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Question

Gases X, Y, Z, P and Q have their van der Waals constants ′a′ and ′b′ (in CGS units) as shown below:
XYZPQa66200.0530b0.0250.150.10.020.2
The gas with the highest critical temperature is:

A
P
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B
Q
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C
Y
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D
Z
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E
X
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Solution

The correct option is E X
For any gas, critical temperature (Tc) is the temperature at or above which the gas cannot be liquefied, Tc=8a27Rb, where a ,b are van der Waals' constant and R is the gas constant.
Greater the value of (ab), more will be the critical temperature of a gas.
a) For gas P, value of ab = 0.050.02=2.5
b) For gas Q, value of ab = 300.2=150
c) For gas Y, value of ab = 60.15=40
d) For gas Z, value of ab = 200.1=200
e) For gas X, value of ab = 60.025=240
For gas X, (ab) has the maximum value. Hence it has the highest critical temperature Tc .

Theory:

Critical Point (Point of inflection):

At this point on critical isotherm, gas and liquid are at equilibrium.

At point J (the tip of the dome) :

(dPdV)=(d2PdV2)=0

At Higher Temperature

T>Tc

Gas can not be liquefied for any T>Tc

Critical Temperature (Tc) : The maximum temperature at which a gas can be liquefied by the application of pressure alone.

Critical Pressure (Pc) :The minimum pressure required to liquefy a gas at critical temperature (Tc)

Critical Volume (Vc) : The volume occupied by one mole of the gas at critical temperature (Tc), and critical pressure (Pc)

Critical constants

Critical Temperature (Tc), Critical Pressure (Pc) and Critical Volume (Vc) are called critical constants.

Significance of Critical Temperature (Tc)

TcIntermolecular attractionsEase of liquefaction

Critical Constants in Terms of van der Waals Constants

Vc=3b

Pc=a27×b2

Tc=8a27Rb

Compressibility Factor and Critical Constants for every gas

Zc=PcVcRTc=27ab(9b)(8a)=38=0.375



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