How many different stereoisomers exist for `1`-chloro-`2`(`3`-chlorocyclobutyl) ethane?

Options

A. `2`
B. `7`
C. `5`
D. `4`

Explanation

To determine the number of different stereoisomers for 1-chloro-2-(3-chlorocyclobutyl)ethane, we will follow these steps:

### Step 1: Understand the Structure
1. **Identify the main chain**: The main chain is ethane (C2H6).
2. **Identify the substituents**: There is a chlorine atom (Cl) at the first carbon (1-chloro) and a cyclobutyl group with another chlorine atom at the second carbon (2-(3-chlorocyclobutyl)).

### Step 2: Draw the Structure
1. **Draw ethane**: Start with the two carbon atoms connected by a single bond.
2. **Add the 1-chloro substituent**: Attach a chlorine atom to the first carbon.
3. **Add the 2-(3-chlorocyclobutyl) substituent**: Draw a cyclobutane ring (4 carbon atoms in a square) and attach it to the second carbon. Add a chlorine atom to one of the carbons in the cyclobutane ring.

### Step 3: Identify Stereocenters
1. **Check for stereocenters**: A stereocenter is a carbon atom bonded to four different groups. In this case, the second carbon (C2) is bonded to:
- The cyclobutyl group (which has different substituents)
- The ethyl group (C1)
- A hydrogen atom
- The chlorine atom

Since C2 has four different groups, it is a stereocenter.

### Step 4: Determine Geometric Isomers
1. **Geometric isomerism**: The presence of a double bond or a ring can lead to cis/trans isomerism. In this case, the cyclobutane ring can have two configurations (cis and trans) based on the position of the chlorine atom and the hydrogen atom.

### Step 5: Calculate Total Stereoisomers
1. **Count the combinations**:
- For the stereocenter at C2, there are 2 configurations (R/S).
- For the cyclobutane ring, there are also 2 configurations (cis/trans).

Thus, the total number of stereoisomers can be calculated as:
\[ \text{Total Stereoisomers} = 2 \text{ (from C2)} \times 2 \text{ (from cyclobutane)} = 4 \]

### Conclusion
The total number of different stereoisomers for 1-chloro-2-(3-chlorocyclobutyl)ethane is **4**.

---