Question

Spermaceti (a wax from the head of the sperm whale) resembles high-molecular weight hydrocarbons in physical properties and inertness toward \(\mathrm{Br}_{2} / \mathrm{CCl}_{4}\) and \(\mathrm{KMnO}_{4} ;\) on qualitative analysis it gives positive tests only for carbon and hydrogen. However, its infrared spectrum shows the presence of an ester group, and quantitative analysis gives the empirical formula \(\mathrm{C}_{16} \mathrm{H}_{32} \mathrm{O}\) A solution of the wax and \(\mathrm{KOH}\) in ethanol is refluxed for a long time. Titration of an aliquot shows that one equivalent of base has been consumed for every \(475 \pm 10\) grams of wax. Water and ether are added to the cooled reaction mixture, and the aqueous and ethereal layers are separated. Acidification of the aqueous layer yields a solid \(\mathrm{A}\), m.p. \(62-3^{\circ}\), neutralization equivalent \(260 \pm 5\). Evaporation of the ether layer yields a solid B, m.p. \(48-9^{\circ}\). Reduction by LiAlHi \(_{4}\) of either spermaceti or A gives \(B\) as the only product. B is normal alcohol. What is the structure of spermaceti?

Short answer

The structure of spermaceti is hexadecyl hexadecanoate, a wax ester composed of 1 hexadecanol and 1 hexadecanoic acid with an ester linkage.

Step-by-step solution

Determination of the Molecule's Molecular Weight

The question states that the amount of wax reacts with one equivalent of \(\mathrm{KOH}\), i.e. 1 mole of \(\mathrm{KOH}\). As we know, \(\mathrm{KOH}\) reacting with an ester will give an acid and an alcohol, hence one equivalent of KOH reacting with one ester assures that one mole of \(\mathrm{KOH}\) is reacting with one mole of spermaceti wax. Considering this, it could be concluded that the 475g of wax represented one mole of spermaceti wax. That is the molecular weight of spermaceti wax.

Determination of the Compound 'A'

Compound 'A', appearing after acidification, should be the carboxylic acid resulting from hydrolysis of the wax ester. The molecular weight can be found by multiplying the neutralization equivalent by the valency (which for carboxylic acids is 1). So the molecular weight of 'A' is approximately 260 g/mol.

Determination of Compound 'B'

In the question, reduction by \(\mathrm{LiAlH}_{4}\) of either spermaceti or 'A' gives 'B' as the only product. \(\mathrm{LiAlH}_{4}\) is a strong reducing agent and it can reduce esters as well as carboxylic acids to alcohols. So, 'B' must be an alcohol, and given it's the only product, its molecular weight must be equal to that of 'A', about 260 g/mol.

Structure of Spermaceti Wax

As per the empirical formula (\(\mathrm{C}_{16} \mathrm{H}_{32}\mathrm{O}\)), and the molecular weight (around 475 g/mol), the simplest structure of spermaceti wax will have a single ester group (\(\mathrm{R-COO-R'}\)). Compound 'A' and 'B' coming out of its hydrolysis should be both 16-carbon straight-chain compounds with molecular weights near 260 g/mol. So, the structures of compounds 'A' and 'B' should be palmitic acid (hexadecanoic acid) (\(\mathrm{C_{15}H_{31}COOH}\)) and hexadecanol (\(\mathrm{C_{16}H_{33}OH}\)) respectively. Thus, the structure of spermaceti would be hexadecyl hexadecanoate, a wax ester composed of 1 hexadecanol and 1 hexadecanoic acid with an ester linkage.

Key concepts

Ester Hydrolysis

During ester hydrolysis, the ester compound reacts with a base such as KOH to form a carboxylic acid and an alcohol. This reaction is crucial for understanding the structure of spermaceti wax. In the explained exercise, the hydrolysis of the ester in spermaceti with KOH results in a carboxylic acid, identified as compound 'A', and an alcohol, identified as compound 'B'.
Hydrolysis usually involves heating the ester with a base in an alcohol solvent, such as ethanol, to ensure the reaction goes to completion. The hydroxide ion from the base attacks the carbon atom of the ester group, breaking the bond between the carbon and the oxygen in the ester linkage. This bond cleavage forms the carboxylate ion, which is later acidified to produce the carboxylic acid.
Understanding ester hydrolysis is vital because it allows us to break down complex compounds like spermaceti into simpler, easily identifiable components, aiding in the determination of their molecular structures.

Infrared Spectroscopy

Infrared (IR) spectroscopy is a technique used to identify functional groups within a molecule based on absorption of infrared light. It is instrumental in the characterization and identification of chemical structures. In the context of the spermaceti exercise, IR spectroscopy confirmed the presence of an ester group in the wax.
The IR spectrum provides peaks at specific wavenumbers corresponding to various molecular vibrations. For esters, characteristic peaks include those around 1735 cm extsuperscript{-1} for the C=O stretch and between 1050 to 1300 cm extsuperscript{-1} for C-O stretches. This spectroscopic evidence ensures that the wax contains ester bonds, despite its similarity to hydrocarbons in other physical properties.
By interpreting these spectroscopic peaks, chemists can deduce the presence of specific functional groups and thus gain insights into the overall structure of the molecule.

Quantitative Analysis

Quantitative analysis involves measuring and analyzing numerical data related to the composition of a substance. This allows chemists to derive the empirical formula of a compound. In this exercise, quantitative analysis was used to determine the empirical formula \(\mathrm{C}_{16} \mathrm{H}_{32} \mathrm{O}\) of the spermaceti.
Performing quantitative analysis typically includes methodologies such as gravimetric analysis, titrations, and instrumental methods. In this case, titration was used to measure how much KOH was required to completely react with a certain amount of wax. The amount of base consumed directly correlates with the number of ester groups present in the wax.
Quantitative analysis provides a foundation for calculating the molecular weight of compounds, which is essential for understanding complex chemical structures and their proportions.

Molecular Weight Determination

Determining the molecular weight of a compound is critical for identifying and understanding its molecular structure. In the original exercise, the molecular weight of spermaceti was approximated to be 475 g/mol.
This was calculated by noting that 475g of spermaceti wax corresponds to one equivalent of KOH used in the reaction. This implies that 475g of spermaceti contains moles equating to those of the base in the reaction. Therefore, this mass represents the molecular weight of one mole of spermaceti.
Such calculation involves not only direct measurements but also understanding the stoichiometry of the reaction. The molecular weight can further be confirmed by comparing the empirical formula to the calculated molecular weight, aiding in deducing the full structure of the compound.