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I am slightly confused as to how I should think of changes in state (especially sublimation and deposition). Should I think of sublimation and deposition as skipping the liquid phase (fig 1) or should I think of it as a circular pattern (fig 2).

fig 1

fig 1

fig 2

fig 2

Why during sublimation and deposition is the liquid phase skipped and how is it skipped, would not all matter have to be a liquid in between solid and gas?

Is it due to the fact that some substances are unable to be liquids? if so what prevents it from being a liquid?

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Firstly, in regards to the diagrams, as mentioned in the comments, both diagrams are correct. One thing that both diagrams imply is that sublimation/deposition is equivalent to the combination of melting/freezing and evaporation/condensation - another way to look at this is the following diagram from the UC Davis ChemWiki page Heat of Sublimation:

An explanation from the webpage is that:

Though in sublimation a solid does not pass through the liquid phase on its way to the gas phase, it takes the same amount of energy that it would to first melt (fuse) and then vaporize.

In regards to your related questions:

Is it due to the fact that some substances are unable to be liquids? if so what prevents it from being a liquid?

Not quite, liquids can occur in the right conditions, the explanation is below.

Why during sublimation and deposition is the liquid phase skipped and how is it skipped, would not all matter have to be a liquid in between solid and gas?

To understand why sublimation occurs requires an understanding of phase diagrams. A generalised phase diagram from UC Davis Chemwiki page Phase Diagrams is shown below:

enter image description here

The sublimation/deposition curve is the line from the origin to the triple point, represented as the red line in the diagram above. A generalisation that can be made is that a substance undergoes sublimation/deposition when either (or both) the temperature and pressure are lower than at the triple point. Consider the following examples comparing the phase diagrams of carbon dioxide and water (from the UC Davis Chemwiki page linked before):

First, carbon dioxide - at 'normal' atmospheric pressure (such as in the typical laboratory - 1 atm), it is lower than the 5.2 atm at the triple point (labelled 'D'). Assuming minimal pressure changes from standard laboratory conditions, as the $\ce{CO2}$ is cooled, it will eventually undergo deposition to the solid phase.

enter image description here

Now, for comparison, consider the phase diagram for water, the triple state (also labelled 'D') occurs at a very low pressure 0.006 atm, pressures lower than that would result in water subliming. Note for the standard laboratory conditions, water maintains the familiar solid, liquid and gas characteristics (depending on temperature).

enter image description here

Note, both do have a liquid phase.

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