Animated Solution for Chemistry - Organic Chemistry: The correct order of heat of combustion for following alkadienes is

Isomers and Combustion

Imagine you are handed three different flasks, each containing a distinct hydrocarbon. Upon analyzing them, you realize they all share the exact same molecular formula: $C_6{H}_{10}$. These are geometrical isomers of 2,4-hexadiene. Because they are isomers, they are composed of the exact same building blocks. If you were to ignite them in a calorimeter, every single one of them would react with oxygen to produce the exact same products: $6C{O}_2$ and $5H_{2}O$.

However, despite producing the same end products, the amount of heat they release—their heat of combustion ($\Delta H_c$)—is not identical. Why? Because the way those atoms are arranged in space dictates their internal potential energy.

Stability vs. Energy

To understand this, we need to establish a golden rule of thermodynamics for isomers: Heat of combustion is inversely proportional to stability.

Think of stability as altitude. A highly stable molecule is like a ball resting on a low shelf. It has already lost a lot of potential energy during its formation. A highly unstable molecule is like a ball perched on a high shelf; it is packed with pent-up potential energy.

When combustion occurs, all these "balls" fall to the exact same ground level (the $C{O}_2$ and $H_{2}O$ products). The unstable molecule falls from a greater height, releasing a massive amount of energy (heat). The stable molecule falls from a lower height, releasing significantly less energy. Therefore, to rank their heat of combustion, we simply need to rank their stabilities and reverse the order!

Let's analyze the geometry of our three alkadienes to determine their relative stabilities.

Structure (A): Look closely at the two double bonds. For both of them, the bulky alkyl groups (the rest of the carbon chain) are pointing in opposite directions across the double bond axis. This is the classic trans configuration. Because the bulky groups are far apart, there is virtually no steric clash. Structure (A) is trans, trans-2,4-hexadiene.

Structure (B): Tracing the chain here reveals a mixed identity. The first double bond has groups on opposite sides (trans), but the second double bond forces the main chain to enter and exit on the same side. This creates a "U" shape, which is the cis configuration. Structure (B) is trans, cis-2,4-hexadiene.

Structure (C): Finally, in this structure, both double bonds force the continuous carbon chain onto the same side of their respective axes. This is the cis, cis configuration.

In open-chain alkenes, a cis double bond is inherently less stable than a trans double bond. Why? Because forcing bulky groups onto the same side causes their electron clouds to repel each other. This is known as steric strain—it's like trying to compress a stiff spring.

Since (A) has two trans bonds, it is completely relaxed and is the most stable. Structure (C), with two cis bonds, suffers from maximum steric strain and is the least stable. Structure (B) sits comfortably in the middle.

We have our stability ranking: Stability: $(A)>(B)>(C)$

Now, we apply our golden rule. The most stable isomer (A) sits at the lowest potential energy and will release the least heat. The least stable isomer (C) sits at the highest potential energy and will release the most heat.

Heat of Combustion: $(A)<(B)<(C)$

This perfectly matches option (b). By simply looking at the spatial arrangement of atoms, we successfully predicted the thermodynamic behavior of these molecules. That is the true elegance of organic chemistry!