States of Matter - Result Question 99

####3. 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=RTVb at T.

Here, b is the van der Waals’ constant. Which gas will exhibit steepest increase in the plot of Z (compression factor) vsp ?

(2019 Main, 9 April II)

(a) Xe

(b) Ar

(c) Kr

(d) Ne

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Answer:

Correct Answer: 3. (d)

Solution:

  1. Noble gases such as Ne,Ar,Xe and Kr found to deviate from ideal gas behaviour.

Xe gas will exhibit steepest increase in plot of Z vs p.

Equation of state is given as:

p=RT(Vb)p(Vb)=RT

pVpb=RTpV=RT+pb pVRT=1+pbRT  As, Z=pVRT  so, Z=1+pbRTy=c+mx

The plot of z vs p is found to be

The gas with high value of b will be steepest as slope is directly proportional to b.b is the van der Waals’ constant and is equal to four times the actual volume of the gas molecules. Xe gas possess the largest atomic volume among the given noble gases ( Ne,Kr,Ar). Hence, it gives the steepest increase in the plot of Z (compression factor) vsp.



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