What is the index of hydrogen deficiency for each of the following molecular formulas?
(b) C₁₂H₁₁NO₃

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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 general formula for IHD: IHD = (2C + 2 + N - H - 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 (if present). For oxygen (O), it does not affect the IHD calculation, so it is ignored.

Step 3: Substitute the values from the molecular formula C₁₂H₁₁NO₃ into the IHD formula. Here, C = 12, H = 11, N = 1, and there are no halogens (X = 0). Oxygen is ignored in the calculation.

Step 4: Perform the substitution into the formula: IHD = (2(12) + 2 + 1 - 11 - 0) / 2. Simplify the expression step by step to determine the IHD value.

Step 5: Interpret the result. The IHD value you calculate will tell you the total 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 calculation used to determine the degree of unsaturation in a molecular formula. It indicates the number of rings and/or multiple bonds present in a compound. Each double bond or ring contributes one to the IHD, while each triple bond contributes two. The formula for IHD is 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.

Molecular Formula Interpretation

A molecular formula provides the number and types of atoms in a molecule but does not indicate the structure. For example, C₁₂H₁₁NO₃ indicates there are 12 carbon atoms, 11 hydrogen atoms, one nitrogen atom, and three oxygen atoms. Understanding how to interpret this formula is crucial for calculating the IHD, as it allows for the identification of the elements involved and their contributions to unsaturation.

Unsaturation in Organic Compounds

Unsaturation refers to the presence of double or triple bonds in organic compounds, which affects their reactivity and physical properties. Compounds with higher unsaturation typically have lower hydrogen counts relative to their carbon counts. Recognizing the implications of unsaturation is essential for predicting the behavior of organic molecules, including their stability and potential reactions, which is directly related to the IHD calculation.

What is the index of hydrogen deficiency for each of the following molecular formulas?(b) C12H11NO3