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ChemistryMediumClass 11

Van der Waals Equation — Real gases, corrections

States of Matter

4

JEE Qs

8%

Hard

75

min

Thoroughly understand the physical significance of 'a' and 'b', practice calculations with consistent units, and memorize the relations between vdW constants and critical constants.

🧮 Key Formulas

(P + a(n/V)^2)(V - nb) = nRT
Units of 'a': L^2 atm mol^-2 (or Pa m^6 mol^-2)
Units of 'b': L mol^-1 (or m^3 mol^-1)
Compressibility Factor, Z = PV / nRT
Critical Temperature, Tc = 8a / (27Rb)
Critical Pressure, Pc = a / (27b^2)
Critical Volume, Vc = 3b

✅ Key Points for JEE

  • 1The Van der Waals equation corrects the ideal gas equation for two main factors: finite volume occupied by gas molecules (volume correction 'b') and intermolecular attractive forces (pressure correction 'a').
  • 2The constant 'a' quantifies the strength of intermolecular attractive forces; a larger 'a' indicates stronger attraction. The constant 'b' represents the excluded volume per mole of gas molecules due to their finite size.
  • 3Real gases behave most ideally at high temperatures and low pressures, where molecular volume is negligible compared to total volume and intermolecular forces are minimal.
  • 4The Van der Waals constants 'a' and 'b' are characteristic properties of a specific gas and are independent of temperature and pressure.
  • 5The Van der Waals equation can be used to derive the critical constants (Tc, Pc, Vc) which define the conditions above which a gas cannot be liquefied, regardless of pressure.

⚠️ Common Mistakes

  • Incorrectly applying the number of moles 'n' in the pressure correction term (a(n/V)^2) or the volume correction term (nb), especially when dealing with one mole (n=1).
  • Confusing the physical significance of 'a' and 'b' or their dependence on temperature/pressure (they are constant for a given gas).
  • Making errors in unit conversions for 'a' and 'b', or using an inconsistent value of the gas constant 'R' (e.g., L atm mol^-1 K^-1 vs J mol^-1 K^-1) in calculations.
  • Not being able to recall or derive the crucial relations between 'a', 'b', and the critical constants (Tc, Pc, Vc), which are frequently tested.

📝 Practice Questions

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Q49.A container of fixed volume contains a gas at 27∘C. To double the pressure of the gas, the temperature of gas should be raised to ______ ∘C.

2025·NumericalEasy

Q42.The ratio of vapour densities of two gases at the same temperature is 4 , then the ratio of r.m.s. velocities will 25 be: (1) 25 (2) 2 4 5 (3) 5 (4) 4 2 25

2025·MCQEasy

Q74.Some CO2 gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of CO2 gas was later passed through an aqueous solution of Ca(OH)2 . The excess unreacted Ca(OH)2 was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of CO2 was x, then x is ________ cm3 (nearest integer). [Given : The entire amount of CO2( g) reacted with exactly half the initial amount of Ca(OH)2 present in the aqueous solution.] 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

2025·NumericalHard

Q36.At 600 K, the root mean square (rms) speed of gas X (molar mass = 40) is equal to the most probable speed of gas Y at 90 K. The molar mass of the gas Y is _____ g mol–1 . (Nearest integer)

2023·NumericalMedium

Q53.At constant temperature, a gas is at a pressure of 940 . 3 mm Hg. The pressure at which its volume decreases by 40% is ______ mm Hg. (Nearest integer) +2 . 2 V +0 . 70 V -0 . 45 V 2 - ⟶ Fe3 + ⟶ Fe2 + ⟶ Fe0

2023·NumericalEasy

Q36. Three bulbs are filled with CH4, CO2 and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be______ atm. (Nearest integer).

2023·NumericalMedium

NCERT Chapters

  • Class 11 Chemistry Ch 5: States of Matter