The effective speed (rms) of the oxygen gas is 293.68 m/s.
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</h3><h3>What is Root-mean-square velocity?</h3>
Root mean square velocity is the square root of the mean of squares of the velocity of individual gas molecules
![v_{rms}=\sqrt[]{\frac{3RT}{M} }](https://tex.z-dn.net/?f=v_%7Brms%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B3RT%7D%7BM%7D%20%7D)
<em>where </em>R = universal gas constant
M = molar mass of the gas in kg/mol
T = temperature in Kelvin
According to the ideal gas law,
PV = nRT
RT = ![\frac{PV}{n}](https://tex.z-dn.net/?f=%5Cfrac%7BPV%7D%7Bn%7D)
Substitute in the rms velocity formula,
![v_{rms} = \sqrt[]{\frac{3PV}{nM} }](https://tex.z-dn.net/?f=v_%7Brms%7D%20%3D%20%5Csqrt%5B%5D%7B%5Cfrac%7B3PV%7D%7BnM%7D%20%7D)
P = 92 kPa, V = 10 L, n = 2 moles and M = 32 x 10⁻³ kg/mol
![v_{rms} = \sqrt[]{\frac{3\times92\times10}{2\times32\times10^-^3} }](https://tex.z-dn.net/?f=v_%7Brms%7D%20%3D%20%5Csqrt%5B%5D%7B%5Cfrac%7B3%5Ctimes92%5Ctimes10%7D%7B2%5Ctimes32%5Ctimes10%5E-%5E3%7D%20%7D)
=293.68 m/s
Thus, the effective speed (rms) of O₂ gas is 293.68 m/s.
Learn more about Root-mean-square velocity:
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