at what temperature rms velocity of SO2 will be same as that of methane gas at 300K?

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Solution

↵The root mean square, rms velocity of a molecule is:

$v_{r m s} = \sqrt{\frac{3 R T}{M_{n}}}$
where, v_rms is the root mean square of the speed in metres per second,
M_m is the molar mass of the gas in kg per mole,
R is the molar gas constant, and
T is the temperature in Kelvin

Rms of methane at 300 K

$v_{r m s, C H_{4}} = \sqrt{\frac{3 \times R \times 300 K}{16 g / mol}} . . . . . i$

Rms of SO₂

_{$v r m s, S O_{2} = \sqrt{\frac{3 \times R \times T}{64 g / mol}} . . . . . . ii$}

Equating equations i and ii, we get

$\sqrt{\frac{3 \times R \times 300 K}{16 g / mol}} = \sqrt{\frac{3 \times R \times T}{64 g / mol}} or, \frac{300 K}{16} = \frac{T}{64} T = 1200 K$

Therefore, at 1200 K, the rms of SO₂ will be equal to rms of methane at 300 K.

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