Question

If someone reported the preparation of a compound with the formula \(\mathrm{C}_{3} \mathrm{H}_{9}\), most chemists would be skeptical. Why?

Short answer

Formula \( \mathrm{C}_3 \mathrm{H}_9 \) contradicts typical bonding patterns.

Step-by-step solution

Understanding the Problem

We need to analyze the molecular formula \( \mathrm{C}_{3} \mathrm{H}_{9} \) to determine if it is a plausible chemical compound. Typically, in organic chemistry, compounds like hydrocarbons follow specific rules based on the types and numbers of atoms present.

Applying the Rule of Saturated Hydrocarbons

A common type of hydrocarbon is a saturated hydrocarbon (alkane), which follows the general molecular formula \( \mathrm{C}_n \mathrm{H}_{2n+2} \). For \( n = 3 \), this formula becomes \( \mathrm{C}_3 \mathrm{H}_8 \).

Comparing Formula with Known Patterns

The given formula \( \mathrm{C}_3 \mathrm{H}_9 \) has one more hydrogen than that of a typical saturated hydrocarbon (alkane). For an alkane of three carbon atoms, the expected formula should be \( \mathrm{C}_3 \mathrm{H}_8 \).

Reasoning the Impossibility

The additional hydrogen atom in \( \mathrm{C}_3 \mathrm{H}_9 \) creates a situation that cannot be explained by simple carbon valency principles, as carbon atoms typically form four bonds, meaning the formula suggests a hydrogen excess, which would leave an unbonded or impossibly bonded atom.

Key concepts

Molecular Formula

The molecular formula is a symbolic representation of a chemical compound using the element symbols and numbers. This formula gives the exact number of each type of atom in a molecule. For example, the molecular formula \( \mathrm{C}_{3} \mathrm{H}_{9} \) indicates there are three carbon atoms and nine hydrogen atoms. This does not necessarily align with any known, stable organic compound patterns.
In organic chemistry, the molecular formula helps determine the structure and properties of a compound. However, it does not provide information about how atoms are bonded. At this point, chemists would look at how this formula fits into known structures.

Saturated Hydrocarbons

Saturated hydrocarbons, also known as alkanes, are a vital class of compounds in organic chemistry. They comprise only carbon and hydrogen atoms connected by single bonds, forming a tetrahedral structure around each carbon atom. The general molecular formula for alkanes is \( \mathrm{C}_n \mathrm{H}_{2n+2} \). This means for every \( n \) number of carbon atoms, there will be \( 2n+2 \) hydrogen atoms.
For example, if \( n = 3 \), the corresponding saturated hydrocarbon is propane with the formula \( \mathrm{C}_3 \mathrm{H}_8 \). This specific pattern ensures that each carbon atom makes four single bonds, adhering to the carbon valency principles. Deviations from this pattern, like having one additional hydrogen without changing the carbon number, often lead to compounds that cannot exist stably under typical conditions.

Carbon Valency

Carbon valency is fundamental in understanding the bonding capabilities of carbon atoms. Carbon atoms are tetravalent, meaning they can form four covalent bonds with other atoms. This ability arises because carbon has four electrons in its outer shell and requires four more to achieve a stable octet. When constructing molecules, carbon bonds with other carbon atoms and different atoms like hydrogen, oxygen, etc., always forming four bonds.
In the molecular formula \( \mathrm{C}_{3} \mathrm{H}_{9} \), if each carbon must follow the four-bond rule, nine hydrogens cannot be stably included without exceeding this rule. Each extra hydrogen suggests that at least one carbon has more than four bonds or doesn't accomplish all four bonds, making this molecular formula impossible for stable compounds in saturated hydrocarbons.