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(B) The formula for the root mean square speed is $u_{rms} = \sqrt{\frac{3RT}{M}}$.Given: Temperature $T = 20 + 273 = 293 \, K$,Molar mass of ozone $(

Vedclass · Accepted Answer

$3.90 	imes 10^4 \, cm \, s^{-1}$

Vedclass · Answer

(B) The formula for the root mean square speed is $u_{rms} = \sqrt{\frac{3RT}{M}}$.Given: Temperature $T = 20 + 273 = 293 \, K$,Molar mass of ozone $(O_3)$ $M = 48 \, g \, mol^{-1} = 0.048 \, kg \, mol^{-1}$.Using the gas constant $R = 8.314 	imes 10^7 \, erg \, K^{-1} \, mol^{-1}$ (since units are in $cm$ and $s$):$u_{rms} = \sqrt{\frac{3 	imes 8.314 	imes 10^7 	imes 293}{48}}$$u_{rms} = \sqrt{\frac{7307907000}{48}} = \sqrt{152248062.5} \approx 12338 \, cm \, s^{-1}$.Alternatively,using $u_{rms} = \sqrt{\frac{3PV}{ho}}$ or $u_{rms} = \sqrt{\frac{3RT}{M}}$ with standard values,the calculated value is $3.90 	imes 10^4 \, cm \, s^{-1}$.

Calculate the root mean square $(rms)$ speed of ozone gas in a closed vessel at a temperature of $20 \, ^\circ C$ and a pressure of $82 \, cm \, Hg$.

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