The mean free path of molecules of a certain gas at STP is 1500d , where d is the diameter of the gas molecules. [2023]

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Solution

Q.
The mean free path of molecules of a certain gas at STP is 1500 $d$ , where $d$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately [2023]

1 1098 $d$

2 2049 $d$

3 750 $d$

4 1500 $d$

Ans.
(2)

$Mean free path, λ = \frac{R T}{\sqrt{2} π d^{2} N_{A} P}$

$λ \propto T$

$\frac{1500 d}{λ} = \frac{273}{373} \Rightarrow λ = 2049 d$

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