Animated Solution for Chemistry - Organic Chemistry: The number of sigma bonds in ${\text{H}}_3\text{C}-\underset{\text{H}}{\underset{|}{C}}=\text{CH}-\text{C}\equiv \text{C}-\text{H}$ is ....... .

Imagine you are diving into the microscopic world of organic chemistry. Every molecule is like a bustling city, and the atoms are the buildings. But what holds these buildings together? The answer lies in the invisible bridges we call chemical bonds.

In this problem, we are tasked with counting the number of sigma ($\sigma$) bonds in a specific organic molecule: ${\text{H}}_3\text{C}-\text{C}(\text{H})=\text{CH}-\text{C}\equiv \text{C}-\text{H}$. At first glance, a condensed structural formula can look like a secret code. The trick to cracking this code is to expand the molecule completely, revealing every single hidden connection.

Let's break down the golden rules of chemical bonding before we start counting. When two atoms share a pair of electrons directly between their nuclei (a head-on overlap of orbitals), they form a sigma ($\sigma$) bond. This is the strongest type of covalent bond and forms the primary skeleton of the molecule.

If atoms want to share more electrons, they can't do it head-on anymore because that space is already occupied. Instead, they share electrons sideways (lateral overlap of unhybridized p-orbitals), creating pi ($\pi$) bonds.

Therefore, the rule is beautifully simple: - A single bond is always exactly $1\sigma$ bond. - A double bond consists of $1\sigma$ bond and $1\pi$ bond. - A triple bond consists of $1\sigma$ bond and $2\pi$ bonds.

To avoid any silly mistakes, we should count the bonds systematically. Let's divide our counting into two phases: the Carbon-Hydrogen (C-H) bonds and the Carbon-Carbon (C-C) bonds.

Phase 1: The Carbon-Hydrogen (C-H) Bonds Hydrogen is a tiny atom with only one electron to share, meaning it can only ever form a single bond. Thus, every C-H bond in the universe is a sigma bond. Let's scan our expanded molecule from left to right: - The first carbon (${\text{CH}}_3$) is bonded to $3$ hydrogens. - The second carbon ($\text{CH}$) is bonded to $1$ hydrogen. - The third carbon ($\text{CH}$) is bonded to $1$ hydrogen. - The fifth carbon ($\text{CH}$) is bonded to $1$ hydrogen.

Adding these up: $3+1+1+1=6\text{ C-H }\sigma \text{ bonds}$.

Phase 2: The Carbon-Carbon (C-C) Bonds Now, let's look at the backbone of the molecule—the connections between the carbon atoms. Remember, regardless of whether the carbons are connected by a single, double, or triple bond, the very first connection between them is always a sigma bond. - Between C1 and C2: A single bond $\to 1\sigma$ bond. - Between C2 and C3: A double bond $\to 1\sigma$ bond (and $1\pi$ bond). - Between C3 and C4: A single bond $\to 1\sigma$ bond. - Between C4 and C5: A triple bond $\to 1\sigma$ bond (and $2\pi$ bonds).

Counting the primary connections gives us exactly $4\text{ C-C }\sigma \text{ bonds}$.

Bringing it all together, we simply add the results from our two phases:

The Mathematical Shortcut: Did you know there is a lightning-fast mathematical trick to verify your answer? For any acyclic (open-chain) molecule, the total number of sigma bonds is always exactly one less than the total number of atoms in the molecule.

Let's test it! Our molecule has $5$ Carbon atoms and $6$ Hydrogen atoms, making a total of $11$ atoms.

The math perfectly aligns with our structural analysis! Whether you draw it out or use the formula, mastering the anatomy of organic molecules is a deeply rewarding skill.