[saippo]

I was confused about the number of modes that diatomic molecules have. I read somewhere that there are 5 because there's 3 translational and 2 "tumbling" (I'm assuming vibrations + rotations). However, in another textbook I read that the number of modes were like solids where there were 2 vibration and rotation for each x, y, z coordinate but one drops in diatomic (could someone could explain this as well?)
Would really appreciate the clarification!

[Corribus]

In general there are 3N degrees of freedom. Three of these always correspond to linear translations in the three possible cardinal directions. Three of them are reserved for rotations and the remainder are vibrational modes. For all linear molecules, there is one less rotational degree of freedom because there is no rotation around the molecular axis.

A diatomic molecule has six degrees of freedom (3x2 = 6).  Three of these correspond to translation in x, y, and z direction. Two of them are rotational modes (rotation around the two possible axes perpendicular to each other and to the molecular axis). The last one is a vibration, along the molecular axis.

A triatomic molecule has 9 degrees of freedom. 3 translational and either 2 or 3 rotational (for linear and nonlinear, respectively) and either 4 or 3 (for linear and nonlinear, respectively) vibrational modes.

[Enthalpy]

The difference relates with the excited modes versus the possible modes.

2 "tumbling" modes can only be the rotations. 3 translations and 2 rotations for a diatomic gas molecule means that this author has neglected the vibration mode. This is correct for N₂, H₂, O₂... at room temperature, because the vibration energy levels for these molecules are too separated, so the ambient heat doesn't excite them, and the molecule stays in its ground state. Gaseous Br₂, as opposed, vibrates more easily, so its mode is largely excited and stores heat too.

At heat, stiff modes gets excites too. Cl₂ is an intermediate case, with its vibration little excited at room temperature but much at heat.

Notice that each well-excited vibration mode stores R per mole, while translations and rotations store only R/2.