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Calculate the \small u_{rms} (in m/sec) of \small O_2 if its density at 1 atm pressure and \small 0^{\circ}C is 1.429g/l.

Answer upto one decimal places

Option: 1

462.2


Option: 2

46.1


Option: 3

56.3


Option: 4

44.2


Answers (1)

best_answer

Root Mean Square Speed urms

It is the square root of the mean of the square of the velocities of different molecules.
\begin{array}{l}{u_{r m s}=\frac{\sqrt{u_{1}^{2}+u_{2}^{2}+\ldots \ldots . .}}{n}} \\ {=\frac{\sqrt{n_{1} u_{1}^{2}+n_{2} u_{2}^{2}+n_{3} u_{3}^{2}}}{n_{1}+n_{2}+n_{3}}} \\ {u_{r m s}=\sqrt{3 R T / M}} \\ {u_{r m s}=\sqrt{3 P V / M}=\sqrt{3 P / d}}\end{array}

 

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We know that rms velocity is given as:

u_{rms}=\frac{3P}{d}

Now, P=1atm=101.3\times10^3Pa

And d = 1.42g/litre = 1.42kg/m^3

u_{rms}=\sqrt{\frac{3\times 101.32\times 10^3}{1.429}}=462.21m/sec

Therefore, Option(1) is correct

Posted by

Divya Prakash Singh

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