Write the molecular formula of ethanol. The color codes are: black (carbon), red (oxygen), and gray (hydrogen).

Understanding chemical symbols is fundamental in grasping the basics of chemistry and molecular structures. A chemical symbol is a shorthand representation of an element from the periodic table. For instance, 'C' stands for Carbon, 'O' for Oxygen, and 'H' for Hydrogen. These symbols are used universally, meaning they are recognized in scientific communities around the globe, regardless of language.

When writing or reading chemical formulas, recognizing these symbols is crucial. They help streamline complex information about a substance into an easily interpretable string of letters. For example, when you see the letter 'C' in a chemical formula, you immediately know that carbon is a component of that molecule. In the context of the exercise, identifying that black represents carbon is step one in translating the colors into a universally understood language of chemistry.

The concept of subscript notation in chemistry is a simple yet vital means of conveying quantity in molecular formulas. Subscripts are small numbers written to the right and slightly below a chemical symbol. They indicate how many atoms of the element are present in a single molecule of the compound. If there is only one atom of an element in the molecule, the subscript '1' is typically omitted.

For instance, in the molecular formula of ethanol, \(\ce{C2H6O}\), the subscript '2' next to the carbon (C) symbol tells you there are two carbon atoms. Similarly, the '6' next to the hydrogen (H) symbol denotes six hydrogen atoms. The oxygen (O) has no subscript, meaning there is just one oxygen atom in ethanol. This efficient method of representation allows anyone to understand the quantity of each element in a molecule at a glance.

Moving to molecular representation, it is a visual depiction of the arrangement of atoms within a molecule. While molecular formulas provide a quick numerical understanding of a molecule's composition, representations can take it one step further by showing the structure. These structures can be in the form of simple stick diagrams, ball-and-stick models, or space-filling models where different colors often denote various elements - mirroring our exercise's use of color codes.

In the step-by-step solution to the exercise, translating the color-coded ethanol molecule into the molecular formula \(\ce{C2H6O}\) is an exercise in converting a visual representation into a chemical formula. While ball-and-stick models give a three-dimensional perspective, the molecular formula is a flat, precise, and size-efficient manner of conveying the same information. This model of communication is essential for chemists and students to discuss and predict the behavior of molecules without the need for elaborate visual models in every instance.