Calculate The Index of Hydrogen Deficiency for The Following Molecule.

The hydrogen deficiency index (HDI) is a measure used in organic chemistry to quantify how many hydrogen atoms are missing from a molecule compared to its theoretical maximum. This index helps chemists understand the degree of unsaturation and functional group content in a compound.

What is Hydrogen Deficiency?

Hydrogen deficiency occurs when a molecule contains fewer hydrogen atoms than expected based on its carbon and hydrogen content. This typically happens in unsaturated compounds containing double or triple bonds, or in compounds with certain functional groups.

The concept is particularly important in:

Organic synthesis planning
Spectroscopic analysis
Molecular formula determination
Reaction mechanism studies

Key Concept

The hydrogen deficiency index is calculated by comparing the actual number of hydrogen atoms in a molecule to the maximum number it could theoretically contain if it were fully saturated.

How to Calculate the Index

The hydrogen deficiency index is calculated using the following formula:

Formula

HDI = (Maximum possible hydrogen atoms) - (Actual hydrogen atoms in the molecule)

Where maximum possible hydrogen atoms = 2 × (Number of carbon atoms + 1)

To calculate:

Count the number of carbon atoms (C) in the molecule
Calculate the maximum possible hydrogen atoms: 2 × (C + 1)
Count the actual number of hydrogen atoms (H) in the molecule
Subtract the actual hydrogen atoms from the maximum possible hydrogen atoms

The result is the hydrogen deficiency index, which indicates the degree of unsaturation in the molecule.

Interpreting the Results

The hydrogen deficiency index provides several important insights:

Degree of unsaturation: Higher HDI values indicate more double or triple bonds in the molecule
Functional group content: Can help identify the presence of certain functional groups
Reactivity potential: Molecules with higher HDI values are often more reactive
Structural analysis: Useful for determining molecular structure from spectral data

Interpretation of Hydrogen Deficiency Index Values
HDI Range	Interpretation	Example Compounds
0	Fully saturated compound	Alkanes (e.g., methane, ethane)
1-2	Mono- or di-unsaturated	Alkenes (e.g., ethene, propene)
3-4	Highly unsaturated	Dienes, alkynes, aromatic compounds
>4	Extremely unsaturated	Polyunsaturated compounds, complex aromatic systems

Worked Examples

Example 1: Ethene (C₂H₄)

For ethene (C₂H₄):

Number of carbon atoms (C) = 2
Maximum possible hydrogen atoms = 2 × (2 + 1) = 6
Actual hydrogen atoms = 4
HDI = 6 - 4 = 2

Interpretation: Ethene has a hydrogen deficiency index of 2, indicating it is a di-unsaturated compound.

Example 2: Benzene (C₆H₆)

For benzene (C₆H₆):

Number of carbon atoms (C) = 6
Maximum possible hydrogen atoms = 2 × (6 + 1) = 14
Actual hydrogen atoms = 6
HDI = 14 - 6 = 8

Interpretation: Benzene has a hydrogen deficiency index of 8, indicating it is a highly unsaturated aromatic compound.

Frequently Asked Questions

What is the difference between hydrogen deficiency and hydrogen excess?

Hydrogen deficiency refers to molecules that contain fewer hydrogen atoms than expected, typically unsaturated compounds. Hydrogen excess refers to molecules that contain more hydrogen atoms than expected, which is less common in organic chemistry.

How does the hydrogen deficiency index relate to molecular weight?

The hydrogen deficiency index is independent of molecular weight. Two different molecules with the same HDI can have very different molecular weights depending on their carbon content.

Can the hydrogen deficiency index be negative?

No, the hydrogen deficiency index cannot be negative. If a molecule contains more hydrogen atoms than the maximum possible, it would have a hydrogen excess rather than a deficiency.

Is the hydrogen deficiency index useful for all types of molecules?

The hydrogen deficiency index is most useful for organic molecules. For inorganic compounds or molecules without carbon-hydrogen bonds, the concept doesn't apply.