Calculate the temperature at which root mean square velocity of `SO_(2)` molecules is the same as that of `O_(2)` molecules at `127^(@)C`. Molecular weights. Of `O_(2) and SO_(2)` are 32 and 64 respectively.

Answer

`527^(@)C`

Explanation

`C_((SO_2))_(t) = C_((SO_2))_(0) sqrt((t+273)/(273))`,
`C_((O_2))_(127) = C_((O_2))_(0) sqrt((127+273)/(273))`
As per question, `C_((SO_2))_(t) = C_((O_2))_(127) `
`:. C_((SO_2))_(0)sqrt((t+273)/(273)) = C_((O_2))_(0) sqrt((400)/(273))`
or `(C_((SO_2))_(0))/(C_((O_2))_(0)) = sqrt((400)/(t+273))` ...(i)
But `(C_((SO_2))_(0))/(C_((O_2))_(0)) = sqrt((rho_(O_2))/(rho_(SO_2))) = sqrt((32)/(64)) = sqrt(1/2)` ..(ii)
From (i) and (ii) , `1/2 = 400/(t+273)`
or `t+273 = 800 or t = 527^(@)C`