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