If valence factor (n-factor) of compound `NaHC_(2)O_(4).2H_(2)C_(2)O_(4).3K_(2)C_(2)O_(4).4Al_(2)(C_(2)O_(4))_(3).3FeC_(2)O_(4)` in acid base titration is x and redox titration with `KMnO_(4)` is y then value of y/x is:

Options

A. 8.4
B. 9
C. 11.25
D. 12

Answer

To solve the problem, we need to determine the n-factor (valence factor) of the compound in two different types of titrations: acid-base titration and redox titration. Let's break down the steps:

### Step 1: Determine the n-factor in Acid-Base Titration (X)

1. **Identify the number of acidic protons (H⁺)** in the compound:
- The compound is `NaHC₂O₄.2H₂C₂O₄.3K₂C₂O₄.4Al₂(C₂O₄)₃.3FeC₂O₄`.
- Count the number of hydrogen atoms (H):
- From `NaHC₂O₄`: 1 H
- From `2H₂C₂O₄`: 2 × 2 = 4 H
- From `3K₂C₂O₄`: 0 H (no H in K₂C₂O₄)
- From `4Al₂(C₂O₄)₃`: 0 H (no H in Al₂(C₂O₄)₃)
- From `3FeC₂O₄`: 0 H (no H in FeC₂O₄)
- Total H = 1 + 4 = 5 H

2. **Determine the n-factor (X)**:
- In acid-base titration, the n-factor is equal to the number of H⁺ ions that can be released.
- Therefore, X = 5.

### Step 2: Determine the n-factor in Redox Titration (Y)

1. **Identify the oxidation states of carbon in oxalate (C₂O₄²⁻)**:
- In C₂O₄²⁻, the oxidation state of carbon is +3.
- When it is oxidized to CO₂, the oxidation state becomes +4.

2. **Calculate the number of electrons transferred per carbon**:
- Each carbon transfers 1 electron during the oxidation process.
- Count the total number of carbon atoms in the compound:
- `2 from NaHC₂O₄`
- `2 from 2H₂C₂O₄` (2 × 2 = 4)
- `2 from 3K₂C₂O₄` (3 × 2 = 6)
- `2 from 4Al₂(C₂O₄)₃` (4 × 3 × 2 = 24)
- `2 from 3FeC₂O₄` (3 × 2 = 6)
- Total number of carbon atoms = 2 + 4 + 6 + 24 + 6 = 42.

3. **Calculate the total number of electrons transferred by carbon**:
- Total electrons from carbon = 42 (1 electron per carbon).

4. **Consider the iron (Fe) contribution**:
- Each Fe²⁺ ion is oxidized to Fe³⁺, transferring 1 electron.
- There are 3 Fe ions, so total electrons from Fe = 3.

5. **Calculate the total n-factor (Y)**:
- Total electrons transferred = 42 (from C) + 3 (from Fe) = 45.
- Therefore, Y = 45.

### Step 3: Calculate the ratio y/x

1. **Calculate y/x**:
- y/x = Y/X = 45/5 = 9.

### Final Answer
The value of y/x is **9**.