The critical constants Pc and Tc for four gases are The gas...

The critical constants $P_{c}$ and $T_{c}$ for four gases are

The gas with smallest value of van der Waal's constant $b$ is
(a) $\mathrm{O}_{2}$
(b) $\mathrm{Cl}_{2}$
(c) $\mathrm{H}_{2}$
(d) $\mathrm{He}$

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Key Concepts

Van der Waals Equation of State

This equation modifies the ideal gas law by incorporating corrections for the finite size of molecules and for intermolecular attractions. The constants 'a' and 'b' in the equation account for these corrections, with 'b' representing the excluded volume, or the effective size of the gas particles. This modification allows for a more accurate description of real gases under various conditions.

Critical Constants

Critical constants, such as the critical temperature (Tc) and critical pressure (Pc), define the unique conditions at the critical point where the liquid and gas phases of a substance become indistinguishable. These constants are mathematically related to the van der Waals constants and provide insight into the behavior of substances near phase transitions.

Molecular Size and Excluded Volume

The constant 'b' in the van der Waals equation is a measure of the excluded volume, reflecting the space occupied by gas molecules. A smaller 'b' indicates a smaller effective molecular size. This concept is used to compare different gases, determining which gas has smaller molecules based on its van der Waals constant 'b'.

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