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BITSAT 2022
Exam
BITSAT
Year
2022
Subject
Chemistry
Chapter
States of Matter

BITSAT 2022 · Chemistry · States of Matter

The given graph represents the variation of compressibility factor...

The given graph represents the variation of compressibility factor (Z)=pVnRT(Z)=\frac{p V}{n R T}, for three real gases A,BA, B and CC. Identify the only incorrect statement. The given graph represents the variation of compressibility factor (Z)=(p V)/(n R T) , for three real gases A, B and C

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 cannot ignore ' bb ' in comparison to VV. However, the team a/V2a / V^2 may be considered negligible in comparison to ' pp ' in van der Waals' equation. (p+aV2)(V−b)=nRTp(V−b)=nRT⇒pV−pb=nRTorpVnRT=1+pbnRTorZ=1+pbnRT\left(p+\frac{a}{V^2}\right)(V-b)=n R Tp(V-b)=n R T\Rightarrow \quad p V-p b=n R T or \frac{p V}{n R T}=1+\frac{p b}{n R T} or Z=1+\frac{p b}{n R T} Thus, ZZ is greater than 1. As pressure is increased (at constant TT ), the factor pbnRT\frac{p b}{n R T} increases. This explains why after minima in the curves, ZZ increase continuously with pressure. Hence, the only incorrect statement is (b).
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