The molecular radius for a certain gas = . What is the reasonable estimate of the magnitude of the v — States of Matter and Gaseous State Chemistry Question
Question
The molecular radius for a certain gas = $1.25\text{ \AA}$. What is the reasonable estimate of the magnitude of the van der Waal's constant, $b$, for the gas?
Answer: C
💡 Solution & Explanation
Constant $b = 4 \times N_A \times \frac{4}{3}\pi r^3$. Given $r = 1.25 \times 10^{-8}\text{ cm}$, $r^3 \approx 1.953 \times 10^{-24}\text{ cm}^3$. $b = 4 \times 6.022\times 10^{23} \times (4/3) \times 3.14 \times 1.953 \times 10^{-24} \approx 19.7\text{ cm}^3\text{/mol}$, which is $1.97 \times 10^{-2}\text{ L/mol}$. Therefore, correct answer is C.
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