Question

Calculate the index of hydrogen deficiency of these compounds. (a) Aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) (b) Ascorbic acid (vitamin \(\mathrm{C}\) ), \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) (c) Pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N}\) (d) Urea, \(\mathrm{CH}_{4} \mathrm{~N}_{2} \mathrm{O}\) (e) Cholesterol, \(\mathrm{C}_{27} \mathrm{H}_{46} \mathrm{O}\) (f) Dopamine, \(\overline{\mathrm{C}}_{\mathrm{g}} \mathrm{H}_{11} \mathrm{NO}_{2}\)

Short answer

Question: Calculate the index of hydrogen deficiency (IHD) for the following compounds: (a) Aspirin (C9H8O4) (b) Ascorbic acid (C6H8O6) (c) Pyridine (C5H5N) (d) Urea (CH4N2O) (e) Cholesterol (C27H46O) (f) Dopamine (C8H11NO2) Answer: (a) Aspirin: IHD = 10 (b) Ascorbic acid: IHD = 5 (c) Pyridine: IHD = 6 (d) Urea: IHD = 2 (e) Cholesterol: IHD = 28 (f) Dopamine: IHD = 7

Step-by-step solution

(a) Aspirin (C9H8O4)

We have 9 carbon atoms, 8 hydrogen atoms, and 4 oxygen atoms. IHD = \(\frac{1}{2}\) (2 × 9 + 2 - 8) IHD = \(\frac{1}{2}\) (20) IHD = 10

(b) Ascorbic acid (C6H8O6)

We have 6 carbon atoms, 8 hydrogen atoms, and 6 oxygen atoms. IHD = \(\frac{1}{2}\) (2 × 6 + 2 - 8) IHD = \(\frac{1}{2}\) (10) IHD = 5

(c) Pyridine (C5H5N)

We have 5 carbon atoms, 5 hydrogen atoms, and 1 nitrogen atom. IHD = \(\frac{1}{2}\) (2 × 5 + 2 - 5 + 1) IHD = \(\frac{1}{2}\) (12) IHD = 6

(d) Urea (CH4N2O)

We have 1 carbon atom, 4 hydrogen atoms, and 2 nitrogen atoms. IHD = \(\frac{1}{2}\) (2 × 1 + 2 - 4 + 2) IHD = \(\frac{1}{2}\) (4) IHD = 2

(e) Cholesterol (C27H46O)

We have 27 carbon atoms, 46 hydrogen atoms, and 1 oxygen atom. IHD = \(\frac{1}{2}\) (2 × 27 + 2 - 46) IHD = \(\frac{1}{2}\) (56) IHD = 28

(f) Dopamine (C8H11NO2)

We have 8 carbon atoms, 11 hydrogen atoms, 1 nitrogen atom, and 2 oxygen atoms. IHD = \(\frac{1}{2}\) (2 × 8 + 2 - 11 + 1) IHD = \(\frac{1}{2}\) (14) IHD = 7

Key concepts

Organic Chemistry

Organic chemistry is the branch of chemistry that deals with the structure, properties, composition, reactions, and preparation of carbon-containing compounds, which include not only hydrocarbons but also compounds with any number of other elements, including hydrogen (most compounds contain at least one carbon–hydrogen bond), nitrogen, oxygen, halogens, phosphorus, silicon, and sulfur. This field of chemistry is fundamental for understanding the biochemical molecules found in living organisms as well as synthetic compounds such as drugs, plastics, and dyes.

At the heart of organic chemistry is the ability to predict and understand how the structure of molecules impacts their function and reactivity. These predictions are often guided by the study of molecular formulas and various indices that can indicate the presence of specific structures within a compound, like double bonds, triple bonds, or rings, which leads us to important tools like the index of hydrogen deficiency.

Degree of Unsaturation Calculation

The degree of unsaturation, also known as the index of hydrogen deficiency (IHD), is a vital concept in organic chemistry that represents the total number of rings and \/ or multiple bonds (double or triple) present within a molecule. Calculating the IHD allows chemists to understand the levels of saturation within the compound and postulate possible structures for unknown molecules based on their molecular formula.

The formula for calculating IHD takes into account the number of hydrogen, carbon, nitrogen, and halogen atoms. The general formula is:

\[\text{IHD} = \frac{1}{2} \times \left(2 \times \text{number of carbon atoms} + 2 + \text{number of nitrogen atoms} - \text{number of hydrogen atoms} - \text{number of halogen atoms}\right)\]

Oxygen does not affect the IHD as it does not change the saturation level of a molecule. For halogens (Cl, Br, I), each atom is treated as an equivalent to a hydrogen atom due to halogens having a similar valency to hydrogen in organic compounds.

Molecular Formula Analysis

Molecular formula analysis involves the determination of the composition of a molecule in terms of the types and numbers of atoms it contains. In organic chemistry, this is crucial for identifying the structure of a molecule and predicting its physical and chemical properties.

The molecular formula provides essential information about the proportions of elements in a compound. However, it doesn't give information about the arrangement of those atoms (that is the domain of structural formulas). By analyzing the molecular formula, one can calculate the molecular weight, empirical formula, or degree of unsaturation.

In exercises like the calculation of the index of hydrogen deficiency, molecular formula analysis is the starting point. Understanding the molecular formula allows a chemist to deduce the amount of saturation in the compound, which helps in pinpointing the structure, especially when combined with other analytical methods such as spectroscopy. The degree of unsaturation is directly deduced from the molecular formula and is a quick indicator of the complexity of the molecule's structure, as found in rings and multiple bonds.