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) How many grams of carbon suboxide could be made from $20.00\mathrm{g}$ of malonic acid? (c) 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.) (d) By using the information in Table 8.5, predict the $\mathrm{C}-\mathrm{C}$ and $\mathrm{C}-\mathrm{O}$ bond lengths in ${\mathrm{C}}_3{\mathrm{O}}_2$. (e) Sketch the Lewis structure of a product that could result by the addition of $2\mathrm{mol}$ of ${\mathrm{H}}_2$ to $1\mathrm{mol}$ of ${\mathrm{C}}_3{\mathrm{O}}_2$ -

Short answer

The balanced reaction for the production of carbon suboxide from malonic acid is $C_3{H}_4{O}_4+2P_2{O}_5\to C_3{O}_2+4P_2{O}_3+2H_{2}O$. From 20.00 g of malonic acid, 13.06 g of carbon suboxide could be made. The suggested Lewis structure for carbon suboxide is $O=C=C=C=O$. The predicted C-C and C-O bond lengths in carbon suboxide are 1.34 Å and 1.21 Å, respectively. The Lewis structure of a product that could result from the addition of 2 mol of H2 to 1 mol of carbon suboxide is $H_{2}C-C=C-O-H$.

Step-by-step solution

Write a balanced reaction for the production of carbon suboxide from malonic acid.

The given reaction is the dehydration of malonic acid by using phosphorus pentoxide (P2O5) to produce carbon suboxide and water. The balanced reaction can be represented as follows: $C_3{H}_4{O}_4+2P_2{O}_5\to C_3{O}_2+4P_2{O}_3+2H_{2}O$

Calculate the mass of carbon suboxide that could be made from 20.00 g of malonic acid.

In this step, we will use the stoichiometry from the balanced reaction to determine how many grams of carbon suboxide could be made from 20.00 g of malonic acid: 1. Find the molar mass of malonic acid and carbon suboxide: $C_3{H}_4{O}_4\to 3(12.01)+4(1.01)+4(16.00)=104.06g/mol$ $C_3{O}_2\to 3(12.01)+2(16.00)=68.03g/mol$ 2. Convert the mass of malonic acid to moles: $\frac{20.00g}{104.06g/mol}=0.192mol{C}_3{H}_4{O}_4$ 3. Use the stoichiometric coefficients from the balanced equation to calculate the moles of carbon suboxide produced: $\frac{1mol{C}_3{O}_2}{1mol{C}_3{H}_4{O}_4}\times 0.192mol{C}_3{H}_4{O}_4=0.192mol{C}_3{O}_2$ 4. Convert the moles of carbon suboxide to mass: $0.192mol{C}_3{O}_2\times 68.03g/mol=13.06g{C}_3{O}_2$ Thus, 13.06 g of carbon suboxide could be made from 20.00 g of malonic acid.

Suggest a Lewis structure for carbon suboxide.

Considering the hint provided and the fact that carbon suboxide has a formula of $C_3{O}_2$, the suggested Lewis structure for carbon suboxide can be represented as: $O=C=C=C=O$

Predict the C-C and C-O bond lengths in carbon suboxide.

According to Table 8.5, the bond lengths for a C-C double bond and a C-O double bond are as follows: C-C double bond: 1.34 Å C-O double bond: 1.21 Å Thus, we can predict the C-C and C-O bond lengths in $C_3{O}_2$ to be 1.34 Å and 1.21 Å, respectively.

Sketch the Lewis structure of a product that could result from the addition of 2 mol of H2 to 1 mol of carbon suboxide.

When we add 2 mol of H2 to 1 mol of carbon suboxide, we essentially add 4 hydrogen atoms to the molecule. The resulting molecule should have the following formula: $C_3{H}_4{O}_2$ The Lewis structure of the product can be sketched as follows: $H_{2}C-C=C-O-H$ Remember that the double bond between carbon and oxygen satisfies its octet rule, and the carbon atoms share their electrons with the hydrogen atoms accordingly.

Key concepts

Malonic Acid

Malonic acid is a dicarboxylic acid with the chemical formula ${\text{HOOC-CH}}_2\text{COOH}$. This compound is an important precursor in organic synthesis due to its reactive methylene group between the two carboxyl groups. Malonic acid can be used to synthesize carbon suboxide by removing water molecules through dehydration, a common chemical reaction in organic chemistry. When malonic acid is dehydrated in the presence of phosphorus pentoxide $({\text{P}}_2{\text{O}}_5)$, carbon suboxide $({\text{C}}_3{\text{O}}_2)$ is formed.

A balanced chemical reaction is critical for understanding this process. The dehydration reaction can be represented as:

$${\text{C}}_3{\text{H}}_4{\text{O}}_4+2{\text{P}}_2{\text{O}}_5\to {\text{C}}_3{\text{O}}_2+4{\text{P}}_2{\text{O}}_3+2{\text{H}}_2\text{O}$$

Recognizing the roles of reactants and products here helps in understanding the stoichiometry of the reaction.

Lewis Structures

Lewis structures are diagrams that illustrate the bonds between atoms in a molecule as well as the lone pairs of electrons that may exist. In simple terms, they help predict the molecule's shape, reactivity, and even properties.

For carbon suboxide $({\text{C}}_3{\text{O}}_2)$, the Lewis structure can be devised as follows:

- Carbon atoms typically form four bonds, and oxygen typically forms two.
- The formula ${\text{C}}_3{\text{O}}_2$ suggests there are more things connecting these atoms than simple single bonds.

A feasible Lewis structure of carbon suboxide is $\text{O}=\text{C}=\text{C}=\text{C}=\text{O}$, where each oxygen atom is double-bonded to a terminal carbon, and the carbons in the center are also double-bonded. This configuration aligns with the typical valence configuration of carbon and oxygen atoms, fulfilling the octet rule for each.

Chemical Bond Lengths

Chemical bond lengths refer to the distance between the nuclei of two bonded atoms. It's a crucial aspect as it influences the molecule's reactivity, stability, and physical properties.

In carbon suboxide, to predict bond lengths, we refer to typical double bond distances:

• C-C double bond length: 1.34 Å
• C-O double bond length: 1.21 Å

Understanding these lengths not only helps in molecular geometry predictions but also aids chemists in visualizing molecular structures. For carbon suboxide, knowing the double bond lengths helps propose a realistic structural model consistent with empirical data.

Stoichiometry

Stoichiometry is the study of quantitative relationships in chemical reactions, helping us understand how molecules combine and the proportions needed. For carbon suboxide from malonic acid, stoichiometry is key to determining how much product can be made from a given amount of reactant.

Example calculation:

• Start with the balanced chemical equation: ${\text{C}}_3{\text{H}}_4{\text{O}}_4+2{\text{P}}_2{\text{O}}_5\to {\text{C}}_3{\text{O}}_2+4{\text{P}}_2{\text{O}}_3+2{\text{H}}_2\text{O}$.
• For instance, if you begin with 20.00 g of malonic acid, convert this to moles using its molar mass 104.06 g/mol: $\frac{20.00}{104.06}=0.192$ mol.
• Use stoichiometry (1:1 ratio in this reaction) to find moles of carbon suboxide produced: 0.192 moles.
• Convert moles of product to grams using its molar mass 68.03 g/mol: $0.192\times 68.03=13.06$ g of ${\text{C}}_3{\text{O}}_2$.

Stoichiometric calculations ensure that you accurately predict the amount of each reactant needed and amount of product formed, which is critical in both laboratory and industrial settings.