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-RTV-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-

P=RT(V b) P(V b) = RT ( P+aV^2 )(V b)=RT At high pressure, P(V b) = RT PV Pb = RT PVRT PbRT=1 Z=1+PbRT Z gt;1, Z∝ b We know that the 'b' is the volume ...

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Standard VIII

Chemistry

Gases

At a given te...

Question

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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Solution

The correct option is C Xe
$P = \frac{R T}{(V - b)}$
$P (V - b) = R T$
$(P + \frac{a}{V^{2}}) (V - b) = R T$
At high pressure,
$P (V - b) = R T P V - P b = R T$
$\frac{P V}{R T} - \frac{P b}{R T} = 1$
$Z = 1 + \frac{P b}{R T}$
$Z > 1, Z \propto b$
We know that the 'b' is the volume occupied by the particles of the gas.

Xe has the highest size so it occupies the highest volume for a certain amount of gases.

Hence, Xe will have the highest slope.

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Similar questions

Q. The van der Waals equation of state represents an approximate behaviour of gases at high pressure and is given by

(P + \frac{a n^{2}}{V^{2}}) (V - n b) = n R T

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van der Waals equation will take the shape of ideal gas equation. For ethane

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Q. The Van der Waal's equation of state for some gases can be expressed as:

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where P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a,b and R are constants.
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The gases which strictly follow the general equation

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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.
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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=RTV−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?

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 $P$ ?