Question

A vessel contains a mixture of nitrogen and oxygen gases.What will be the ratio of root mean square velocity of these gases

Answer 1

Hey, there!

Here's your answer.

$P= \frac{1}{3}\frac{M {v}^{2} }{V} \\ \\ \\ P = pressure \\ M = mass \: of \: the \: gas \\ v = rms \: velocity \\ V = volume \: of \: the \: vessel$

So,
${v} \: = \sqrt{\frac{3PV}{M} }$

For Oxygen,
${v(02 )} \: = \sqrt{\frac{3PV}{32} }$

For Nitrogen,
${v(N2)} \: = \sqrt{\frac{3PV}{28} }$

Ratio of rms velocities is,

$\frac{v(02)}{v(N2)} = \frac{ \sqrt{28} }{ \sqrt{32} } = \sqrt{ \frac{7}{8} } \\ \\ \\ v(02): \: v(N2) = \sqrt{7} : \sqrt{8}$


Hope this helps.

Thanks.

Answer 2

Explanation:

Hey, there!

Here's your answer.

\begin{gathered}P= \frac{1}{3}\frac{M {v}^{2} }{V} \\ \\ \\ P = pressure \\ M = mass \: of \: the \: gas \\ v = rms \: velocity \\ V = volume \: of \: the \: vessel\end{gathered}

P=

3

1

V

Mv

2

P=pressure

M=massofthegas

v=rmsvelocity

V=volumeofthevessel

So,

{v} \: = \sqrt{\frac{3PV}{M} }v=

M

3PV

For Oxygen,

{v(02 )} \: = \sqrt{\frac{3PV}{32} }v(02)=

32

3PV

For Nitrogen,

{v(N2)} \: = \sqrt{\frac{3PV}{28} }v(N2)=

28

3PV

Ratio of rms velocities is,

\begin{gathered} \frac{v(02)}{v(N2)} = \frac{ \sqrt{28} }{ \sqrt{32} } = \sqrt{ \frac{7}{8} } \\ \\ \\ v(02): \: v(N2) = \sqrt{7} : \sqrt{8} \end{gathered}

v(N2)

v(02)

=

32

28

=

8

7

v(02):v(N2)=

7

:

8

Hope this helps.

Thanks.