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 regarding phosphorus acid (H₃PO₃), we need to determine the values of X, Y, and Z, where:

- X = number of non-bonding electron pairs
- Y = number of sigma bonds
- Z = number of pi bonds

### Step-by-Step Solution:

1. **Draw the Lewis Structure of Phosphorus Acid (H₃PO₃)**:
- Phosphorus (P) is the central atom.
- It is bonded to three hydrogen (H) atoms and three oxygen (O) atoms.
- One of the oxygen atoms is double-bonded to phosphorus, while the other two are single-bonded and each has a hydrogen atom attached.

2. **Count Non-Bonding Electron Pairs (X)**:
- In the Lewis structure, phosphorus has one lone pair of electrons.
- The oxygen atoms also have lone pairs. Each of the two single-bonded oxygen atoms has two lone pairs.
- Therefore, the total number of non-bonding electron pairs is:
- Phosphorus: 1 lone pair
- Oxygen 1: 2 lone pairs
- Oxygen 2: 2 lone pairs
- Oxygen 3 (double-bonded): 0 lone pairs
- Total = 1 (from P) + 2 (from O1) + 2 (from O2) = 5 non-bonding electron pairs.
- So, **X = 5**.

3. **Count Sigma Bonds (Y)**:
- Each single bond counts as one sigma bond.
- The double bond consists of one sigma bond and one pi bond.
- In H₃PO₃, we have:
- 3 H-O single bonds (3 sigma bonds)
- 1 P=O double bond (1 sigma bond)
- Total sigma bonds = 3 (H-O) + 1 (P=O) = 4.
- So, **Y = 4**.

4. **Count Pi Bonds (Z)**:
- Pi bonds are present in double bonds.
- In H₃PO₃, there is only one double bond (P=O), which contributes one pi bond.
- So, **Z = 1**.

5. **Calculate the Expression (Y * Z - X)**:
- Now we substitute the values of Y, Z, and X into the expression:
- Y * Z - X = 4 * 1 - 5 = 4 - 5 = -1.

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