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Kinetic energy kx is 1/2mvx2. evaluate the mean square kinetic energy < kx2 >in one dimension for n2 molecules at 25°c (hint: in the derivation of < kx2 > use f (vx.) )

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The mean kinetic energy of the N₂ molecules at 25 °C is 3593.519 joules per mole.

How to estimate the mean square kinetic energy associated to gas molecules

Let suppose that the gas sample behaves ideally. The Graham's law establishes a connection between the ideal gas model and the kinetic theory of gases.

In this question we need to use this law to estimate the average kinetic energy (Kₐ), in joules per mole, of a diatomic gas (N₂), which is defined by the following expression:

[tex]K_{a} = \frac{3}{2}\cdot R_{u}\cdot T[/tex]   (1)

Where:

  • [tex]R_{u}[/tex] - Ideal gas constant, in joules per mole-Kelvin.
  • [tex]T[/tex] - Temperature, in Kelvin

If we know that [tex]R_{u} = 8.314\,\frac{J}{mol\cdot K}[/tex] and [tex]T = 288.15\,K[/tex], then the average kinetic energy is:

[tex]K_{a} = \frac{3}{2}\cdot \left(8.314\,\frac{J}{mol\cdot K} \right) \cdot (288.15\,K)[/tex]

[tex]K_{a} = 3593.519\,\frac{J}{mol}[/tex]

The mean kinetic energy of the N₂ molecules at 25 °C is 3593.519 joules per mole. [tex]\blacksquare[/tex]

To learn more on kinetic theory of gases, we kindly invite to check this verified question: https://brainly.com/question/15064212

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