The compressibility factor of a Vanderwaal gas is 0.5 at $27 ° C$ and 24 atm. The value of Vanderwaal constant 'a' (in atm-L²/mol²) is (b = 0.10 L/mol, R = 0.08 L-atm/K-mol)

Option 1 - 2.4

Option 2 - 4.0

Option 3 - 3.6

Option 4 - 9.0

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Vishal Baghel | Contributor-Level 10

5 months ago

Correct Option - 4

Detailed Solution:

^{$Z = \frac{P V_{m}}{R T} \Rightarrow 0.5 = \frac{24 * V_{m}}{24}$}

^{$V_{m} = 0.5 l / m o l e$}

^{$(P + \frac{a}{V_{m}^{2}}) (V_{m} - b) = R T$}

^{$(24 + \frac{a}{0 . 5^{2}}) (0.5 - 0.1) = 24$}

^{$24 + \frac{a}{0 . 5^{2}} = 60$}

^{$\frac{a}{0 . 5^{2}} = 36$}

^{$a = 36 * 0 . 5^{2} = 9 \frac{a t m - l^{2}}{m o l^{2}}$}

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The compressibility factor of a Vanderwaal gas is 0.5 at 2 7 ° C and 24 atm. The value of Vanderwaal constant 'a' (in atm-L2/mol2) is (b = 0.10 L/mol, R = 0.08 L-atm/K-mol)

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