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BaLLatris [955]
3 years ago
10

Kinetic energy kx is 1/2mvx2. evaluate the mean square kinetic energy < kx2 >in one dimension for n2 molecules at 25°c (hi

nt: in the derivation of < kx2 > use f (vx.) )
Engineering
1 answer:
mash [69]3 years ago
3 0

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

<h3>How to estimate the mean square kinetic energy associated to gas molecules</h3>

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

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

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

Where:

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

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

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

K_{a} = 3593.519\,\frac{J}{mol}

The <em>mean kinetic</em> energy of the N₂ molecules at 25 °C is 3593.519 joules per mole. \blacksquare

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

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