Which of the following hazardous material states is identified by having no fixed shape or volume?

The correct answer is gas. Gases are unique in that they do not have a fixed shape or volume. Instead, they will expand to fill the entirety of their container, taking on the shape of the container as well. This characteristic is due to the high energy and movement of gas molecules, which allows them to occupy available space freely.

In contrast, liquids have a definite volume but take the shape of their container, retaining their volume while conforming to the shape. Solids maintain both a fixed shape and volume, as their particles are closely packed and only vibrate in place. Aerosols consist of tiny solid or liquid particles suspended in a gas, but the aerosol itself does not represent a state of matter like gas, liquid, or solid; rather, it describes a mixture in which particles are suspended in a gaseous medium. Therefore, gas clearly fits the criteria of having no fixed shape or volume.