why would it be dangerous to heat a liquid in a distillation apparatus that had no vent or opening to the laboratory?

- is this because the liquid will create vapor pressure and could cause a serious injury to a student?

- is this because the liquid will create vapor pressure and could cause a serious injury to a student?

The likely hood is for the joints on the apparatus to come apart, possibly very rapidly, and the a large volume of the material to escape as a gas. If the apparatus is "quick fit" with ground glass joints then these are designed to take a vacuum and, with clips attached, a low positive pressure.

There are a few occasions where distillation is carried out in a sealed apparatus. This is carried out with a vacuum line and is used where the material is very expensive or toxic or maybe unstable in the air and low boiling.

If you are interested in reading further on these techniques see:
http://en.wikipedia.org/wiki/Schlenk_line
and some of the links in the article.

also "Guide for the Perplexed Organic Experimentalist"
by H J E Loewenthal.
which was written for grad students but has some interesting insights.

Yes, that's correct. Heating a liquid in a distillation apparatus without a vent or opening to the laboratory can be dangerous because the liquid can generate vapor pressure as it gets heated. This pressure buildup can cause the apparatus to rupture or explode, which can result in serious injuries to the student or anyone nearby.

When a liquid is heated, its molecules gain energy and become more active. As a result, some of the liquid molecules will escape the surface and turn into vapor. In a closed system without a vent, these vapor molecules cannot escape, leading to an increase in pressure inside the apparatus.

If the pressure continues to rise due to the heating process, the apparatus may not be able to withstand the internal force, causing it to rupture or explode. This can release hot liquid, vapor, or fragments of the apparatus, posing a significant risk of injury to anyone in the vicinity.

To prevent such dangers, it is essential to ensure that a distillation apparatus has a properly designed vent or opening that allows for the controlled release of pressure during the heating process. This venting mechanism helps to maintain a safe operating pressure and prevents any potential hazards associated with excessive pressure buildup.