Ch. 14 - Structural Identification I: Infrared Spectroscopy and Mass Spectrometry

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 14 - Structural Identification I: Infrared Spectroscopy and Mass Spectrometry

Problem 1d

Chapter 13, Problem 1d

Given the molecular formula, calculate the index of hydrogen deficiency.
(d) C₈H₉OBr

Verified step by step guidance

Step 1: Understand the concept of the Index of Hydrogen Deficiency (IHD). The IHD, also known as the degree of unsaturation, indicates the number of rings, double bonds, or triple bonds in a molecule. Each degree of unsaturation corresponds to the loss of two hydrogens compared to a fully saturated molecule.

Step 2: Use the formula for IHD: IHD = (2C + 2 - H + N - X) / 2, where C is the number of carbons, H is the number of hydrogens, N is the number of nitrogens, and X is the number of halogens (e.g., Br, Cl, F, I). For this problem, the molecular formula is C₈H₉OBr.

Step 3: Substitute the values from the molecular formula into the IHD formula. Here, C = 8, H = 9, N = 0 (no nitrogen), and X = 1 (one bromine atom). Oxygen (O) does not affect the IHD calculation, so it is ignored.

Step 4: Simplify the formula step by step. First, calculate the numerator: (2 × 8) + 2 - 9 + 0 - 1. Then divide the result by 2 to find the IHD.

Step 5: Interpret the result. The IHD value will tell you the number of rings and/or multiple bonds in the molecule. For example, an IHD of 1 indicates one double bond or one ring, while an IHD of 2 could indicate two double bonds, one triple bond, or one ring and one double bond.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Index of Hydrogen Deficiency (IHD)

The Index of Hydrogen Deficiency (IHD) is a measure of the degree of unsaturation in a molecule, indicating the number of rings and/or multiple bonds present. It is calculated using the formula IHD = (2C + 2 + N - H - X) / 2, where C is the number of carbons, N is the number of nitrogens, H is the number of hydrogens, and X is the number of halogens. A higher IHD value suggests more unsaturation, which can affect the reactivity and properties of the compound.

Molecular Formula Interpretation

A molecular formula provides the number and types of atoms in a compound, which is essential for calculating the IHD. In the formula C₈H₉OBr, there are 8 carbon atoms, 9 hydrogen atoms, 1 oxygen atom, and 1 bromine atom. Understanding how to interpret this formula allows for the correct application of the IHD formula and helps in identifying the structure and potential functional groups present in the compound.

Halogens in Organic Compounds

Halogens, such as bromine, are important in organic chemistry as they can influence the saturation of a molecule. When calculating IHD, halogens are treated similarly to hydrogens, as they can replace hydrogen atoms in a saturated hydrocarbon. In the case of C₈H₉OBr, the presence of bromine must be accounted for in the IHD calculation, as it affects the overall hydrogen count and thus the degree of unsaturation in the compound.

Given the molecular formula, calculate the index of hydrogen deficiency.(d) C8H9OBr