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Standard XIII

Chemistry

Compressibility Factor

The ideal gas...

Question

The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of $Z = \frac{P V}{R T}$ v/s P gives us an idea of the deviation.

Curve C could be ____.

H e

at 650 K

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C O_{2}

at 20 K

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N H_{3}

at 300 K

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N_{2}

at 473 K

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Solution

The correct option is C $N H_{3}$ at 300 K
At moderate $P$ , Z < 1, i.e. high force of attraction and gas is compressible.
$H e, H$ and $N_{2}$ could not show such curve at low temperature. Because at low temperature, repulsive forces dominate leading to Z > 1.
$N H_{3}$ at 300 K can best fit in the curve C.

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Similar questions

Q. The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of

Z = \frac{P V}{R T}

v/s P gives us an idea of the deviation.

Curve C could be ____.

Q. The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of

Z = \frac{P V}{R T}

v/s P gives us an idea of the deviation.

For curve C, find

Z

for 1 l of the gas at a pressure where

b

is negligible and

a = 4.225 a t m l^{2} m o l^{2}

The gases which strictly follow the general equation

(P V = n R T)

are called ideal or perfect gases. Actually, there is no gas which is perfect or ideal. A real gas is one which actually exists, whether it obeys gas laws strictly or not. Under ordinary conditions, only those gases nearly behave as ideal or perfect which have very low boiling points such as nitrogen, hydrogen, etc. The most easily liquefiable and highly soluble gases such as ammonia, carbon dioxide, sulphur dioxide show large deviations.
A very convenient method of studying deviation of real gases from ideal behaviour is through a compressibility factor

(Z)

Z = \frac{P V}{n R T}

(i)

Z = 1

, for ideal gases.
(ii)

Z \neq 1

, for real gases.

The behaviour of a real gas is usually depicted by plotting compressibility factor

Z

versus pressure

P

at a constant temperature. At high temperature and pressure,

Z

is usually more than one. This fact can be explained by Van der Waals' equation when :

Q. Real gases show deviations from ideal gas law because molecules interact with each other. At high pressures molecules of gases are very close to each other. At very low temperatures intermolecular forces become significant. The deviation from ideal gas behaviour can be measured in terms of compressibility factor

Z

, which is the ratio of product

P V

and

n R T

(

Z = P V / n R T

) . Taking the pressure and volume corrections due to intermolecular forces vander waals corrected the ideal gas equation.
In vander waals equation of state for non ideal gases, the term that accounts for intermolecular forces

Q. At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as

P = \frac{R T}{V - b}

at T.
Here, b is the van der Waals constant. Which gas will exhibit steepest increase in the plot of

Z

(compression factor) vs

P

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The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of Z=PVRT v/s P gives us an idea of the deviation. Curve C could be ____.

The correct option is C NH3 at 300 KAt moderate P, Z < 1, i.e. high force of attraction and gas is compressible. He, H and N2 could not show such curve at low temperature. Because at low temperature, repulsive forces dominate leading to Z > 1. NH3 at 300 K can best fit in the curve C.

The ideal gas law, although convenient, has limitations. Most gases tend to deviate from ideal behaviour. For 1 mole of gas, plotting a curve of $Z = \frac{P V}{R T}$ v/s P gives us an idea of the deviation.

Curve C could be ____.