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# Answer to Question #7957 in Physical Chemistry for Ashley

Question #7957
what is th eroot-mean squared velocity of a sulfur dioxide, SO2, molecule at 275C ?
1
2012-03-30T11:26:10-0400
To solve this, we apply the law stating that the average kinetic energy of a gas molecule is directly proportional to the temperature in Kelvin:

<KE> = 1/2(mv^2) = 3/2(KT), where m is the mass of the gas molecule, v is the velocity, T is the temperature and K is the Boltzmann
constant(1.38x10^-23m^2s^-2K^-1.

Expressing it in terms of v, we get v = √(3KT/m)

Relative Molecular Mass (RMM) of SO2 = 64
6.02x10^23 molecules of SO2 = 64 g
1 molecule of SO2 = 64/6.02x10^23 = 1.06x10^-22g = 1.06x10^-25kg

Thus, v = √(3)(1.38x10^-23)(275+273)/1.06x10^-25) = 462.6 m/s (root mean square velocity of an SO2 molecule)

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