States of Matter

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×‌

64

32

=300×2=600K