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In organic chemistry, isomers are compounds with the same molecular formula but different arrangements of atoms in space. Among these isomers, cis-trans isomers, also known as geometric isomers, are particularly interesting. These isomers occur when there is a restriction on rotation around a bond, commonly around a carbon-carbon double bond (C=C).
For cis-trans isomers:

• Cis isomers have groups positioned on the same side of the double bond or ring.
• Trans isomers have groups on opposite sides of the double bond or ring.

Because of these structural differences, cis and trans isomers can exhibit varying physical and chemical properties. For example, they may have different melting points, boiling points, and solubilities. In the exercise given, cis-3-hexene and trans-3-hexene are such isomers, which only differ in the spatial arrangement of atoms around the double bond. However, despite these physical differences, they can sometimes give the same chemical product under specific reactions, which leads us to Markovnikov's rule and hydration reaction.

Markovnikov's rule is a guiding principle in organic chemistry used to predict the outcome of certain addition reactions. The rule primarily applies to the addition of reagents like hydrogen halides and water to alkenes. In simple terms, the rule states:
The component of the reagent that forms the most stable intermediate (usually an ion) will add to the more substituted carbon atom of the alkene.
This means that in a hydration reaction, where water (as \( \text{H}^+\) and \( \text{OH}^-\)) is added to an alkene:

• The hydrogen (\( \text{H}^+\)) will attach to the less substituted carbon.
• The hydroxyl group (\( \text{OH}^-\)) will bond with the more substituted carbon, promoting stability.

This rule helps explain the formation of the same product, 3-hexanol, from both cis-3-hexene and trans-3-hexene. Despite different initial configurations, both isomers follow the same mechanistic path, consistently leading to the connection of the hydroxyl group at the more substituted carbon, ultimately creating the same alcohol.

A hydration reaction in organic chemistry involves the addition of water to a substrate, often an alkene. In the given exercise, when cis-3-hexene and trans-3-hexene undergo hydration, they are treated with water in the presence of an acid ($H\_2SO\_4$), which acts as a catalyst and promotes the reaction.
The process involves the following key steps:

• The alkene's double bond opens up as it forms a bond with a hydrogen ion, creating a carbocation at the more substituted carbon atom.
• The hydroxyl group (\( \text{OH}^-\)) from water then attacks this carbocation, attaching to the same carbon.

This type of addition to the alkene is a markovnikov addition, adhering to Markovnikov's Rule. Importantly, the result of this reaction for both isomers, cis and trans, is the formation of the alcohol 3-hexanol. The reaction proceeds similarly because the carbocation formation and stabilization drive the reaction mechanism, regardless of the starting material's geometry.