2mol `FeSO_(4)` in acid medium are oxidised by x mole of `KMnO_(4)`, where as 2 moleof `FeC_(2)O_(4)` in acid medium are oxidized by y mole of `KMnO_(4)`. The ratioof x and y is

Options

A. `1//3`
B. `1//2`
C. `1//4`
D. `1//5`

Answer

To solve the problem, we need to find the ratio of moles of `KMnO4` required to oxidize `FeSO4` and `FeC2O4`. Let's break this down step by step.

### Step 1: Determine the reaction for `FeSO4` with `KMnO4`
The balanced chemical equation for the oxidation of ferrous sulfate (`FeSO4`) by potassium permanganate (`KMnO4`) in acidic medium is:

\[ 2 \text{KMnO}_4 + 10 \text{FeSO}_4 + 8 \text{H}_2\text{SO}_4 \rightarrow \text{K}_2\text{SO}_4 + 2 \text{MnSO}_4 + 5 \text{Fe}_2(\text{SO}_4)_3 + 8 \text{H}_2\text{O} \]

From this equation, we can see that 2 moles of `KMnO4` oxidize 10 moles of `FeSO4`.

### Step 2: Calculate moles of `KMnO4` required for 2 moles of `FeSO4`
To find out how many moles of `KMnO4` are required for 2 moles of `FeSO4`, we set up a proportion based on the balanced equation:

\[ \text{Moles of } KMnO4 = \frac{2 \text{ moles of } KMnO4}{10 \text{ moles of } FeSO4} \times 2 \text{ moles of } FeSO4 \]

Calculating this gives:

\[ x = \frac{2}{10} \times 2 = \frac{2}{5} \]

### Step 3: Determine the reaction for `FeC2O4` with `KMnO4`
The balanced chemical equation for the oxidation of ferrous oxalate (`FeC2O4`) by potassium permanganate in acidic medium is:

\[ 6 \text{KMnO}_4 + 10 \text{FeC}_2\text{O}_4 + 24 \text{H}_2\text{SO}_4 \rightarrow 5 \text{Fe}_2(\text{SO}_4)_3 + 20 \text{CO}_2 + 6 \text{MnSO}_4 + 3 \text{K}_2\text{SO}_4 + 24 \text{H}_2\text{O} \]

From this equation, we can see that 6 moles of `KMnO4` oxidize 10 moles of `FeC2O4`.

### Step 4: Calculate moles of `KMnO4` required for 2 moles of `FeC2O4`
To find out how many moles of `KMnO4` are required for 2 moles of `FeC2O4`, we set up a proportion based on the balanced equation:

\[ \text{Moles of } KMnO4 = \frac{6 \text{ moles of } KMnO4}{10 \text{ moles of } FeC2O4} \times 2 \text{ moles of } FeC2O4 \]

Calculating this gives:

\[ y = \frac{6}{10} \times 2 = \frac{6}{5} \]

### Step 5: Find the ratio of x to y
Now we have:

- \( x = \frac{2}{5} \)
- \( y = \frac{6}{5} \)

The ratio \( \frac{x}{y} \) is:

\[ \frac{x}{y} = \frac{\frac{2}{5}}{\frac{6}{5}} = \frac{2}{5} \times \frac{5}{6} = \frac{2}{6} = \frac{1}{3} \]

### Final Answer
Thus, the ratio of \( x \) to \( y \) is \( \frac{1}{3} \).

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