What is the index of hydrogen deficiency for each of the following molecular formulas?
(c) C₈H₁₄Cl₂

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 alkane.

Step 2: Use the general formula for calculating 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., Cl, Br, I).

Step 3: Substitute the values from the molecular formula C₈H₁₄Cl₂ into the IHD formula. Here, C = 8, H = 14, and X = 2 (for the two chlorine atoms). There are no nitrogens in this molecule, so N = 0.

Step 4: Perform the substitution into the formula: IHD = (2(8) + 2 - 14 + 0 - 2) / 2. Simplify the expression step by step to determine the IHD value.

Step 5: Interpret the result. The calculated IHD value will tell you the number of rings and/or multiple bonds present 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 used in organic chemistry 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 calculating 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 convey structural information. In the formula C₈H₁₄Cl₂, there are 8 carbon atoms, 14 hydrogen atoms, and 2 chlorine 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 the overall structure and saturation of the compound.

Halogens in IHD Calculation

Halogens, such as chlorine, are treated similarly to hydrogen in the IHD calculation. Each halogen atom present in the molecular formula effectively replaces a hydrogen atom, which influences the degree of saturation. In the case of C₈H₁₄Cl₂, the two chlorine atoms reduce the number of hydrogen atoms that would otherwise be present, thus affecting the overall calculation of the IHD and the interpretation of the compound's structure.

What is the index of hydrogen deficiency for each of the following molecular formulas? (c) C8H14Cl2