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Chemistry Question on Gas laws

The molecules of which of the following gases has the highest speed?

A

O2{O_2} at 0∘C0^{\circ} C

B

N2{N_2} at 1000∘C1000^{\circ} C

C

CH4{CH_4} at 298K

D

H2{H_2} at −50∘C - 50^{\circ} C

Answer

H2{H_2} at −50∘C - 50^{\circ} C

Explanation

Solution

(a) Velocity of particle (vrms)=3RTM\left(v_{rms}\right)=\sqrt{\frac{3RT}{M}}
O2O_{2} at 0∘C=3×R×27332=25.5R0^{\circ}C=\sqrt{\frac{3\times R\times273}{32}}=\sqrt{25.5R}
(b) N2N_2 at 1000∘C1000^{\circ}C
=3×R×127328=136.3R=\sqrt{\frac{3\times R\times1273}{28}}=\sqrt{136.3R}
(c) CH4CH_4 at 298 K=3×R×29816=55.8R298\,K=\sqrt{\frac{3\times R\times298}{16}}=\sqrt{55.8R}
(d) H2H_2 at −50∘C-50^{\circ}C
=3×R×2232=\sqrt{\frac{3\times R\times223}{2}}
=334.5R=\sqrt{334.5R}
Hence, H2H_2 has the highest speed.