The molar ration of `Fe^(++)` to `Fe^(+++)` in a mixture of `FeSO_(4)` and `Fe_(2)(SO_(4))_(3)` having equal number of sulphate ions in both ferrous and ferric sulphate is:

Options

A. `1:2`
B. `3:2`
C. `2:3`
D. can't be determined

Answer

To find the molar ratio of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \) in a mixture of \( \text{FeSO}_4 \) and \( \text{Fe}_2(\text{SO}_4)_3 \) having equal numbers of sulfate ions, we can follow these steps:

### Step 1: Analyze the dissociation of \( \text{FeSO}_4 \)
- \( \text{FeSO}_4 \) dissociates into:
\[ \text{FeSO}_4 \rightarrow \text{Fe}^{2+} + \text{SO}_4^{2-} \]
- From this dissociation, we see that for every 1 mole of \( \text{FeSO}_4 \), we get 1 mole of \( \text{Fe}^{2+} \) and 1 mole of \( \text{SO}_4^{2-} \).

### Step 2: Analyze the dissociation of \( \text{Fe}_2(\text{SO}_4)_3 \)
- \( \text{Fe}_2(\text{SO}_4)_3 \) dissociates into:
\[ \text{Fe}_2(\text{SO}_4)_3 \rightarrow 2\text{Fe}^{3+} + 3\text{SO}_4^{2-} \]
- Here, for every 1 mole of \( \text{Fe}_2(\text{SO}_4)_3 \), we get 2 moles of \( \text{Fe}^{3+} \) and 3 moles of \( \text{SO}_4^{2-} \).

### Step 3: Establish the relationship between sulfate ions
- We are given that the number of sulfate ions from both compounds is equal. Let’s denote the number of moles of \( \text{FeSO}_4 \) as \( x \) and the number of moles of \( \text{Fe}_2(\text{SO}_4)_3 \) as \( y \).
- The total number of sulfate ions from \( \text{FeSO}_4 \) is \( x \) and from \( \text{Fe}_2(\text{SO}_4)_3 \) is \( 3y \).
- Setting these equal gives us:
\[ x = 3y \]

### Step 4: Calculate the moles of \( \text{Fe}^{2+} \) and \( \text{Fe}^{3+} \)
- The total moles of \( \text{Fe}^{2+} \) from \( \text{FeSO}_4 \) is \( x \) (since each \( \text{FeSO}_4 \) gives 1 \( \text{Fe}^{2+} \)).
- The total moles of \( \text{Fe}^{3+} \) from \( \text{Fe}_2(\text{SO}_4)_3 \) is \( 2y \) (since each \( \text{Fe}_2(\text{SO}_4)_3 \) gives 2 \( \text{Fe}^{3+} \)).

### Step 5: Substitute \( x \) in terms of \( y \)
- From \( x = 3y \), we can substitute:
- Moles of \( \text{Fe}^{2+} = 3y \)
- Moles of \( \text{Fe}^{3+} = 2y \)

### Step 6: Find the molar ratio
- The molar ratio of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \) is:
\[ \text{Ratio} = \frac{\text{Fe}^{2+}}{\text{Fe}^{3+}} = \frac{3y}{2y} = \frac{3}{2} \]

### Conclusion
- Therefore, the molar ratio of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \) is \( 3:2 \).