# 18.2 Index of Hydrogen Deficiency or Unsaturation The **Index of Hydrogen Deficiency (IHD)**, also known as the **degree of unsaturation**, is a calculation used in organic chemistry to determine the total number of rings and pi ($\pi$) bonds within a molecule from its molecular formula. It works by comparing the number of hydrogen atoms in the given compound to the number of hydrogen atoms in its corresponding saturated, acyclic counterpart. --- ### Concept of Unsaturation In a fully saturated, acyclic hydrocarbon (an alkane with no rings), the number of hydrogen atoms is related to the number of carbon atoms by the formula: $$ \text{Number of hydrogens} = (2 \times \text{number of carbons}) + 2 $$ This is the maximum number of hydrogens a given carbon skeleton can hold. Each multiple bond (a double or triple bond) or ring structure present in a molecule reduces the hydrogen count by two. Each of these structural features is referred to as a **degree of unsaturation**. --- ### Calculating the Index of Hydrogen Deficiency (IHD) The IHD for a molecule can be calculated directly from its molecular formula using the following general equation: $$ \text{IHD} = \frac{(2C + 2 + N) - (H + X)}{2} $$ Where: - **$C$** = number of carbon atoms - **$N$** = number of nitrogen atoms - **$H$** = number of hydrogen atoms - **$X$** = number of halogen atoms (F, Cl, Br, I) Oxygen and sulfur atoms do not affect the calculation and can be ignored. This calculation provides the *sum* of multiple bonds and rings. It does not distinguish between them. For example, an IHD of 1 could mean one double bond or one ring. An IHD of 2 could mean two double bonds, one triple bond, two rings, or one ring and one double bond. This simple calculation is a crucial first step when determining the structure of an unknown molecule. --- ## Worked Examples ### Example 18.1: Ethene ($\mathrm{C_2H_4}$) Calculate the degree of unsaturation in ethene ($\mathrm{C_2H_4}$). 1. **Write the given values:** - Number of Carbons ($C$) = 2 - Number of Hydrogens ($H$) = 4 - Number of Nitrogens ($N$) = 0 - Number of Halogens ($X$) = 0 2. **Apply the formula:** $$ \text{IHD} = \frac{(2C + 2 + N) - (H + X)}{2} $$ 3. **Show the calculation:** $$ \text{IHD} = \frac{(2 \times 2 + 2 + 0) - (4 + 0)}{2} $$ $$ \text{IHD} = \frac{(4 + 2) - 4}{2} = \frac{6 - 4}{2} = \frac{2}{2} $$ $$ \text{IHD} = 1 $$ The degree of unsaturation for ethene is **1**. This corresponds to the one double bond ($C=C$) in its structure. --- ## Possible Questions/Answers This section is based on **CONCEPT ASSESSMENT EXERCISE 18.1**. - **Q:** Calculate the degree of unsaturation in **benzene** ($\mathrm{C_6H_6}$). **A:** - Given: $C = 6$, $H = 6$ - Calculation: $$ \text{IHD} = \frac{(2 \times 6 + 2) - 6}{2} = \frac{14 - 6}{2} = \frac{8}{2} = 4 $$ - The IHD of benzene is **4**. This accounts for its structure, which contains **one ring** and **three double bonds**. - **Q:** Calculate the degree of unsaturation in **ethyne** ($\mathrm{C_2H_2}$). **A:** - Given: $C = 2$, $H = 2$ - Calculation: $$ \text{IHD} = \frac{(2 \times 2 + 2) - 2}{2} = \frac{6 - 2}{2} = \frac{4}{2} = 2 $$ - The IHD of ethyne is **2**. This corresponds to the one triple bond ($C \equiv C$) in its structure. --- ## Summary - The **Index of Hydrogen Deficiency (IHD)** or **degree of unsaturation** quantifies the number of $\pi$ bonds and rings in a molecule. - A saturated, acyclic alkane has an IHD of 0 and follows the formula $C_nH_{2n+2}$. - Each ring or double bond contributes 1 to the IHD. - Each triple bond contributes 2 to the IHD. - The general formula for calculation is: $$ \text{IHD} = \frac{(2C + 2 + N) - (H + X)}{2} $$ - **Significance:** IHD is a fundamental tool in analytical chemistry, particularly in combination with spectroscopic methods like and Mass Spectrometry, to quickly narrow down possible structures for an unknown compound. --- ## References (Derived from FBISE textbook)