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JEE Main 2023 · 29 Jan · Shift 1

JEE Main 2023 Chemistry question on States of Matter

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?

  1. A.
    1. 1−bV1 - \dfrac{b}{V}
  2. B.
    2. 1+bv1 + \dfrac{b}{v}
  3. C.
    3. 1−aRTV1 - \dfrac{a}{RTV}
  4. D.
    4. 1+aRTV1 + \dfrac{a}{RTV}
Show answer and solution

Correct option: C

Solution

For a van der Waals gas, the equation is (p + a/V²)(V - b) = RT. At low pressures (which is where point A lies on the pV vs p plot — on the descending part below the ideal line), the b term is negligible compared to V, so we approximate: p ≈ RT/V - a/V². Then pV ≈ RT - a/V, giving the compressibility factor Z = pV/RT = 1 - a/(RTV). This matches the observed negative deviation from ideality seen at point A, confirming Z = 1 - a/(RTV).

[JEE Main 2023 · 29 Jan · Shift 1]

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