Question

Write the structural formulas for as many alcohols as you can think of that have empirical formula ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$.

Short answer

We have three distinct alcohols with the empirical formula ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$: 1) Propan-1-ol: ${\mathrm{CH}}_2\mathrm{OH}-{\mathrm{CH}}_2-{\mathrm{CH}}_3$ 2) Propan-2-ol: ${\mathrm{CH}}_3-\mathrm{CH}(\mathrm{OH})-{\mathrm{CH}}_3$ 3) 2-Methylpropan-2-ol: ${\mathrm{CH}}_3-\mathrm{C}({\mathrm{CH}}_3)(\mathrm{OH})-{\mathrm{CH}}_3$

Step-by-step solution

Identify the molecular formula from the empirical formula.

First, we need to find the molecular formula based on the empirical formula given: ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$. Since the empirical formula represents the simplest whole number ratio of atoms in a compound and the molecular formula represents the actual number of atoms, in this case, the molecular formula is also ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$.

Primary isomers with structural arrangement of carbon atoms.

Now, we will find different isomers by rearranging the carbon and oxygen atoms in the molecule: 1) First isomer: A linear structure with three carbon atoms bonded together: ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$ 2) Second isomer: A branched structure where one carbon atom is connected to two other carbon atoms and a hydrogen atom: ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$ These are the primary structures we can form with the molecular formula ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$.

Connect the -OH group to primary isomers.

We need to place the -OH group in the primary isomers found in step 2. We can have different distinct arrangements, resulting in different alcohols. 1) Linear structure: a) $-\mathrm{OH}$ attached to the first carbon atom: ${\mathrm{CH}}_2\mathrm{OH}-{\mathrm{CH}}_2-{\mathrm{CH}}_3$ b) $-\mathrm{OH}$ attached to the middle carbon atom: ${\mathrm{CH}}_3-\mathrm{CH}(\mathrm{OH})-{\mathrm{CH}}_3$ 2) Branched structure: a) $-\mathrm{OH}$ attached to the carbon atom bonded to two other carbon atoms: ${\mathrm{CH}}_3-\mathrm{C}({\mathrm{CH}}_3)(\mathrm{OH})-{\mathrm{CH}}_3$

Write the final structural formulas for alcohols.

Based on the above arrangements, we have three distinct alcohols with the empirical formula ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$: 1) Propan-1-ol: ${\mathrm{CH}}_2\mathrm{OH}-{\mathrm{CH}}_2-{\mathrm{CH}}_3$ 2) Propan-2-ol: ${\mathrm{CH}}_3-\mathrm{CH}(\mathrm{OH})-{\mathrm{CH}}_3$ 3) 2-Methylpropan-2-ol: ${\mathrm{CH}}_3-\mathrm{C}({\mathrm{CH}}_3)(\mathrm{OH})-{\mathrm{CH}}_3$ These are the structural formulas for alcohols with the empirical formula ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$.

Key concepts

Structural Formulas

Let's break down what a structural formula is and why it's essential for understanding alcohol isomers. A structural formula shows the arrangement of atoms within a molecule. It visually represents how atoms are connected, making it an important tool for studying different isomers of the same empirical formula.
For the empirical formula ${\text{C}}_3{\text{H}}_6\text{O}$, we derive possible structural formulas by rearranging carbon, hydrogen, and the oxygen atom as well as the position of the hydroxyl $-\text{OH}$ group.
Here are examples:

• Propan-1-ol: ${\text{CH}}_2\text{OH}-{\text{CH}}_2-{\text{CH}}_3$ with the $-\text{OH}$ group on the first carbon atom.
• Propan-2-ol: ${\text{CH}}_3-\text{CH}(\text{OH})-{\text{CH}}_3$ with the $-\text{OH}$ group on the second carbon atom.
• 2-Methylpropan-2-ol: ${\text{CH}}_3-\text{C}({\text{CH}}_3)(\text{OH})-{\text{CH}}_3$ represents a branched structure.

Understanding structural formulas helps in recognizing these unique isomers and predicting their chemical behavior.

Empirical Formula

An empirical formula is the simplest way of showing the ratio of elements in a compound. It doesn't give information about the actual number of atoms, but rather the simplest whole number proportion between them.
For example, the empirical formula ${\text{C}}_3{\text{H}}_6\text{O}$ indicates that the compound contains carbon, hydrogen, and oxygen in a 3:6:1 ratio.
This formula is a basic representation and does not specify how these atoms are connected or arranged, which is where structural and molecular formulas come in.
It's a starting point from which more detailed formulas are derived, helping chemists to understand different isomers that share this simple formula but differ in structural layout.

Molecular Structure

Molecular structure refers to the 3D arrangement of atoms in a molecule. Understanding the molecular structure is crucial as it influences the physical and chemical properties of a compound.
Each alcohol isomer we discussed has a unique molecular structure:

• Propan-1-ol has a linear chain with the $-\text{OH}$ group on one end.
• Propan-2-ol has the $-\text{OH}$ group in the center, making it more symmetrical.
• 2-Methylpropan-2-ol features a more branched arrangement.

These different molecular structures result in varying properties such as boiling points, reactivity, and solubility. By analyzing these structures, we can predict how each isomer may behave in different chemical reactions or applications. These insights are essential in fields ranging from organic chemistry to pharmaceuticals.