STATEMENT-1: Volume required for 0.1 M solution is in order `V_(KMnO_(4)) lt V_(K_(2)Cr_(2)O_(7)) lt V_(H_(2)O_(2))`
STATEMENT-2: The number of equivalents required will be in order `H_(2)O_(2) gt KMnO_(4) gt K_(2)Cr_(2)O_(7)`
STATEMENT-3: The `n_("factor")` is in order `n_(H_(2)O_(2)) lt n_(KMnO_(4)) lt n_(K_(2)Cr_(2)O_(7)`

Options

A. T T F
B. T F T
C. F F T
D. F T F

Answer

To solve the problem, we need to analyze the three statements provided regarding the volume required for 0.1 M solutions, the number of equivalents required, and the n-factor of the compounds involved: KMnO4, K2Cr2O7, and H2O2.

### Step 1: Calculate the Molar Mass of Each Compound
1. **KMnO4**:
- K = 39 g/mol
- Mn = 55 g/mol
- O = 16 g/mol (4 O atoms)
- Molar mass = 39 + 55 + (16 × 4) = 158 g/mol

2. **K2Cr2O7**:
- K = 39 g/mol (2 K atoms)
- Cr = 52 g/mol (2 Cr atoms)
- O = 16 g/mol (7 O atoms)
- Molar mass = (39 × 2) + (52 × 2) + (16 × 7) = 294 g/mol

3. **H2O2**:
- H = 1 g/mol (2 H atoms)
- O = 16 g/mol (2 O atoms)
- Molar mass = (1 × 2) + (16 × 2) = 34 g/mol

### Step 2: Determine the Volume Required for 0.1 M Solutions
Using the formula for molarity:
\[ \text{Molarity} = \frac{\text{Weight}}{\text{Molar Mass} \times \text{Volume}} \]
For a fixed weight, the volume required is inversely proportional to the molar mass. Therefore, the order of volume required for a 0.1 M solution will be:
- H2O2 (lowest molar mass, highest volume)
- KMnO4 (middle molar mass)
- K2Cr2O7 (highest molar mass, lowest volume)

Thus, the order is:
\[ V_{H2O2} > V_{KMnO4} > V_{K2Cr2O7} \]
**Conclusion for Statement 1**: False (the order is incorrect as stated).

### Step 3: Calculate the n-factor for Each Compound
1. **KMnO4**:
- Reaction: MnO4^- + 8H^+ + 5e^- → Mn^2+ + 4H2O
- n-factor = 5

2. **H2O2**:
- Reaction: H2O2 + 2e^- → 2H2O
- n-factor = 2

3. **K2Cr2O7**:
- Reaction: Cr2O7^2- + 14H^+ + 6e^- → 2Cr^3+ + 7H2O
- n-factor = 6

### Step 4: Determine the Number of Equivalents
Using the formula:
\[ \text{Number of equivalents} = \frac{\text{Molar Mass}}{\text{n-factor}} \]
1. **KMnO4**:
- Equivalents = 158 g/mol / 5 = 31.6

2. **H2O2**:
- Equivalents = 34 g/mol / 2 = 17

3. **K2Cr2O7**:
- Equivalents = 294 g/mol / 6 = 49

**Conclusion for Statement 2**: False (the order is incorrect as stated).

### Step 5: Order of n-factors
From the calculations:
- n-factor for H2O2 = 2
- n-factor for KMnO4 = 5
- n-factor for K2Cr2O7 = 6

Thus, the order of n-factors is:
\[ n_{H2O2} < n_{KMnO4} < n_{K2Cr2O7} \]
**Conclusion for Statement 3**: True.

### Final Summary
- Statement 1: False
- Statement 2: False
- Statement 3: True