To determine which molecule is a stereoisomer of trans-2-butene, let's first analyze the structure of trans-2-butene.
Trans-2-butene has the following arrangement:
[tex]\[ \text{H} \quad \quad \text{H} \][/tex]
[tex]\[ \quad \backslash \quad / \][/tex]
[tex]\[ \text{C} = \text{C} \][/tex]
[tex]\[ / \ \textbackslash \][/tex]
[tex]\[ \text{CH3} \quad \text{CH3} \][/tex]
In this structure, the two methyl groups (CH3) are on opposite sides of the double bond, which is characteristic of the "trans" configuration.
The stereoisomer of trans-2-butene is cis-2-butene, where the methyl groups are on the same side of the double bond. The structure of cis-2-butene is arranged as follows:
[tex]\[ \text{H} \quad \quad \text{CH3} \][/tex]
[tex]\[ \quad \backslash \quad / \][/tex]
[tex]\[ \text{C} = \text{C} \][/tex]
[tex]\[ / \ \textbackslash \][/tex]
[tex]\[ \text{H} \quad \quad \text{CH3} \][/tex]
Looking at the provided options, we need to identify the molecule that corresponds to the cis-2-butene structure:
1. Option A:
[tex]\[ \text{H} \quad \quad \text{H} \][/tex]
[tex]\[ \quad \backslash \quad / \][/tex]
[tex]\[ \text{C} \quad = \ \text{C} \][/tex]
[tex]\[ / \ \textbackslash \][/tex]
[tex]\[ \text{CH3} \quad \text{CH3} \][/tex]
This is actually the trans-2-butene structure.
2. Option B:
[tex]\[ \text{H} \quad \quad \text{H} \][/tex]
[tex]\[ \quad \backslash \quad / \][/tex]
[tex]\[ \text{C} \quad = \ \text{C} \][/tex]
[tex]\[ / \quad \textbackslash \][/tex]
[tex]\[ \text{CH3} \quad \text{CH3} \][/tex]
This is the structure of cis-2-butene, as the two methyl groups are on the same side of the double bond.
3. Option C:
[tex]\[ \text{H} - \text{C} \equiv \text{C} - \text{C} - \text{H} \][/tex]
This is a different molecule and is not a stereoisomer of 2-butene.
Given our analysis, the molecule that is a stereoisomer of trans-2-butene (trans-configuration) is Option B, which represents cis-2-butene (cis-configuration).
Thus, the answer is:
Option B.
