In compound `PCl_(x)F_(5-x)`, possible values of x are 0 to 5, then calculate value of `x_(1)+x_(2)+x_(3)` (where `x_(1), x_(2) and x_(3)`… are possible values of x, with zero dipole moment for given compound).

Explanation

To solve the problem, we need to find the possible values of \( x \) in the compound \( PCl_xF_{5-x} \) that result in a zero dipole moment. A zero dipole moment indicates that the molecule is symmetrical.

### Step-by-Step Solution:

1. **Understanding the Compound**: The compound is \( PCl_xF_{5-x} \). The values of \( x \) can range from 0 to 5. This means we can have:
- \( x = 0 \): \( PCl_0F_5 \) or \( PF_5 \)
- \( x = 1 \): \( PCl_1F_4 \) or \( PClF_4 \)
- \( x = 2 \): \( PCl_2F_3 \)
- \( x = 3 \): \( PCl_3F_2 \)
- \( x = 4 \): \( PCl_4F_1 \) or \( PCl_4F \)
- \( x = 5 \): \( PCl_5F_0 \) or \( PCl_5 \)

2. **Analyzing Each Case for Symmetry**:
- **For \( x = 0 \)**: The compound is \( PF_5 \). This is symmetrical (trigonal bipyramidal) and has a zero dipole moment.
- **For \( x = 1 \)**: The compound is \( PClF_4 \). This is not symmetrical (trigonal bipyramidal with one Cl) and has a non-zero dipole moment.
- **For \( x = 2 \)**: The compound is \( PCl_2F_3 \). This is not symmetrical and has a non-zero dipole moment.
- **For \( x = 3 \)**: The compound is \( PCl_3F_2 \). This can be arranged in a way that is symmetrical (trigonal bipyramidal with three Cl and two F) and has a zero dipole moment.
- **For \( x = 4 \)**: The compound is \( PCl_4F_1 \). This is not symmetrical (tetrahedral with one F) and has a non-zero dipole moment.
- **For \( x = 5 \)**: The compound is \( PCl_5 \). This is symmetrical (trigonal bipyramidal) and has a zero dipole moment.

3. **Identifying Values of \( x \) with Zero Dipole Moment**:
- From the analysis, the values of \( x \) that give a zero dipole moment are:
- \( x_1 = 0 \)
- \( x_2 = 3 \)
- \( x_3 = 5 \)

4. **Calculating \( x_1 + x_2 + x_3 \)**:
\[ x_1 + x_2 + x_3 = 0 + 3 + 5 = 8 \]

### Final Answer:
The value of \( x_1 + x_2 + x_3 \) is **8**.