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2 years ago

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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 molec

ule is?

1 answer:

Luba_88 [7]2 years ago

8 0

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.

Learn more about calculation of mean free path -

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The question is incomplete, the complete question is:

A 7.00 L tank at $21.4^oC$ is filled with 5.43 g of sulfur hexafluoride gas and 14.2 g of sulfur tetrafluoride gas. You can assume both gases behave as ideal gases under these conditions. Calculate the mole fraction and partial pressure of each gas. Round each of your answers to significant digits.

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<u>Explanation:</u>

The number of moles is defined as the ratio of the mass of a substance to its molar mass. The equation used is:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$ ......(1)

<u>For sulfur hexafluoride:</u>

Given mass of sulfur hexafluoride = 5.43 g

Molar mass of sulfur hexafluoride = 146.06 g/mol

Putting values in equation 1, we get:

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<u>For sulfur tetrafluoride:</u>

Given mass of sulfur tetrafluoride = 14.2 g

Molar mass of sulfur tetrafluoride = 108.07 g/mol

Putting values in equation 1, we get:

$\text{Moles of sulfur tetrafluoride }=\frac{14.2g}{108.07g/mol}=0.1314mol$

Total moles of gas in the tank = [0.0372+ 0.1314] mol = 0.1686 mol

Mole fraction is defined as the moles of a component present in the total moles of a solution. It is given by the equation:

$\chi_A=\frac{n_A}{n_A+n_B}$ .....(2)

where n is the number of moles

Putting values in equation 2, we get:

$\chi_{SF_6}=\frac{0.0372}{0.1686}=0.221$

$\chi_{SF_4}=\frac{0.1314}{0.1686}=0.779$

Hence, the mole fraction of sulfur hexafluoride is 0.221 and that of sulfur tetrafluoride is 0.779

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