The formula for the root mean square velocity is:
Vrms = √(3RT/M)
R = universal gas constant
T = temperature
M = molar mass
In this instance, R and T will be equal when comparing the two gases. The molar mass of CO2 = 44 g/mol and SO2 = 64 g/mol. We simply fill in the Vrms for each gas and take the ratio:
Vrms(CO2) = √(3RT/44)
Vrms(SO2) = √(3RT/64)
Vrms(CO2)/Vrms(SO2) = √(3RT/44) /√(3RT/64)
Vrms(CO2)/Vrms(SO2) = √(3RT/44) · √(64/3RT)
Vrms(CO2)/Vrms(SO2) = √64/√44
Vrms(CO2)/Vrms(SO2) = 1.207
The ratio of root-mean-square of CO2 to SO2 is 1.207.