Question

Assume that you have a compound with formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\). (a) How many double bonds and/or rings does your compound contain? (b) Propose as many structures as you can that fit the molecular formula. (c) If your compound shows an infrared absorption peak at \(1715 \mathrm{~cm}^{-1}\), what functional group does it have? (d) If your compound shows a single \({ }^{1} \mathrm{H}\) NMR absorption peak at \(2.1 \delta\), what is its structure?

Short answer

(a) 1 double bond/ring. (b) Acetone, propanal, cyclopropanol, etc. (c) Carbonyl group. (d) Acetone.

Step-by-step solution

- Calculate Degrees of Unsaturation

The degree of unsaturation can be determined by using the formula: \[ n = C + 1 - \frac{H+X-N}{2} \]Where \( C \) is the number of carbons, \( H \) is the number of hydrogens, \( X \) is the number of halogens, and \( N \) is the number of nitrogens. For \( \text{C}_3\text{H}_6\text{O} \), this simplifies to:\[ n = 3 + 1 - \frac{6}{2} = 1 \]Thus, the compound has 1 degree of unsaturation, which can represent one double bond or one ring.

- Propose Structures

Given that the compound \( \text{C}_3\text{H}_6\text{O} \) has 1 degree of unsaturation, possible structures include propanal (a straight-chain aldehyde), propanone (acetone, a ketone), cyclopropanol (a cyclic alcohol), and others such as prop-1-en-1-ol.

- Interpret IR Spectroscopy Data

The infrared absorption peak at \( 1715 \text{ cm}^{-1} \) is characteristic of carbonyl groups (\( \text{C}=\text{O} \)). This suggests that the compound could be a ketone or an aldehyde, since those typically absorb around this wavelength.

- Analyze NMR Data

The \( {}^1 \text{H} \) NMR absorption peak at \( 2.1 \delta \) is indicative of hydrogens in a methylene group (\( \text{CH}_2 \)) next to a carbonyl group. This matches the signature for acetone \( \text{(CH}_3\text{)}_2\text{C=O} \), where equivalent protons appear as a single peak due to symmetry.

- Determine the Compound Structure

Since the IR absorption suggests the presence of a carbonyl group and the NMR data aligns with acetone, we conclude that the correct structure for \( \text{C}_3\text{H}_6\text{O} \) in these conditions is acetone.

Key concepts

Molecular Formula

A molecular formula is a straightforward way of indicating the kinds and numbers of atoms present in a molecule. For a given compound like \( \text{C}_3\text{H}_6\text{O} \), the molecular formula tells us that it contains three carbon atoms, six hydrogen atoms, and one oxygen atom. This information is crucial because it gives insight into the potential structure and properties of the molecule.

By analyzing the molecular formula, we can calculate the degrees of unsaturation, also sometimes known as the index of hydrogen deficiency. The degree of unsaturation helps determine the number of rings or double bonds present within the compound. The formula to calculate this is \( n = C + 1 - \frac{H+X-N}{2} \), meaning, with three carbons and six hydrogens, one degree of unsaturation is indicative of either one double bond or one ring present in the compound.

Infrared Spectroscopy

Infrared (IR) spectroscopy is an analytical technique used to identify functional groups in a molecule by measuring the absorption of light in the infrared part of the electromagnetic spectrum. When a compound absorbs IR radiation, its molecular bonds stretch, bend, or vibrate at certain characteristic frequencies. This creates a spectrum useful for identifying specific functional groups.

An absorption peak at 1715 cm\(^{-1}\) typically signifies the presence of a carbonyl group (\( \text{C}=\text{O} \)) in the molecule. Such peaks are found in aldehydes, ketones, and carboxylic acids. The distinctness of these IR signals makes it easier to identify the presence of these functional groups, guiding us to focus on structures like acetone or propanal for \( \text{C}_3\text{H}_6\text{O} \).

NMR Spectroscopy

Nuclear Magnetic Resonance (NMR) Spectroscopy is another vital tool used by chemists for determining the structure of organic compounds. It works by identifying the environments of hydrogen atoms (protons) within a molecule. Hydrogen nuclei absorb radiofrequency radiation to provide a spectrum presenting distinct peaks.

For \( \text{C}_3\text{H}_6\text{O} \), a single \(^1\text{H} \) NMR absorption peak at 2.1 \( \delta \) falls within the chemical shift range of the hydrogen nuclei of a methylene group (\( \text{CH}_2 \)), which is directly bound to a carbonyl group. It suggests that the protons are equivalent and in a symmetric environment, supporting the fact that the compound could be acetone, where both methyl groups are identical.

Carbonyl Group

Carbonyl groups, characterized by a carbon double-bonded to an oxygen atom (\( \text{C}=\text{O} \)), are a fundamental functional group in organic chemistry. They appear in various forms such as ketones, aldehydes, carboxylic acids, and esters, each with different properties and reactivities.

In the case of \( \text{C}_3\text{H}_6\text{O} \), the presence of the carbonyl group is confirmed by the IR absorption at 1715 cm\(^{-1}\) and further supported by NMR data. Identifying the carbonyl group can help narrow down potential structures, leading us toward ketonic or aldehydic forms of the compound, specifically acetone in this example. This understanding of carbonyl chemistry is essential for comprehending reactions and transformations that such groups can undergo.