Question

Calculate the index of hydrogen deficiency of compound " 2,5 -dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid".

Short answer

The index of hydrogen deficiency (IHD) for the compound "2,5-dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid" is 20.

Step-by-step solution

Determine the molecular formula

Determine the molecular formula of the given compound based on the name "2,5-dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid". The benzene carboxylic acid core consists of a benzene ring with a carboxylic acid group (COOH) attached. The numbering for the substituent positions in the ring are as follows: 1 - Carboxylic acid 2 - Cyano (CN) group 3 - Formyl (CHO) group 4 - Phenyl group (another benzene ring) 5 - Cyano (CN) group 6 - Formyl (CHO) group Therefore, the molecular formula for the compound is C19H10N2O4.

Calculate IHD using the formula

Now that we have the molecular formula (C19H10N2O4), we can use the IHD formula to determine the index of hydrogen deficiency. Remember: \(IHD = \frac {(2 * C + 2 - H + N - X)}{2} \). For our molecule, C = 19, H = 10, N = 2, and X = 0 (as there are no halogens). Plugging these values into the IHD formula, we get: \[IHD = \frac {(2 * 19 + 2 - 10 + 2 - 0)}{2} = \frac {40}{2} = 20\] Therefore, the index of hydrogen deficiency (IHD) for the compound "2,5-dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid" is 20.

Key concepts

Molecular Formula Determination

The determination of a molecular formula is a fundamental task in organic chemistry, which sets the stage for understanding a compound's structure and properties. Starting with the name of an organic compound such as '2,5-dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid', the molecular formula can be constructed by identifying the functional groups and their corresponding symbols. For instance, 'benzene carboxylic acid' implies a benzene ring (C₆H₅) with a carboxylic acid group (COOH), adding up to C₇H₅O₂ for this part of the molecule alone.

By further analyzing the nomenclature, each substituent is accounted for: cyano groups (CN) add one carbon and one nitrogen each, formyl groups (CHO) add one carbon and one oxygen each, and an additional phenyl group brings in another benzene ring. Recognizing these patterns is crucial for error-free calculation of the molecular formula. Once all groups are accounted for, the individual atoms are totaled, yielding the molecular formula C₁₉H₁₀N₂O₄ for the given compound.

Organic Chemistry Nomenclature

Properly understanding organic chemistry nomenclature is not just a matter of memorization; it requires the ability to deconstruct and interpret complex names. Each part of a compound's name provides insights into its structure. The name '2,5-dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid' is a mouthful, but it's systematically crafted. Benzene carboxylic acid indicates the core structure, while the numbers and prefixes identify the position and number of substituents. The prefixes 'di-' signify two of a kind, 'cyano' refers to a CN group, and 'formyl' identifies an aldehyde group (CHO).

Furthermore, 'phenyl' describes an additional benzene ring attached to the core structure. These terms are the building blocks of organic chemistry nomenclature, allowing chemists to paint a picture of the compound’s molecular structure just by reading its name. Mastery of this nomenclature is essential for students, enabling them to transit seamlessly into more advanced chemical analyses.

IHD Formula Application

The Index of Hydrogen Deficiency (IHD) is a valuable calculation revealing unsaturation within an organic molecule, which includes double bonds, triple bonds, and rings. The IHD is calculated using the formula: \[IHD = \frac {(2 \cdot C + 2 - H + N - X)}{2} \],where 'C' is the number of carbons, 'H' represents hydrogens, 'N' for nitrogens, and 'X' for halogens. An IHD of 1 indicates the presence of either one ring or one double bond, and higher values indicate additional unsaturation.

For '2,5-dicyano-3,6-diformyl-4-phenyl benzene carboxylic acid', with the determined molecular formula C₁₉H₁₀N₂O₄, the IHD is calculated to be 20. This high number indicates a significantly unsaturated molecule, with a combination of multiple rings and multiple pi bonds. Understanding IHD helps students predict the chemical behavior of the compound, such as its reactivity towards addition reactions, and is a powerful tool in structure elucidation in organic chemistry.