Question

At which temperature Vrms of SO2 gas is doubled to that of Vrms of O2 gas ai 27°C

Answer 1

Vrms = (3RT/M)1/2

Where, M = molar mass of the molecule

For O2

Vrms = (3 x 8.314 x 303 / 0.032)1/2 ----------- since R is in kg molar mass of O = 32 g = 0.032 kg

= 485.97 m/s

For SO2 molar mass = 64 g = 0.064 kg

Now we want the temperature at which Vrms should be 485.97 m/s

Therefore,

485.97 = (3 x 8.314 x T / 0.064)1/2

taking square on both sides

(485.97)2 = 3 x 8.314 x T/ 0.064

(485.97)2 / 389 = T

T = 606 K