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JEE Advanced 2006
Exam
JEE Advanced
Year
2006
Subject
Chemistry
Chapter
States of Matter

JEE Advanced 2006 · Chemistry · States of Matter

The given graph represent the variations of compressibility factor...

The given graph represent the variations of compressibility factor (Z)=PVnRT(Z)=\frac{P V}{n R T} versus PP, for three real gases A,BA, B and CC. Identify the only incorrect statement The given graph represent the variations of compressibility factor (Z)=(P V)/(n R T) versus P , for three real gases A,
The given graph represent the variations of compressibility factor (Z)=(P V)/(n R T) versus P , for three real gases A,

Options

  1. AFor the gas A,a=0A, a=0 and its dependence on PP is linear at all pressure.
  2. BFor the gas B,b=0B, b=0 and its dependence on PP is linear at all pressure.
  3. CFor the gas CC, which is typical real gas for which neither aa nor b=0b=0. By knowing the minima and point of the intersection, with Z=1,aZ=1, a and bb can be calculated.
  4. DAt high pressure, the slope is positive for all real gases.

Correct answer

B. For the gas B,b=0B, b=0 and its dependence on PP is linear at all pressure.

Step-by-step solution

From the graph it is clear that the value of ZZ decreases with increase of pressure. We can explain as follows on the basis of van der Waals' equation. At high pressure, when ' PP ' is large, VV will be small and one can not ignore ' bb ' in comparison to VV. However, the term aV2\frac{a}{V^2} may be considered negligible in comparison to ' pp ' in van der Waals' equation or (p+aV2)(V−b)=nRTP(V−b)=nRTpV−pb=nRTpVnRT=1+pbnRTZ=1+pbnRT\begin{aligned}\left(p+\frac{a}{V^2}\right)(V-b) & =n R T \\ P(V-b) & =n R T \\ p V-p b & =n R T \\ \frac{p V}{n R T}& =1+\frac{p b}{n R T}\\ Z & =1+\frac{p b}{n R T} \end{aligned} or Here, ZZ is greater than one and it increases linearly with pressure. Hence, statement (b) is false.
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