Which one of the following nonmetals exhibits allotropy even in its liquid state, showing different liquid forms at different temperatures?

Introduction / Context:
Allotropy is the phenomenon where an element exists in two or more different structural forms in the same physical state, such as solid carbon existing as diamond, graphite, and fullerene. While solid allotropy is widely discussed, some elements also show interesting behaviour in the liquid state. This question tests whether you know which nonmetal has distinct liquid forms, not just solid allotropes, making it a favourite conceptual point in basic inorganic chemistry.

Given Data / Assumptions:

• The nonmetals listed are carbon, sulphur, phosphorous, and bromine.
• Allotropy refers to different forms of the same element in the same physical state.
• We are specifically asked about allotropy in the liquid state.
• We assume standard descriptions from school level inorganic chemistry regarding sulphur's unusual liquid behaviour.

Concept / Approach:
Carbon shows allotropy mainly in the solid state (diamond, graphite, amorphous carbon, fullerenes). Phosphorus also has several solid allotropes (white, red, black phosphorus). Bromine is a liquid at room temperature but does not exhibit commonly discussed liquid allotropy; it exists essentially as Br2 molecules. Sulphur, on the other hand, is famous for having multiple forms not only in the solid state (rhombic and monoclinic sulphur) but also in the liquid state. When sulphur is heated, its molecular structure changes: at lower temperatures it mainly contains S8 rings, but at higher temperatures, these rings break and form long chain polymers, leading to different liquid forms with changing viscosity and colour. This is often cited as an example of liquid allotropy.

Step-by-Step Solution:
Step 1: Recall solid allotropes for each element. Carbon has diamond and graphite; phosphorus has white and red forms; sulphur has rhombic and monoclinic forms. Step 2: Focus on the liquid state. Liquid bromine is simply Br2 molecules; no common liquid allotropes are discussed. Step 3: Examine sulphur's behaviour when heated. As sulphur melts and is further heated, its S8 rings open and form long-chain molecules, changing its viscosity and appearance, indicating different liquid forms. Step 4: Conclude that sulphur is the nonmetal that shows allotropy even in the liquid state.

Verification / Alternative check:
Textbooks often include a graph or discussion of the viscosity of liquid sulphur as a function of temperature. As temperature rises, the initially low-viscosity liquid becomes much more viscous due to the formation of long chain molecules, then thins again at higher temperatures when the chains break. This behaviour is tied to structural changes in the liquid and is treated as an example of allotropy beyond the solid state. Neither carbon nor phosphorus is normally studied in liquid form in school courses, and bromine is not said to have distinct liquid allotropes. This emphasis on sulphur's unusual liquid properties confirms that it is the correct choice.

Why Other Options Are Wrong:
Option A (Carbon): Carbon shows solid allotropy (diamond, graphite), but liquid allotropy is not a standard topic at this level. Option C (Phosphorous): Phosphorus has several solid allotropes; liquid allotropy is not commonly mentioned in basic courses. Option D (Bromine): Bromine is a liquid at room temperature but is essentially present as Br2 molecules without distinct liquid allotropes discussed in textbooks.

Common Pitfalls:
Students often think of carbon first because it is the most famous example of allotropy, but the question specifically asks about the liquid state. Another trap is selecting bromine simply because it is a liquid nonmetal at room temperature, without considering whether it actually has different liquid forms. To avoid such mistakes, read the question carefully and recall the unique case of sulphur, whose liquid state exhibits changing structures and viscosities, making it a textbook example of allotropy beyond solids.

Final Answer:
The nonmetal that shows allotropy in the liquid state is Sulphur.