Question

The temperature of H2, at which the rms velocity of its molecules is seven times the rms velocity of the molecules of nitrogen at 300 is
2100 K
1700 K
1350 K
1050 K​

Answer 1

Answer:

1050 K

Explanation:

vrms=3RTm−−−−√

v1v2=T1M1×M2T2−−−−−−−√

vHvN=THMH×MNTN−−−−−−−−√

7 = TH×282×300−−−−−√

49 = TH×28600

TH=49×60028=1050K

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Answer 2

The temperature of $H_2$, at which the rms velocity of its molecules is seven times the rms velocity of the molecules of nitrogen at 300 K is 1050 K

Explanation:

The formula used for root mean square speed is:

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

where,  = root mean square speed

R = gas constant

T = temperature

M = atomic mass of nitrogen = 28 g/mole

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

$\nu_{rms}=\sqrt{\frac{3\times R\times 300}{28}$

For $H_2$,  $\nu_{rms}'=7\times \sqrt{\frac{3\times R\times 300}{28}$

$\sqrt{\frac{3\times R\times T}{2}}=7\times \sqrt{\frac{3\times R\times 300}{28}$

$\sqrt{\frac{3\times R\times T}{2}}=7\times \sqrt{\frac{3\times R\times 300}{28}$

${\frac{3\times R\times T}{2}}=49\times {\frac{3\times R\times 300}{28}$

$T=1050K$

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