`"Phenol "overset(Na_(2)Cr_(2)O_(7))underset(H_(2)SO_(4))rarrX` The ratio of the number of `sigma` to `pi` bonds in the products X is

Answer

To solve the problem, we need to determine the product of the reaction between phenol and sodium dichromate (Na2Cr2O7) in the presence of sulfuric acid (H2SO4), and then calculate the ratio of sigma (σ) to pi (π) bonds in that product.

### Step-by-Step Solution:

1. **Identify the Reactants**: The reactant is phenol (C6H5OH).

2. **Understand the Reaction**: Sodium dichromate (Na2Cr2O7) is a strong oxidizing agent. When phenol reacts with Na2Cr2O7 in the presence of sulfuric acid, it gets oxidized to benzoquinone (C6H4O).

3. **Write the Reaction**:
\[ \text{C}_6\text{H}_5\text{OH} \xrightarrow{\text{Na}_2\text{Cr}_2\text{O}_7, \text{H}_2\text{SO}_4} \text{C}_6\text{H}_4\text{O} \text{ (Benzoquinone)} \]

4. **Draw the Structure of Benzoquinone**: The structure of benzoquinone can be represented as follows:
```
O
//
C6H4
```

5. **Count the Bonds**:
- **Sigma (σ) Bonds**:
- Each C-H bond contributes 1 σ bond. There are 4 C-H bonds.
- Each C-C bond contributes 1 σ bond. There are 4 C-C bonds in the ring.
- The C=O bond contributes 1 σ bond.
- Total σ bonds = 4 (C-H) + 4 (C-C) + 1 (C=O) = 9 σ bonds.

- **Pi (π) Bonds**:
- The C=C bonds in the ring contribute 1 π bond each. There are 2 C=C bonds.
- The C=O bond contributes 1 π bond.
- Total π bonds = 2 (C=C) + 1 (C=O) = 3 π bonds.

6. **Calculate the Ratio of σ to π Bonds**:
\[ \text{Ratio of σ to π bonds} = \frac{\text{Number of σ bonds}}{\text{Number of π bonds}} = \frac{9}{3} = 3:1 \]

### Final Answer:
The ratio of the number of sigma to pi bonds in the product X (benzoquinone) is **3:1**.