Question

the ratio of average speed of an O2 molecule to the rms speed of N2 molecule at the same temperature is​

Answer 1

Explanation:

√ 8RT/π×32

√3RT/28

7

√66

Answer 2

Answer: $\sqrt{\frac{7}{3\pi}}$

Explanation:

The formula for average speed is  

$\nu_{av}=\sqrt{\frac{8RT}{\pi M}}$

where,

R = gas constant  

T = temperature  

M = 32.0 g/mol ( for oxygen)

The formula used for root mean square speed is:

$\nu_{rms}=\sqrt{\frac{3RT}{M}}$

where,

$\nu_{rms}$ = root mean square speed

R = gas constant  

T = temperature  

M = atomic mass = 28.0 g/mol  ( for nitrogen)

Now put all the given values:

$\frac{\nu_{av}}{\nu_{rms}}=\frac{\sqrt{\frac{8RT}{\pi M_{O_2}}}}{\sqrt{\frac{3RT}{M_{N_2}}}}$

$\frac{\nu_{av}}{\nu_{rms}}=\frac{\sqrt{\frac{8}{\pi M_{O_2}}}}{\sqrt{\frac{3}{M_{N_2}}}}$

$\frac{\nu_{av}}{\nu_{rms}}=\frac{\sqrt{\frac{8}{\pi \times 32}}}{\sqrt{\frac{3}{28}}}$

$\frac{\nu_{av}}{\nu_{rms}}=\sqrt{\frac{7}{3\pi}}$

Thus ratio of average speed of an O2 molecule to the rms speed of N2 molecule at the same temperature is $\sqrt{\frac{7}{3\pi}}$