Question

How many esters are possible with molecular formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2} ?\) (A) 2 (B) 3 (C) 4 (D) 5

Short answer

There are 3 unique combinations of R and R' groups that result in the given molecular formula \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\). Therefore, there are 3 possible esters with this molecular formula. The correct answer is (B) 3.

Step-by-step solution

Recall the ester functional group and general structure

The general structure of an ester is \(\mathrm{R-COO-R'}\). R and R' are alkyl groups that can be the same or different. We will use this general structure to identify unique combinations of R and R' groups that result in the given molecular formula, \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\).

Find the total number of C and H in R and R' groups

The carbonyl carbon and the two oxygen atoms in the ester functional group account for 1 carbon and 2 oxygen atoms. Subtract these from the molecular formula to find the total number of carbon and hydrogen atoms in the R and R' groups: Carbon atoms: \(\mathrm{C}_{4} - \mathrm{C}_{1} = \mathrm{C}_{3}\) Hydrogen atoms: \(\mathrm{H}_{8} - \mathrm{H}_{0} = \mathrm{H}_{8}\) So, the R and R' groups together should have 3 carbon and 8 hydrogen atoms.

Find unique combinations of R and R' groups

Now, we need to find unique combinations of R and R' groups that add up to the remaining carbon and hydrogen atoms. These can be visualized as: 1. R group: \(\mathrm{-CH}_{3}\), R' group: \(\mathrm{-CH_{2}-CH_{2}-CH_{3}}\) 2. R group: \(\mathrm{-CH_{2}-CH_{3}}\), R' group: \(\mathrm{-CH_{2}-CH_{3}}\) 3. R group: \(\mathrm{-CH_{2}-CH_{2}-CH_{3}}\), R' group: \(\mathrm{-CH_{3}}\) These are the three unique combinations of R and R' groups that result in the given molecular formula.

Count the number of possible esters and choose the correct option

We have found 3 unique combinations of R and R' groups that produce the molecular formula \(\mathrm{C}_{4}\mathrm{H}_{8}\mathrm{O}_{2}\). Therefore, there are 3 possible esters with this molecular formula. The correct answer is (B) 3.

Key concepts

Molecular Formula

The molecular formula of a compound provides vital information about the number and type of atoms present in that compound. For organic compounds like esters, the molecular formula represents the overall count of carbon (C), hydrogen (H), and oxygen (O) atoms. An ester with the molecular formula \( \mathrm{C}_4 \mathrm{H}_8 \mathrm{O}_2 \) tells us that in each molecule, there are four carbon atoms, eight hydrogen atoms, and two oxygen atoms.

To better understand esters, it’s essential to recognize that the molecular formula alone does not reveal the structure or arrangement of atoms, and different structures can exist with the same molecular formula—a concept known as isomerism. In the context of our exercise, identifying how many esters correspond to the same molecular formula \( \mathrm{C}_4 \mathrm{H}_8 \mathrm{O}_2 \) involves understanding their structures and how they adhere to the rules of ester formation.

Ester Functional Group

Esters are fascinating organic compounds characterized by a specific functional group known as the ester group. The ester group consists of a carbon atom double-bonded to an oxygen atom (carbonyl group) and single-bonded to another oxygen atom which, in turn, is bonded to an alkyl or aryl group (\( \mathrm{R-COO-R'} \) ).

These alkyl or aryl components, represented as \( \mathrm{R} \) and \( \mathrm{R'} \) in the general structure of an ester, can vary, creating a variety of esters even with the same molecular formula. This versatility is due to the numerous possible combinations for \( \mathrm{R} \) and \( \mathrm{R'} \) groups. The exercise's step-by-step solution leverages this very principle to solve for the number of possible esters by manipulating these variable groups within the fixed molecular formula.

Isomerism in Organic Compounds

Isomerism is a captivating concept in organic chemistry that describes the existence of compounds with the same molecular formula but different arrangements of their atoms. There are various types of isomerism; in the case of our exercise, we consider structural isomerism, particularly the different combinations of \( \mathrm{R} \) and \( \mathrm{R'} \) groups in esters.

When applying isomerism to find the number of possible esters for a given molecular formula, we’re actually exploring the different ways we can arrange the carbon and hydrogen atoms within the ester groups without altering the overall atomic counts. Each unique structural arrangement represents a different ester isomer. This is why the problem-solving approach focuses on these permutations to correctly identify the number of esters with formula \( \mathrm{C}_4 \mathrm{H}_8 \mathrm{O}_2 \). Through this method, a fascinating array of isomers can be revealed, each with unique characteristics and properties despite having the same molecular formula.