Question

Carbon forms an unusual, unstable oxide of formula \(\mathrm{C}_{3} \mathrm{O}_{2}\) called carbon suboxide. Carbon suboxide is made by using \(\mathrm{P}_{2} \mathrm{O}_{5}\) to dehydrate the dicarboxylic acid called malonic acid, which has the formula \(\mathrm{HOOC}-\mathrm{CH}_{2}-\mathrm{COOH}\). (a) Write a balanced reaction for the production of carbon suboxide from malonic acid. (b) Suggest a Lewis structure for \(\mathrm{C}_{3} \mathrm{O}_{2}\). (Hint: The Lewis structure of malonic acid suggests which atoms are connected to which.) (c) By using the information in Table \(8.5\), predict the \(\mathrm{C}-\mathrm{C}\) and \(\mathrm{C}-\mathrm{O}\) bond lengths in \(\mathrm{C}_{3} \mathrm{O}_{2}\). (d) Sketch the Lewis structure of a product that could result by the addition of \(2 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) to 1 mol of \(\mathrm{C}_{3} \mathrm{O}_{2}\)

Short answer

(a) The balanced chemical equation for the production of carbon suboxide from malonic acid is: \( \mathrm{HOOC-CH}_{2}\mathrm{-COOH} \) + \( \frac{1}{2}\mathrm{P}_{2}\mathrm{O}_{5} \) → \( \mathrm{C}_{3}\mathrm{O}_{2} \) + \( \mathrm{H}_{2}\mathrm{O} \) + \( \frac{1}{2}\mathrm{H}_{3}\mathrm{PO}_{4} \) (b) The Lewis structure for carbon suboxide: O=C=C=C=O (c) The C-C bond length is approximately \(1.54 \ \mathrm{\overset{\circ}{A}}\), and the C-O bond length is approximately \(1.43 \ \mathrm{\overset{\circ}{A}}\). (d) The Lewis structure of the product with added hydrogen molecules: H-O-C=C=C-O-H

Step-by-step solution

(a) Balanced Chemical Reaction

To write the balanced chemical equation for the production of carbon suboxide from malonic acid, we first need to recognize that the given malonic acid will dehydrate by reacting with phosphorus pentoxide, P2O5. The dehydration reaction will lead to the loss of water molecules and the formation of carbon suboxide. The balanced chemical equation for this reaction will be: \( \mathrm{HOOC-CH}_{2}\mathrm{-COOH} \) + \( \frac{1}{2}\mathrm{P}_{2}\mathrm{O}_{5} \) → \( \mathrm{C}_{3}\mathrm{O}_{2} \) + \( \mathrm{H}_{2}\mathrm{O} \) + \( \frac{1}{2}\mathrm{H}_{3}\mathrm{PO}_{4} \)

(b) Lewis Structure of Carbon Suboxide

Based on the Lewis structure of malonic acid, we can see that the oxygen atoms are connected to the carbon atoms. Using this hint, we can suggest a Lewis structure for carbon suboxide, C3O2, where the carbon atoms are connected in a linear fashion with the oxygen atoms connected to the terminal carbons, like so: O=C=C=C=O

(c) Predicting Bond Lengths

Using the information in Table \(8.5\), we can predict the C-C and C-O bond lengths in carbon suboxide. The table suggests a C-C bond length of approximately \(1.54 \ \mathrm{\overset{\circ}{A}}\), and a C-O bond length of approximately \(1.43 \ \mathrm{\overset{\circ}{A}}\).

(d) Lewis Structure with Added Hydrogen Molecules

When two moles of hydrogen are added to one mole of carbon suboxide, the hydrogen atoms can bond with the terminal oxygen atoms, forming a product with the following Lewis structure: H-O-C=C=C-O-H

Key concepts

Balanced Chemical Reaction

A balanced chemical reaction is critical for accurately representing how molecules interact in a chemical process. It ensures that the number of atoms for each element is equal on both sides of the equation, honoring the law of conservation of mass. In the case of carbon suboxide (\texttt{C3O2}), it is synthesized from malonic acid by a dehydration reaction facilitated by phosphorus pentoxide (\texttt{P2O5}). The balanced equation for this reaction is:
\[ \texttt{HOOC-CH2-COOH} + \frac{1}{2}\texttt{P2O5} \rightarrow \texttt{C3O2} + \texttt{H2O} + \frac{1}{2}\texttt{H3PO4} \]
This shows us that from one molecule of malonic acid, after losing water, one molecule of carbon suboxide is formed. Ensuring the reaction is balanced helps students to understand the stoichiometry involved and how to calculate reactants or products required or formed in a given reaction, which is a crucial skill in chemistry.

Lewis Structure

The Lewis structure is a diagrammatic method to represent the valence electrons of atoms within a molecule, showing how the atoms are bonded together and the pairs of shared and unshared electrons. When constructing the Lewis structure for carbon suboxide, we consider that it is a linear molecule, as suggested by the structure of malonic acid. The carbon atoms form a chain with double bonds, and the oxygen atoms are double-bonded to the terminal carbons. The suggested Lewis structure is:

O=C=C=C=O

This visualization allows us to see the arrangement of electron pairs and predict molecular shapes, based on which we can infer the reactive properties of the molecule. For instance, the presence of double bonds in the carbon suboxide molecule implies areas of higher electron density and potential sites for reactions, such as the addition of hydrogen molecules.

Bond Lengths

Bond length is the distance between the nuclei of two bonded atoms. It's a critical aspect that influences the physical and chemical properties of molecules. For carbon suboxide, the C-C and C-O bond lengths can be estimated using empirical data from similar molecules.

According to Table 8.5, a typical carbon-carbon single bond (\texttt{C-C}) length is approximately \(1.54 \text{ \r{A}}\), and the carbon-oxygen double bond (\texttt{C=O}) is about \(1.21 \text{ \r{A}}\). Since carbon suboxide has double bonds between its carbon atoms, as well as between carbon and oxygen, we can predict the \texttt{C=C} bond lengths to be shorter than that of a single bond, and similar to or slightly longer than a double bond in \texttt{C=O}, reflecting the character of the multiple bonds in the molecule. The understanding of bond length in molecules like carbon suboxide informs students about the molecule's size, shape, and how tightly the atoms are held together, impacting reactivity and stability of the molecule.