At what temperature will the root mean square velocity of SO2 be same

1.	At what temperature will the root mean square velocity of SO2 be same as that of methane at 27°C?
Answer» C_rms= \(\sqrt{\frac{3RT}{M}}\) For CH₄, M = 16, T = 300 K C_rms = \(\sqrt{\frac{3R\times300}{16}}\) For SO₂, M = 64, T = ? C_rms = \(\sqrt{\frac{3R\times T}{64}}\) \(\sqrt{\frac{300}{16}}=\sqrt{\frac{T}{64}}\) T = \(\frac{300\times64}{16}\) = 1200 t = 1200 - 273 = 927ºC.

At what temperature will the root mean square velocity of SO2 be same as that of methane at 27°C?

Answer»

C_rms= \(\sqrt{\frac{3RT}{M}}\)

For CH₄, M = 16, T = 300 K

C_rms = \(\sqrt{\frac{3R\times300}{16}}\)

For SO₂, M = 64, T = ?

C_rms = \(\sqrt{\frac{3R\times T}{64}}\)

\(\sqrt{\frac{300}{16}}=\sqrt{\frac{T}{64}}\)

T = \(\frac{300\times64}{16}\)

= 1200

t = 1200 - 273

= 927ºC.