We want to find the temperature where the rms (root mean square) speed of SO2 molecules is equal to the rms speed of O2 molecules at 27∘C. The formula for rms velocity is: Vrms=√‌
3RT
M
where R is the gas constant, T is temperature in Kelvin, and M is molar mass. We set the rms speeds equal: Vrms(SO2)=Vrms(O2)So,√‌
3RTSO2
MSO2
=√‌
3RTO2
MO2
Squaring both sides removes the square root: ‌
TSO2
MSO2
=‌
TO2
MO2
Rearrange for TSO2:TSO2=TO2×‌
MSO2
MO2
The temperature given for O2 is 27∘C. Convert this to Kelvin: 27+273=300K The molar mass of SO2 is 64 , and of O2 is 32 . Plug in the values: TSO2=300×‌