A 10-liter container has 2 moles of oxygen at a pressure of 92 kpa. The effective speed (rms) of the oxygen molecules in the gas

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bezimeni [28] · Answer 1 · 2024-05-21T06:15:33+03:00

The effective speed (rms) of the oxygen gas is 293.68 m/s.

<h3></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

$v_{rms}=\sqrt[]{\frac{3RT}{M} }$

<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 = $\frac{PV}{n}$

Substitute in the rms velocity formula,

$v_{rms} = \sqrt[]{\frac{3PV}{nM} }$

P = 92 kPa, V = 10 L, n = 2 moles and M = 32 x 10⁻³ kg/mol

$v_{rms} = \sqrt[]{\frac{3\times92\times10}{2\times32\times10^-^3} }$

=293.68 m/s

Thus, the effective speed (rms) of O₂ gas is 293.68 m/s.

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