Which has the maximum internal energy at 290 K - Neon gas , Nitrogen Gas , or ozone gas ?

To determine which gas has the maximum internal energy at 290 K, let's break this down step-by-step.

Internal Energy and Factors Affecting It
The internal energy (
𝑈
U) of a gas depends on several factors:

Temperature: All gases at the same temperature have the same average kinetic energy per molecule.
Degrees of Freedom: Gases with more degrees of freedom (such as rotational and vibrational modes) store more energy at a given temperature.
Monoatomic gases (like Neon) have only translational degrees of freedom.
Diatomic gases (like Nitrogen) have translational and rotational degrees of freedom, and at higher temperatures, vibrational degrees of freedom also contribute.
Polyatomic gases (like Ozone) have translational, rotational, and vibrational degrees of freedom.
Now, let's analyze the three gases.

1. Neon (Ne)
Neon is a monoatomic gas (atomic formula: Ne).
It has 3 translational degrees of freedom and no rotational or vibrational modes.
Its internal energy at a given temperature is lower compared to gases with more degrees of freedom.
2. Nitrogen (N₂)
Nitrogen is a diatomic gas (molecular formula: N₂).
It has 3 translational degrees of freedom and 2 rotational degrees of freedom.
At higher temperatures, vibrational degrees of freedom might contribute, but at 290 K (close to room temperature), vibrational modes are typically not excited.
Thus, the internal energy is higher than Neon but still moderate.
3. Ozone (O₃)
Ozone is a triatomic gas (molecular formula: O₃).
It has 3 translational degrees of freedom, 3 rotational degrees of freedom, and vibrational modes.
Even at 290 K, the vibrational modes of ozone can contribute significantly to its internal energy, giving it more energy storage capacity compared to monoatomic and diatomic gases.
Conclusion
Ozone (O₃) has the most degrees of freedom (translational, rotational, and vibrational), which means it can store more internal energy at 290 K compared to both Neon (Ne) and Nitrogen (N₂).

Answer: Ozone (O₃) has the maximum internal energy at 290 K.