Total number of stereoisomers of truxillic acid are :

Explanation

To determine the total number of stereoisomers of truxillic acid, we will follow these steps:

### Step 1: Understand the Structure of Truxillic Acid
Truxillic acid has a four-membered carbon ring with two phenyl (pH) groups and two carboxylic acid (COOH) groups attached to it. The arrangement of these groups can lead to different stereoisomers.

**Hint:** Visualize the structure of truxillic acid, focusing on the positions of the phenyl and carboxylic acid groups.

### Step 2: Identify Chiral Centers
In truxillic acid, we need to identify the chiral centers. A carbon atom is considered chiral if it is bonded to four different substituents. In truxillic acid, there are two chiral centers due to the arrangement of the phenyl and carboxylic acid groups.

**Hint:** Look for carbon atoms in the structure that have different groups attached to them.

### Step 3: Count the Stereoisomers
The formula to calculate the maximum number of stereoisomers is \(2^n\), where \(n\) is the number of chiral centers. Since truxillic acid has 2 chiral centers, we can calculate the number of stereoisomers as follows:

\[ \text{Number of stereoisomers} = 2^n = 2^2 = 4 \]

However, we also need to consider the geometric isomerism due to the presence of double bonds in the structure, which can lead to additional stereoisomers.

**Hint:** Remember to account for both chiral centers and geometric isomerism when counting the total number of stereoisomers.

### Step 4: List the Possible Stereoisomers
1. **Alpha Truxilic Acid:** Both phenyl groups and carboxylic acids are in specific orientations.
2. **Gamma Truxilic Acid:** One phenyl group is in a wedge position while the other is in a dash position.
3. **Epsilon Truxilic Acid:** Both phenyl groups are in wedge positions, and both carboxylic acids are in dash positions.
4. **Perituxilic Acid:** All substituents are in wedge positions.
5. **Epitruxilic Acid:** One carboxylic acid is in a dash position, while the rest are in wedge positions.

**Hint:** Draw out each stereoisomer to visualize the differences in their structures.

### Step 5: Conclusion
After analyzing the structure and counting the stereoisomers, we conclude that the total number of stereoisomers of truxillic acid is **5**.

**Final Answer:** The total number of stereoisomers of truxillic acid is 5.