Three gases CO2, O2 and Cl2 are at the same temperature at 25 °C. Which of the following relations for the average kinetic energy (E) is true?

# Three gases  and ${\mathrm{Cl}}_{2}$ are at the same temperature at 25 °C. Which of the following relations for the average kinetic energy (E) is true?

1. A

$\overline{E}\left({\mathrm{CO}}_{2}\right)=\overline{E}\left({\mathrm{O}}_{2}\right)=\overline{E}\left({\mathrm{Cl}}_{2}\right)$

2. B

$\overline{E}\left({\mathrm{CO}}_{2}\right)>\overline{E}\left({\mathrm{O}}_{2}\right)>\overline{E}\left({\mathrm{Cl}}_{2}\right)$

3. C

$\overline{E}\left({\mathrm{CO}}_{2}\right)<\overline{E}\left({\mathrm{O}}_{2}\right)<\overline{E}\left({\mathrm{Cl}}_{2}\right)$

4. D

$\overline{E}\left({\mathrm{CO}}_{2}\right)>\overline{E}\left({\mathrm{O}}_{2}\right)<\overline{E}\left({\mathrm{Cl}}_{2}\right)$

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### Solution:

Energy of motion of 1 mole of gas$=\frac{3}{2}RT\cdots \left(1\right)$

where R is the gas constant and T is the temperature.
The Maxwell generalisation, or Eq (1), states that at a given temperature, a mole of every gas has the same kinetic energy, which is equal to $\frac{3}{2}\mathrm{RT}$

As a result, the kinetic energy of all three gases—CO2, O2, and Cl2 is $\frac{3}{2}\mathrm{RT}$