Question

Draw two different structural formulas based on the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} .\) Is the fact that you can have more than one compound with the same molecular formula consistent with Dalton's atomic theory?

Short answer

You can draw ethanol and dimethyl ether, illustrating structural isomerism not explained by Dalton's atomic theory.

Step-by-step solution

Understand the Molecular Formula

The molecular formula given is \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\). This indicates that each compound must contain 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom.

Consider Possible Structures

Based on the formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\), think about how the atoms can be rearranged to form different compounds. Consider different ways to connect these atoms to create structurally distinct molecules.

Draw First Structural Formula (Ethanol)

Draw the structural formula for ethanol. It consists of two carbon atoms connected, with an \(-\mathrm{OH}\) (hydroxyl group) connected to the end: \(\mathrm{CH}_3\mathrm{CH}_2\mathrm{OH}\).

Draw Second Structural Formula (Dimethyl Ether)

Now, draw the structural formula for dimethyl ether. Both carbon atoms are connected via an oxygen atom, creating an ether: \(\mathrm{CH}_3\mathrm{OCH}_3\).

Confirm Structural Differences

Ensure that the two drawn structures are distinct. Ethanol and dimethyl ether have different connectivity among atoms, which means they are different compounds, even with the same molecular formula.

Dalton's Atomic Theory and Isomerism

Dalton's atomic theory states that compounds are made of atoms in fixed ratios, but it does not account for how those atoms are arranged. This exercise demonstrates that different arrangements (isomers) of the same atoms yield different compounds, which was not originally addressed by Dalton's theory.

Key concepts

Molecular Formula

The concept of a molecular formula is critical in understanding chemical compounds. A molecular formula expresses the number and type of atoms present in a molecule. For instance, the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) tells us the molecule consists of:

• 2 carbon atoms
• 6 hydrogen atoms
• 1 oxygen atom

However, a molecular formula does not provide information about the specific arrangement of these atoms. Different arrangements can lead to different molecules, which is where the concept of structural isomers comes into play. This is seen in the example of ethanol and dimethyl ether, both sharing the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\), but exhibiting distinct structures.

Dalton's Atomic Theory

Dalton's atomic theory was a groundbreaking concept in the early 19th century. It laid the foundation for modern chemistry by introducing the idea that matter is composed of indivisible atoms. According to Dalton, each chemical element consists of one type of atom, and these atoms combine in fixed ratios to form compounds. This means that compounds have specific compositions that are consistent each time the compound is formed.

However, Dalton’s theory did not account for structural isomerism, where the same combination of atoms can be arranged differently to form different compounds. The example of ethanol and dimethyl ether, both having the formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) but different structures, highlights an aspect that Dalton’s theory could not explain. This highlights the limitations of the theory in explaining modern chemistry concepts like isomerism.

Ethanol Chemical Structure

Ethanol is a well-known alcohol with the chemical structure represented by the formula \(\mathrm{CH}_3\mathrm{CH}_2\mathrm{OH}\). In this structure:

• The two carbon atoms are connected in a chain.
• A hydroxyl group \(-\mathrm{OH}\) is attached to the terminal carbon atom.

This specific arrangement makes ethanol distinct as an alcohol. Its hydroxyl group plays a critical role in its chemical behavior, allowing it to form hydrogen bonds, which influence its physical properties like boiling point and solubility. Ethanol is mainly used in alcoholic beverages and sanitizers, showcasing its important role in both industrial and everyday applications. Understanding its structure helps explain its properties and uses.

Dimethyl Ether Chemical Structure

Dimethyl ether is an ether, represented by the structure \(\mathrm{CH}_3\mathrm{OCH}_3\). Unlike ethanol, the oxygen atom connects the two carbon-containing groups, forming a different class of chemical compound known as an ether. Ethers like dimethyl ether generally have low polarity because of their symmetrical structure, which affects their interactions compared to alcohols.

The chemical structure of dimethyl ether has significant implications for its properties. For example, its lack of a hydroxyl group means it doesn't participate in hydrogen bonding as ethanol does, resulting in a lower boiling point. Dimethyl ether is used as a propellant in aerosol products and as a precursor in organic synthesis. Understanding its unique structure explains its distinct properties and contrasts with ethanol, despite sharing the same molecular formula.