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  • 1 mol of  at temperature <img alt="27^0 C" src="https://entrancecorner.oncodecogs.com/gif.latex?27%5E0%20C"

1 mol of o_2 at temperature 27^0 C at STP \left(1.01 \times 10^5 \mathrm{~N} / \mathrm{m}^2\right) is kept in  vessel. Find the number of collisions the molecules experience (in SI) per second per unit area with the wall of the vessel \left[k=1.38 \times 10^{13} \mathrm{~J} / \mathrm{k}\right]

Option: 1

1.9 \times 10^{27}


Option: 2

1.9\times10^{20}


Option: 3

2.9\times10^{27}


Option: 4

2.9\times10^{20}


Answers (1)

best_answer

Number of molecules in 1 mol of O_2=6.023\times10^{23}

\therefore Mass of a molecule 

\begin{aligned} m & =\frac{32}{6.023 \times 10^{23} \times 1000} \\\\ & =5.316 \times 10^{-26} \mathrm{~kg} \end{aligned}

Momentum of the molecule p=mv= m \sqrt{\frac{3 k T}{m}}=\sqrt{3 k T m}

Change in momentum due to each collision,

\begin{aligned} \Delta P=2 p & =2 \sqrt{3 \mathrm{kTm}} \\ & =2 \sqrt{3 \times 1.38 \times 10^{-23} \times 300 \times 5.316 \times 10^{-26}} \\ & =5.139 \times 10^{-23} \mathrm{kgm} / \mathrm{s} . \end{aligned}

If the molecules experience 'n' number of collsions per second per square meter of the wall, then the pressure of the gas will be-

\begin{gathered} p=n \Delta p \Rightarrow 1.01 \times 10^5=n \times 5.139 \times 10^{-23} \\ \Rightarrow n=1.965 \times 10^{27} \end{gathered}

Posted by

shivangi.bhatnagar

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