# As water is cooled, at what temperature do its particles become fixed?

Jan 12, 2016

That depends on what you mean by "fixed"... The answer could be ${0}^{\circ} \text{C}$ (when water freezes and becomes a solid) or at $- {273.15}^{\circ} \text{C}$ (at absolute zero, when all translational and rotational motions for the water particles cease to occur).

NOTE: We would be neglecting the fact that the molecules themselves would continue vibrating with zero-point energy $\frac{1}{2} h \nu$. That is, vibrational internal motions are nonzero at absolute zero.

#### Explanation:

All particles have 3 types of motion: vibrational, rotational (spinning on an axis) and translational (moving from point A to point B). When water is in liquid form, it's particles are packed closely together and you may only see a small amount of rotational and translational motion.

When water cools enough to solidify (which occurs at ${0}^{\circ} \text{C}$), then particles pack together, and rotational and translational motion pretty much stops. Therefore, as a solid, water has essentially only vibrational motion occurring.

At absolute zero, which is $- {273.15}^{\circ} \text{C}$ or $\text{0 K}$, all motion stops completely, EXCEPT for those vibrational motions that correspond to the zero-point energy ${E}_{0} = \frac{1}{2} h \nu$. The harmonic oscillator is the only quantum chemical model in which the zero-point energy is not zero.