What is the rms speed of oxygen molecules at `225^(@)C` ? Density of oxygen at NTP is `1.42 kg m^(-3)` and one atmosphere is `1.013xx10^(5)Nm^(-2)` .

Options

A. `624.8ms^(-1)`
B. `618.6ms^(-1)`
C. `328.5ms^(-1)`
D. `320.7ms^(-1)`

Answer

A

Explanation

Given , temparature, T=225+273=498K,
density,`p=1.42" kg m"^(-3)`
pressure , `p=1.013xx10^(5)Nm^(-2)`
and `rms speed , v_(rms)` ?
The rms speed of oxygen molecules at NTP,
`v_(rms)=sqrt((3p)/(p))=sqrt((3xx1.013xx10^(5))/(1.42))=4.626xx10^(2)`
`v_(rms)=462.6ms^(-1)`
Now , rms speed at 489 K `("or" 225^(@)C)`
`because v_(rms)propsqrt(T)`
`therefore ((v_("rms")))/((v_("rms"))_(O_(2)))=sqrt((T)/(T_(0)))rArr((v_("rms")))/(462.6)=sqrt((498)/(273))`
`v_("rms")=1.350xx462.6=624.80ms^(-1)`