Question:

For 1 mol of gas, the plot of pV vs. p is shown below. p is the pressure and V is the volume of the gas. What is the value of compressibility factor at point A?
Pv vs V graph

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When solving compressibility factor problems: 
Start by expressing Z=PVRTZ = \frac{PV}{RT} and substitute the appropriate gas law (e.g., Van der Waals equation). 
Expand and simplify using the given conditions to isolate terms involving VV, aa, and bb
Pay attention to the behavior of ZZ in real gas scenarios.

Updated On: Jan 9, 2025
  • 1aRTV1-\frac{a}{RTV}

  • 1+bV1+\frac{b}{V}

  • 1bV1-\frac{b}{V}

  • 1+aRTV1+\frac{a}{RTV}

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The Correct Option is A

Solution and Explanation

For 1 mole of real gas, PV=ZRT PV = ZRT From the graph, PVPV for a real gas is less than PVPV for an ideal gas at point A. Thus, Z<1Z < 1. The compressibility factor ZZ is given by: Z=1aVmRT Z = 1 - \frac{a}{V_m RT} Substituting into the definition of ZZ and simplifying: Z=1aRTV Z = 1 - \frac{a}{RTV}

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