Question

A 1 l container contains O2 gas at stp. if the diameter of the O2 molecule is 3.75 * 10^-10 m the mean free path of the o2 molecule is?

Answer 1

The mean free path of the O₂ molecule is $5.97*10^{-5}$ m.

The mean free path of the O₂ molecule is calculated by the formula -

λ = $\frac{1}{\sqrt{2}*\pi *d^{2}*n}$

In this formula, λ represents mean free path of gas, d represents diameter and n is number of molecules.

As per the known fact, 1 mole of gas occupies 22.4 liter at STP.

So. 1 liter of O₂ gas will have number of moles = $\frac{1*1}{22.4}$

Number of moles = 0.045

Also, we are aware that 1 mole contains $6.02*10^{23}$ molecules.

So, 0.045 moles will contain number of molecules = $6.02*10^{23}*0.045$

Number of molecules = $2.7*10^{22}$ molecules

Now, keeping the values in formula to find mean free path of gas -

λ =  $\frac{1}{1.4*3.14*(3.75*10^{-10})^{2} *2.7*10^{22} }$

λ = $\frac{1}{16746.7}$

λ = $5.97*10^{-5}$ m

Hence, the mean free path of the O₂ molecule is $5.97*10^{-5}$ m.

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