction (p')
$\mathrm{P_{real\: gas}=P+p^{\prime}}$
Here p' is pressure loss due to force of attraction between molecules or inward pull
$\\\begin{array}{l}{\text{As}:p^{\prime} \propto n^{2},\left[n^{2} \text { is the number of molecules attracting or attracted }\right]}\\{p^{\prime} \propto n^{2} \propto d^{2} \propto \frac{1}{V^{2}}}\end{array}$
$\mathrm{Thus,\: p^{\prime}=\frac{a}{V^{2}}=\frac{a n^{2}}{V^{2}}}$
Here 'a' is Van der Waal's force of attraction constant, d is density and V is volume.
Hence
$\begin{array}{l}{P_{real\:gas}=P+a / V^{2}} \\ {P+\frac{n^{2} a}{V^{2}} \ldots \ldots(2)}\end{array}$
Now ideal gas equation can be written after correction of pressure and volume for n moles
$\mathrm{\left(P+\frac{n^{2} a}{V^{2}}\right) \cdot(V-n b)=n R T}$
Units of a and b
$\begin{aligned} \mathrm{a}=& \text { lit}^{2} \, \mathrm{mol}^{-2}\, \mathrm{atm} \\ & \text { or } \mathrm{cm}^{4}\, \mathrm{mol}^{-2} \, \mathrm{dyne} \\ & \text { or } \mathrm{m}^{4} \, \mathrm{mol}^{-2} \text {Newton } \\ \mathrm{b}=& \text { lit/mol } \\ & \text { or } \mathrm{cm}^{3} / \mathrm{mol} \\ \text {or} & \: \mathrm{m}^{3} / \mathrm{mol} \end{aligned}$
The values of 'a' and 'b' are 0.1 to 0.01 and 0.01 to 0.001 respectively.

Variation of compressibility factor for some gases

Value of Compressibility Factor at High P and Low P

Explanations for Real Gas Behaviour

At very low pressure for one mole of a gas, the value of 'p' and 'b' can be ignored so Van der Waal's equation becomes equal to ideal gas.
PV=RT
At moderate pressure the value of 'nb' or 'b' can be ignored so Van der Waal's equation becomes

$\begin{array}{l}{\left[P+a / V^{2}\right][V]=R T} \\\\ {P V+\frac{a}{V}=R T} \\\\ {P V=R T-\frac{a}{V}}\end{array}$
Hence PV < RT
so,
$\begin{array}{l}{Z=\frac{PV}{RT}} \\\\ {Z<1}\end{array}$
At high pressure, the value of 'p' can be ignored so Van der Waal's equation can be written as

$\begin{array}{l}{P(V-b)=R T} \\\\ {P V-P b=R T} \\\\ {P V=R T+P b} \\\\ {Z=\frac{P V}{R T}} \\\\ {S o, Z>1}\end{array}$