Problem 46 - Chemistry The Central Science In Si Units

Question

(a) Give the empirical formula and structural formula for a cyclic ether containing four carbon atoms in the ring. (b) Write the structural formula for a straight-chain compound that is a structural isomer of your answer to part (a).

Step-by-Step Solution

Answer

(a) Empirical and structural formula: C4H8O. (b) Isomer: Butanol CH3(CH2)3OH.

Step 1: Understanding Cyclic Ether

A cyclic ether is a heterocyclic compound where one of the atoms in the ring is an oxygen. Considering the requirement for a four-carbon ring, we construct a four-membered carbon ring with one oxygen atom. Therefore, the compound has the molecular formula C4H8O. This is a tetrahydrofuran where the structural formula is a square with an oxygen atom replacing one of the carbon atoms in the ring: \( \text{C}_4\text{H}_8\text{O} \).

Step 2: Determining Empirical Formula

The empirical formula is the simplest whole-number ratio of the elements in the compound. Fortunately, for cyclic ethers like tetrahydrofuran, the empirical formula is the same as the molecular formula. Hence, the empirical formula is also \( \text{C}_4\text{H}_8\text{O} \).

Step 3: Identifying a Structural Isomer

A structural isomer has the same molecular formula but a different structural formula. The molecular formula C4H8O has potential for isomerism. Create a straight-chain compound with this formula: an alcohol such as butanol (CH3(CH2)3OH). This is a different structural formula compared to the cyclic ether.

Key Concepts

Empirical Formula

The empirical formula of a compound provides the simplest whole-number ratio of its constituent elements. To find the empirical formula, you should look at the proportions of each element present rather than the exact number of atoms. For example, in a compound with a molecular formula of \( \text{C}_4\text{H}_8\text{O} \), we need to check if we can simplify the ratio of carbon, hydrogen, and oxygen atoms.
In this specific case of a cyclic ether like tetrahydrofuran, the empirical formula and the molecular formula are identical. This means the simplest ratio of the atoms in this compound still results in \( \text{C}_4\text{H}_8\text{O} \). This is not always the case for other compounds, but because the number of each atom is already a simple ratio, the empirical formula remains the same.
Remember that an empirical formula does not show the actual arrangement of atoms in the compound; it only provides the lowest ratio.

Structural Formula

A structural formula is a more detailed type of chemical formula than an empirical one. It displays not only the total number of each type of atom but also their specific arrangement within the molecule. For cyclic compounds, like the cyclic ether tetrahydrofuran, this form of formula is useful for demonstrating the ring structure and showing how atoms are bonded.
A structural formula for tetrahydrofuran would be represented with a square (to depict the cyclic structure) where oxygen replaces one carbon in a four-membered carbon ring. This representation highlights the spatial organization and connectivity of atoms:

• The depicted shape or geometric arrangement helps in visualizing the compound's 3D shape.
• Specific lines represent bonds between the atoms, indicating single, double, or triple bonds where applicable.

Understanding the structural formula helps chemists predict physical and chemical properties of the compound.

Structural Isomerism

Structural isomerism occurs when compounds have the same molecular formula but differ in the arrangement of atoms within their structure. This concept demonstrates the incredible diversity and flexibility of organic molecules by showing that different structures can yield drastically different properties.
For example, the molecular formula \( \text{C}_4\text{H}_8\text{O} \) applies to both tetrahydrofuran and butanol, demonstrating structural isomerism. Tetrahydrofuran forms a cyclic structure, while butanol forms a straight-chain alcohol:

• Tetrahydrofuran: A cyclic ether with an oxygen atom within the carbon ring.
• Butanol: A straight-chain alcohol with OH (hydroxyl) group at the terminal carbon, depicted as \( \text{CH}_3(\text{CH}_2)_3\text{OH} \).

Structural isomers can exhibit varied reactivities, boiling and melting points, and even different scents or tastes, all while sharing the same atoms in different arrangements. Understanding structural isomerism is crucial for exploring organic synthesis and reactivity.