At what temperature, the root-mean-square velocity of `SO_(2)` will be the same as that of `CH_(4)` at `27^(@)C`?

Options

A. `3000 K`
B. `1345 K`
C. `1200 K`
D. `1700 K`

Answer

C

Explanation

Root-mean-square velocity `=sqrt((3RT)/(M))`
The value of `CH_(4)` at `27^(@)C` or `300 K= sqrt((3Rxx300)/(16))`
Now for `SO_(2)`
Root-mean-square velocity `=sqrt((3RT)/(64))`
Or, `sqrt((3Rxx300)/(16))=sqrt((3RxxT)/(64))` or `T= 1200K`