This question involves the concepts of average kinetic energy and velocity.
Complete question: Calculate the root mean square velocity of the nitrogen molecules, at 25°C, in meters per second (m/s). Do not include the unit of measure in your answer.
The root mean square velocity of the nitrogen molecule at 25°C is "727.66 m/s".
The average kinetic energy of gas molecules is given by the following formula:
[tex]K.E=\frac{3}{2}KT[/tex]
Also,
[tex]K.E = \frac{1}{2}mv^2[/tex]
Comparing both equations we get:
[tex]\frac{3}{2}KT=\frac{1}{2}mv^2\\\\v=\sqrt{\frac{3KT}{m}}[/tex]
where,
v = root men square velocity = ?
K = Boltzman's constant = 1.38 x 10⁻²³ J/k
T = absolute temperature = 25°C + 273 = 298 k
m = mass of nitrogen molecule = 2.33 x 10⁻²⁶ kg
Therefore,
[tex]v=\sqrt{\frac{3(1.38\ x\ 10^{-23}\ J/k)(298\ k)}{2.33\ x\ 10^{-26}\ kg}}[/tex]
v = 727.66 m/s
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