Problem 216 - A Complete Resource Book in Chemistry for JEE Main

Question

The general formula \(\mathrm{C}_{\mathrm{m}} \mathrm{H}_{2 \mathrm{n}} \mathrm{O}_{2}\) could be for open chain (a) carboxylic acid (b) diols (c) diketones (d) dialdehydes

Step-by-Step Solution

Answer

The general formula could be for (a) carboxylic acid.

Step 1: Analyze the General Formula

The given general formula is \( \text{C}_m\text{H}_{2n}\text{O}_2 \). Analyze the components of the formula: it contains carbon, hydrogen, and two oxygen atoms.

Step 2: Evaluate Possible Functional Groups

Identify the functional groups that could match a formula with two oxygens. Carboxylic acids have one \(-\text{COOH}\) group, diols have two \(-\text{OH}\) groups, diketones have two \(-\text{C}=\text{O}\) groups, and dialdehydes have two aldehyde groups \(-\text{CHO}\).

Step 3: Determine Hydrogen Count

For each option, calculate the hydrogen atoms: - Carboxylic acid \( \text{RCOOH} \): \( n \) hydrogen- Diols \( \text{R(OH)}_2 \): \( n \) hydrogen- Diketones \( \text{RCOR} \): \( n-4\) hydrogen after considering each \(-\text{C}=\text{O}\) consumes 1 hydrogen.- Dialdehydes \( \text{RCHO} \): \( n-2 \) hydrogen.Evaluate how these affect the general formula provided.

Step 4: Match Functional Groups to Formula

Carboxylic acids match the general formula \( \text{C}_m\text{H}_{2n}\text{O}_2 \) as they account for two oxygens in one carboxyl group while maintaining the ≈\(2n\) hydrogen ratio in an open chain structure. The hydrogen count in diols, diketones, or dialdehydes does not match unless constrained otherwise.

Step 5: Conclusion

Upon matching the hydrogen and oxygen atoms in the structures for an open chain, carboxylic acids fit the general formula. Other options either have unequal hydrogen or oxygen counts. Thus, the most fitting answer is (a) carboxylic acid.

Key Concepts

Functional Groups

In organic chemistry, functional groups are specific groups of atoms within molecules that are responsible for the characteristic chemical reactions of those molecules. A functional group behaves in a similar way in all molecules of which it is a part.
These groups can contain various atoms, and they are most often the site of chemical reactivity. Common examples include:

• Hydroxyl groups ({OH})
• Carbonyl groups (C=O)
• Carboxyl groups ({COOH})

A functional group can determine properties such as solubility, acidity, and reactivity. It defines the class of compound the molecule belongs to, such as alcohol, ketone, aldehyde, or acid.
Understanding which functional groups are present can help you predict the behavior of the molecule under different chemical conditions. The step-by-step solution identifies the crucial functional groups needed for analyzing the chemical formula.

Carboxylic Acid

Carboxylic acids are a type of organic acid that contain a carboxyl (00H) functional group, which consists of a carbonyl (1700) and a hydroxyl (0b{OH}) group bonded to the same carbon atom. They are known for their acidic properties, primarily due to the donation of the hydrogen from the 1900H group, which is relatively easy compared to other hydrogen bonds.
The general formula for a carboxylic acid is often written as 1a00HCOOH. This indicates the presence of both an oxygen atom double bonded to the carbon (the carbonyl part) and an 0b{OH} group (the hydroxyl part).
In the context of the given problem, carboxylic acids perfectly fit into the formula 1a00Hb_{2n}O_2" because they accommodate two oxygen atoms and a number of hydrogens that often conforms to the 2n rule. This ability to fit such a specific formula is due to the unique structure of the carboxylic group, which aligns with open chain organic compounds.

Chemical Formula Analysis

Chemical formula analysis involves examining the arrangement and number of atoms in a molecule's formula to predict the structure and behavior of the molecule. It is essential to understand which elements are present and in what proportions as this guides potential functional groups and overall molecular properties.
The general formula of 700Hb_{2n}O_2" indicates the presence of carbon, hydrogen, and oxygen atoms. By analyzing this formula:

• We can determine the potential presence of certain functional groups.
• The two oxygen atoms strongly suggest a carboxylic acid, as it is one of the few groups with exactly two oxygens and that aligns with open-chain structures.
• The count of hydrogens matching the 2n rule further confirms a carboxylic acid's conformity to the formula.

By understanding how to dissect and interpret general formulas, you can efficiently deduce the structural possibilities of organic compounds.