Problem 107 - A Complete Resource Book in Chemistry for JEE Main

Question

State the correct general formula of carbohydrates (a) \(\mathrm{C}_{x}\left(\mathrm{H}_{2}\right)_{y} \mathrm{O}\) (b) \(\mathrm{C}_{x-1}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y}\) (c) \(\mathrm{C}_{x}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y}\) (d) \(\mathrm{C}_{x}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y+2}\)

Step-by-Step Solution

Answer

The correct option is (c) \( \mathrm{C}_{x}(\mathrm{H}_2 \mathrm{O})_{y} \).

Step 1: Understand what carbohydrates are

Carbohydrates are organic molecules composed of carbon, hydrogen, and oxygen, typically represented by the formula \\( \text{C}_x(\text{H}_2\text{O})_y \). This indicates they are hydrates of carbon, meaning their formula includes water molecules combined in a specific proportion.

Step 2: Identify the correct pattern in the options

The general formula for carbohydrates suggests a pattern of carbon atoms \\( (\text{C}_x) \) linked with water molecules \\((\text{H}_2\text{O})_y \). The subscript \\(y\) represents hydrogen and oxygen in a 2:1 ratio, which matches water composition. From the given options, observe which one satisifes this pattern.

Step 3: Evaluate the options given

Option (a) \\( \mathrm{C}_x(\mathrm{H}_2)_y \mathrm{O} \) does not match the hydrate formula as it separates water into \\( \mathrm{H}_2 \) and \\( \mathrm{O} \). Option (b) \\( \mathrm{C}_{x-1}(\mathrm{H}_2\mathrm{O})_y \) reduces the carbon atoms by one unit, which does not fit. Option (d) \\( \mathrm{C}_x(\mathrm{H}_2\mathrm{O})_{y+2} \) adds extra water molecules, changing the proportion. Only option (c) \\( \mathrm{C}_{x}(\mathrm{H}_2 \mathrm{O})_{y} \) properly includes carbon linked with water molecules in the correct ratio.

Step 4: Conclude the correct formula

After evaluating each option, it's clear that option (c) \\( \mathrm{C}_{x}(\mathrm{H}_2 \mathrm{O})_{y} \) correctly reflects the general formula of carbohydrates: carbon atoms linked with water molecules. This establishes the ratio needed for a carbohydrate molecule.

Key Concepts

Organic Molecules

Organic molecules are essential to life and are primarily made of carbon atoms along with other elements. They contain carbon as their backbone, which allows them to form complex structures. The versatility of carbon makes organic molecules incredibly diverse, supporting a wide range of biological functions.
Common examples of organic molecules include carbohydrates, proteins, lipids, and nucleic acids. Carbohydrates, our focus here, are organic because they have a specific carbon-based structure, forming molecules that are vital for energy storage and supply.
By understanding organic molecules, we grasp how living organisms function and interact at a molecular level. Carbohydrates, in particular, are crucial as they often serve as a quick energy source in living beings.

Carbon Hydrogen Oxygen

Carbohydrates consist of three primary elements: carbon, hydrogen, and oxygen. These are arranged in a specific chemical formula that generally follows a particular pattern, allowing carbohydrates to perform their biological roles efficiently.

• Carbon (C): Serves as the main framework, allowing carbohydrates to form cyclic and linear structures.
• Hydrogen (H) and Oxygen (O): These elements are usually present in a 2:1 ratio, much like water. This sets the foundation for categorizing carbohydrates as hydrates of carbon.

In the formulation of carbohydrates, these elements combine to form monosaccharides like glucose or complex structures like starch and cellulose. The interplay of carbon, hydrogen, and oxygen enables carbohydrates to serve essential functions such as energy storage and structural support in cell walls.

Hydrates of Carbon

The term 'hydrates of carbon' refers to the classic structure of carbohydrates, balancing carbon atoms with water molecules. The standard general formula, \( ext{C}_x( ext{H}_2 ext{O})_y \), suggests that for every carbon atom, a corresponding water molecule is typically present.
Although not all carbohydrates precisely fit this formula, it serves as a foundational concept in understanding their basic composition.

• Monosaccharides, the simplest form of carbohydrates, adhere closely to this hydrate principle.
• Complex carbohydrates, like polysaccharides, build on this by linking multiple monosaccharides together, although the perfect water-molecule symmetry may not always remain intact.

Understanding carbohydrates as hydrates of carbon helps in visualizing their structural formation and their ability to store and release energy efficiently in living organisms. This perspective is essential for studying biochemical processes and nutritional science.