Question

at what temp the RMS velocity of oxygen will be same as that of methane at 27 degree celsius

Answer 1

See the attachment

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Answer 2

Answer: $327^0C$

Explanation:

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 = $8.314J/Kmol$

T = temperature = $27^0C=(27+273)K=300K$

M = atomic mass of methane = 0.016 kg/mole

Now put all the given values in the above root mean square speed formula, we get:

$\nu_{rms}=\sqrt{\frac{3\times 8.314\times 300}{0.016kg/mol}}$

for oxygen , $\nu_{rms}$ is same as methane and let temperature is T'

$\sqrt{\frac{3\times 8.314\times 300}{0.016kg/mol}}=\sqrt{\frac{3\times 8.314\times T'}{0.032}$

$T'=600K=(600-273)^0C=327^0C$

Thus the RMS velocity of oxygen will be same as that of methane at 27 degree celsius at 327 degree celsius.