Physics · Ch 9 — Kinetic Theory of Gases
Triatomic Molecules
Triatomic Molecules
Molecules built from three atoms come in two structurally distinct shapes -- linear, where all three atoms lie on one straight line, and non-linear (bent), where the three atoms form a triangle -- and this geometric difference directly changes how many independent axes the molecule can rotate about, and hence its total degrees of freedom. The two cases …
Linear Triatomic Molecule
In a linear triatomic molecule, two outer atoms sit on directly opposite sides of a central atom, all three lying on one common straight line (Figure 9.6) -- the classic example being carbon dioxide, O=C=O.
Degrees of freedom. Because the molecule's overall shape and mass distribution along the molecular axis is essentially the same as a diatomic molecule (just with an extra atom bolted onto the exact centre, contributing no extra moment of inertia about the shared axis), a linear triatomic molecule has exactly the same structure of degrees of freedom as a diatomic molecule: three translational degrees of freedom plus two rotational degrees of freedom (about the two axes perpendicular to the line of atoms) at normal temperature, giving . At high temperature, vibrational modes activate along the molecular axis, adding two more degree …
What this figure shows. Three atoms are drawn arranged in a single straight line, an oxygen atom, a carbon atom, and another oxygen atom, with the carbon atom sitting exactly at the centre -- the structure of a carbon dioxide molecule (O=C=O). All three atomic centres lie on one common axis, which is exactly the geometric feature that gives this molecule only two independent rotational degrees of freedom rather than three, since spinning about the shared axis itself inv …
Non-linear Triatomic Molecule
In a non-linear (bent) triatomic molecule, the three atoms sit at the corners of a triangle rather than in a straight line (Figure 9.7) -- the classic example being water, H-O-H, where the two O-H bonds meet at an angle rather than lying end to end.
Degrees of freedom. Because the three atoms are not collinear, there is no single axis through the molecule about which the moment of inertia is negligible -- every one of the three mutually perpendicular axes now carries genuine rotational inertia. This gives the molecule three translational degrees of freedom plus three genuine rotational degrees of freedom (one about each of the three mutually orthogonal axes), for a total of
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What this figure shows. Three atoms are drawn arranged at the corners of a bent, triangular shape, an oxygen atom at the apex with a hydrogen atom at each of the other two corners -- the structure of a water molecule (H-O-H), with the two O-H bonds meeting at an angle rather than lying in a straight line. Because the three atoms do not lie on a single axis, there is no direction about which rotation involves zero moment of inertia, so the molecule has three genuinely independent rotational degrees of freedom, one abo …