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) \(\mathrm{C}_{r}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y}\) (d) \(\mathrm{C}_{x}\left(\mathrm{H}_{2} \mathrm{O}\right)_{v+2}\)

Step-by-Step Solution

Answer

The correct general formula for carbohydrates is (c) \(\mathrm{C}_r\left(\mathrm{H}_{2} \mathrm{O}\right)_y\).

Step 1: Understanding the Basic Formula for Carbohydrates

The general formula for carbohydrates can be represented as \(\mathrm{C}_n\left(\mathrm{H}_2\mathrm{O}\right)_m\), where carbohydrates consist of carbon, hydrogen, and oxygen. Their structure can be described as hydrates of carbon, where water molecules (\(\mathrm{H}_2\mathrm{O}\)) are paired with carbon atoms.

Step 2: Analyzing the Given Options

Let's break down each option:- **(a)** \(\mathrm{C}_{x}\left(\mathrm{H}_{2}\right)_{y}\mathrm{O}\) - This formula separates hydrogen atoms from oxygen, not representing \(\mathrm{H}_2\mathrm{O}\).- **(b)** \(\mathrm{C}_{x-1}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y}\) - Here, the carbon count differs from the common pattern seen in carbohydrate formulas.- **(c)** \(\mathrm{C}_{r}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y}\) - This correctly represents carbohydrates as hydrates of carbon, as each carbon atom pairs with water.- **(d)** \(\mathrm{C}_x\left(\mathrm{H}_{2} \mathrm{O}\right)_{v+2}\) - The expression of this formula with \(v+2\) is not the standard representation.

Step 3: Identifying the Correct Formula

The pattern in the correct formula should explicitly group water with carbon which matches the general carbohydrate formula. Option (c) \(\mathrm{C}_{r}\left(\mathrm{H}_{2} \mathrm{O}\right)_{y}\) properly expresses this relationship providing a balanced formula where water is associated directly with each carbon unit as expected.

Step 4: Conclusion

Considering the breakdown of each option, the correct representation of the general formula for carbohydrates is found in option (c), \(\mathrm{C}_r\left(\mathrm{H}_{2} \mathrm{O}\right)_y\). This reflects the idea that carbohydrates are composed of carbon atoms hydrated with water molecules.

Key Concepts

Basic Chemistry

In the world of basic chemistry, we learn about different types of chemical compounds and how they are structured and formulated. Chemistry is the science that explains how substances interact, combine, and change to form new substances. A core principle in chemistry is the understanding of elements and atoms. Elements are pure substances composed of only one type of atom.

Atoms are the smallest particle of an element that retains its properties. Each atom consists of protons, neutrons, and electrons. The combination of different atoms forms molecules and compounds. Compounds are substances made from two or more different elements that are chemically bonded together.

Understanding basic chemistry concepts is essential because it forms the foundation for more specific fields, like organic chemistry. For instance, when we talk about carbohydrates, we are diving into a specific group of chemical compound formed primarily from three elements: carbon (C), hydrogen (H), and oxygen (O). These elements react with each other to form complex structures that have unique properties and functions in many biological processes.

Chemical Formulas

Chemical formulas are a shorthand way to represent the composition of chemical compounds. These formulas detail the elements present in a compound and the ratios in which these elements combine.

For carbohydrates, the chemical formula can be generalized as \( \mathrm{C} _r\left(\mathrm{H} _2 \mathrm{O}\right)_y \). This implies that every carbon atom is combined with water molecules, depicting carbohydrates as 'hydrated carbons.' In this context, the formula provides a clear visual of how the atoms are associated within a molecule.

• A chemical formula is typically written with element symbols followed by subscript numbers indicating the number of each type of atom present.
• When there is a subscript of one, it is often omitted for simplicity (e.g., H instead of H\(_1\)).

Formulas are pivotal because they allow chemists to communicate information about particular compounds seamlessly. Chemical formulas not only reveal the composition but also give insights into the proportions and the likely structure of compounds, which is incredibly useful in understanding and predicting chemical reactions.

Organic Chemistry

Organic chemistry is a branch of chemistry that focuses primarily on compounds containing carbon. The presence of carbon allows for the formation of a vast array of complex molecules, which is why carbon is often referred to as the "backbone of life." Carbohydrates are a prime example of organic compounds, holding a central place in organic chemistry due to their biological importance. They serve as energy sources and structural elements in living organisms.

In organic chemistry, understanding the carbon chains and how they interact with other elements such as hydrogen and oxygen is crucial. Carbohydrates are composed of carbon atoms bonded to hydrogen and oxygen in specific configurations that result in useful functional groups.

Each category of organic compounds, such as carbohydrates, proteins, and lipids, has its unique structure and properties. Carbohydrates often form ring structures, which are stabilized by the presence of the aforementioned water molecules.

Organic chemistry delves into exploring how these carbon-containing compounds are synthesized, manipulated, and utilized both in nature and in synthetic processes to create everything from medicines to new materials.