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Langmuir Isotherm

Using van der...

Question

Using van der Waals equation, find the constant $^{'} a^{'}$ (in $a t m$ $L^{2} m o l^{- 2}$ ) when two moles of a gas confined in $4 L$ flask exerts a pressure of $11.0$ atmospheres at a temperature of $300 K$ . The value of $b$ is $0.05 L m o l^{- 1}$ . $(R = 0.082 a t m L / K m o l)$ (as nearest integer)

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Solution

$\begin{matrix} By Vanderwaal's Gas Equation (P + \frac{a n^{2}}{v^{2}}) (v - n b) = n R T \end{matrix}$

$\begin{matrix} Given P = 11, n = 2, V = 4, b = 0.05, R = 0.082 T = 300 \end{matrix}$

$\begin{matrix} (11 + \frac{a}{4}) \times (4 - 0.1) = 2 \times 0.082 \times 300 11 + \frac{a}{4} = 12.61 \Rightarrow a = 6.46 \end{matrix}$
Answer is 6.

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