In phosphorus acid, if X is number of non bonding electron pairs. Y is number of `sigma`-bonds and Z is number of `pi`- bonds. Then, calculate value of `Yxx Z -X`.

Explanation

To solve the problem, we need to analyze the structure of phosphorus acid (H₃PO₃) and determine the values of X, Y, and Z.

### Step-by-Step Solution:

1. **Identify the Structure of Phosphorus Acid (H₃PO₃)**:
- Phosphorus acid has the molecular formula H₃PO₃. The central atom is phosphorus (P), which is bonded to three hydrogen (H) atoms and one oxygen (O) atom that is double-bonded to phosphorus.

2. **Count the Valence Electrons**:
- Phosphorus (P) is in group 15 and has 5 valence electrons.
- Oxygen (O) is in group 16 and has 6 valence electrons. Since there are two oxygen atoms, they contribute a total of 12 valence electrons (6 from each).
- Each hydrogen (H) contributes 1 valence electron. With three hydrogen atoms, that adds 3 valence electrons.
- Total valence electrons = 5 (from P) + 12 (from O) + 3 (from H) = 20 valence electrons.

3. **Draw the Lewis Structure**:
- Place phosphorus in the center. Connect it to three hydrogen atoms and one oxygen atom.
- The oxygen atom connected to phosphorus has a double bond, while the other oxygen atom is connected with a single bond.
- Distribute the remaining electrons to satisfy the octet rule for oxygen.

4. **Determine Non-Bonding Electron Pairs (X)**:
- In the Lewis structure, the oxygen atom that is single-bonded to phosphorus has 3 lone pairs (6 non-bonding electrons).
- The double-bonded oxygen has no lone pairs.
- Therefore, X = 3 (the number of non-bonding electron pairs).

5. **Count the Sigma Bonds (Y)**:
- Each single bond (P-H and P-O) is a sigma bond.
- The double bond (P=O) consists of one sigma bond and one pi bond.
- Total sigma bonds = 3 (P-H) + 1 (P-O) = 4 sigma bonds.
- Therefore, Y = 4.

6. **Count the Pi Bonds (Z)**:
- There is only one double bond (P=O) in the structure, which contributes one pi bond.
- Therefore, Z = 1.

7. **Calculate the Expression Y * Z - X**:
- Substitute the values into the expression:
- Y * Z - X = 4 * 1 - 3 = 4 - 3 = 1.

### Final Answer:
The value of Y * Z - X is **1**.