# Step-by-Step Solution ## 1. **Understand the Problem** We need to: - Draw a six-carbon alkyne (molecule with a triple bond and 6 carbons) - The structure must be able to exist as **diastereomers** (stereoisomers that are not mirror images). ## 2. **Recall Concepts** - **Alkyne**: Contains a C≡C triple bond. - **Diastereomers**: Occur when there are **two or more stereocenters** and the molecule is not superimposable or mirror-image related. - Simple alkynes and alkynes with *one* chiral center can't have diastereomers. We need **at least two stereocenters**. ## 3. **Building the Structure** Let’s build a six-carbon alkyne with two stereocenters. ### Step 1: Start with the carbon chain C1–C2–C3–C4–C5–C6 ### Step 2: Put the triple bond somewhere Let’s try a triple bond between C2 and C3: C1–C≡C–C4–C5–C6 2 3 ### Step 3: Add substituents to create stereocenters A triple bond carbon cannot be a stereocenter (it’s linear, only 2 substituents). So, stereocenters must be on the single-bonded carbons. Let’s try putting **two different groups** on both C4 and C5. Example: Attach a methyl group (–CH₃) to C4 and C5: - C4: Attach –CH₃ - C5: Attach –CH₃ So, the structure: CH3–C≡C–CH(CH3)–CH(CH3)–CH3 Let’s write it more clearly: **2,3-dimethylhex-3-yne** Or, full structure: CH3–C≡C–CH(CH3)–CH(CH3)–CH3 - C4 is "CH(CH3)" (i.e., C4 has a methyl and a propyl group) - C5 is "CH(CH3)" (i.e., C5 has a methyl and an ethyl group) Both C4 and C5 are **stereocenters**. ## 4. **Identify Diastereomers** With two stereocenters, there are up to 4 stereoisomers (RR, SS, RS, SR). **Diastereomers** are any pair that are not mirror images. ## 5. **Final Answer** ### **Structure:** ``` CH3 CH3 | | CH3–C≡C–C–C–CH3 | CH3 ``` Or, condensed: **2,3-dimethylhex-3-yne** ### **Explanation:** - The molecule has a 6-carbon chain with a triple bond between C3 and C4. - Methyl groups at C2 and C3, both of which are chiral centers. - This allows for diastereomers. ## 6. **Summary Table** | Carbon # | Substituent(s) | Stereocenter? | |----------|-----------------------|---------------| | 1 | CH3 | No | | 2 | C≡C, CH3, C3 | Yes | | 3 | C2, CH3, C4 | Yes | | 4 | C3, C5 | No | | 5 | C4, CH3, C6 | No | | 6 | CH3 | No | ## 7. **Final Structure** **2,3-dimethylhex-3-yne** This compound can exist as diastereomers. --- **Image:** (Sketch not provided, but a text description is above. If you need a structural diagram, please specify!) --- **Summary:** A six-carbon alkyne that can exist as diastereomers is **2,3-dimethylhex-3-yne**. It has two stereocenters (at C2 and C3) and thus can have diastereomers.

# Step-by-Step Solution ## 1. **Understand the Problem** We need to: - Draw a six-carbon alkyne that can exist as diastereomers. ## 2. **Recall Concepts** - **Alkyne**: Contains a C≡C triple bond. - **Diastereomers**: Stereoisomers that are not mirror images and occur when there are two or more stereocenters. ## 3. **Building the Structure** ### Step 1: Start with the carbon framework We will use a cyclopropane ring to create a six-carbon structure. ### Step 2: Add the triple bond Place a triple bond between one of the carbons in the ring and an external carbon: - Start with a cyclopropane (3 carbons) and add 3 more. ### Step 3: Add substituents to create stereocenters Create two stereocenters by adding different substituents: - **1-ethynyl-2-methylcyclopropane** can be drawn as follows: ``` CH3 | C≡C–C | C ``` This structure consists of: - A triple bond between C1 and an external carbon. - A methyl group on C2 of the cyclopropane. ### Step 4: Identify the stereocenters The molecule has two chiral centers: 1. The carbon bearing the ethynyl group (C1). 2. The carbon bearing the methyl group (C2). ## 4. **Identify Diastereomers** With two stereocenters, the molecule can exhibit four stereoisomers (RR, SS, RS, SR). Any two of these that are not mirror images are diastereomers. ## 5. **Final Answer** ### **Structure:** - **1-ethynyl-2-methylcyclopropane** ### **Explanation:** - The molecule contains a six-carbon structure with a triple bond. - It has two stereocenters, allowing for the existence of diastereomers. ## 6. **Summary Table** | Carbon # | Substituent(s) | Stereocenter? | |----------|-----------------------|---------------| | 1 | C≡C | Yes | | 2 | CH3 | Yes | | 3 | CH3 | No | | 4 | C3 (cyclopropane) | No | | 5 | C1 (ethynyl) | Yes | | 6 | C2 (methyl) | No | ## 7. **Final Structure** **1-ethynyl-2-methylcyclopropane** This compound can exist as diastereomers. --- **Image:** (Sketch not provided, but a text description is above. If you need a structural diagram, please specify!) --- **Summary:** A six-carbon alkyne that can exist as diastereomers is **1-ethynyl-2-methylcyclopropane**, featuring two stereocenters.