**Core Concept**
Dark urine discoloration, particularly when exposed to air, is often related to the oxidation of phenolic compounds in the urine. This phenomenon is a common clinical observation that requires a basic understanding of urine composition and its biochemical properties.

**Why the Correct Answer is Right**
The correct answer is associated with the presence of **myoglobin** in the urine. Myoglobin is a protein that stores oxygen in muscles, and its breakdown products can cause urine to darken upon standing. When myoglobin is released into the bloodstream due to muscle damage, it can be filtered by the kidneys and excreted in the urine, leading to its characteristic dark color. This process is particularly noticeable when the urine is exposed to air, as oxygen facilitates the oxidation of myoglobin to form pigmented compounds.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not directly relate to the darkening of urine on standing. While **bilirubin** can cause urine to darken, this effect is typically observed in conditions of jaundice or hemolysis, where bilirubin levels are elevated.
* **Option B:** This option is incorrect because **hemoglobinuria**, or the presence of hemoglobin in the urine, is not directly associated with darkening of urine on standing. Hemoglobin can cause urine to darken, but this effect is typically more pronounced and not necessarily related to oxidation.
* **Option C:** This option is incorrect because **porphobilinogen**, a precursor in the biosynthesis of heme, can cause urine to darken, but this effect is typically observed in conditions of porphyria, where porphobilinogen levels are elevated.

**Clinical Pearl / High-Yield Fact**
In clinical practice, the darkening of urine on standing can be an important clue to the presence of myoglobinuria, which may indicate rhabdomyolysis or another form of muscle damage.

**Correct Answer:** C.