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

Explanation

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: Identify the compounds and their sulfate ions
- \( \text{FeSO}_4 \) contains 1 sulfate ion (\( \text{SO}_4^{2-} \)) per formula unit and provides 1 \( \text{Fe}^{2+} \) ion.
- \( \text{Fe}_2(\text{SO}_4)_3 \) contains 3 sulfate ions per formula unit and provides 2 \( \text{Fe}^{3+} \) ions.

### Step 2: Set up the equation for equal sulfate ions
Let’s assume we have \( x \) moles of \( \text{FeSO}_4 \) and \( y \) moles of \( \text{Fe}_2(\text{SO}_4)_3 \). The total number of sulfate ions from both compounds must be equal:

\[ x + 3y = \text{Total sulfate ions} \]

### Step 3: Determine the total iron ions
From \( x \) moles of \( \text{FeSO}_4 \), we get \( x \) moles of \( \text{Fe}^{2+} \).
From \( y \) moles of \( \text{Fe}_2(\text{SO}_4)_3 \), we get \( 2y \) moles of \( \text{Fe}^{3+} \).

### Step 4: Express the ratio of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \)
Now we can express the ratio of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \):

\[ \text{Ratio} = \frac{\text{Fe}^{2+}}{\text{Fe}^{3+}} = \frac{x}{2y} \]

### Step 5: Solve for the ratio using the sulfate equation
From the sulfate equation \( x + 3y = \text{Total sulfate ions} \), we can express \( x \) in terms of \( y \):

Assuming a total of 3 sulfate ions (for simplicity, let’s take \( y = 1 \)):
- If \( y = 1 \), then \( x + 3(1) = 3 \) gives \( x = 0 \).
- If \( y = 0 \), then \( x + 3(0) = 0 \) gives \( x = 0 \).

To maintain the equality of sulfate ions, we can set \( y = 1 \) and \( x = 3 \) (for example).

### Step 6: Calculate the ratio
Using \( x = 3 \) and \( y = 1 \):

\[ \text{Ratio} = \frac{3}{2 \times 1} = \frac{3}{2} \]

### Conclusion
The molar ratio of \( \text{Fe}^{2+} \) to \( \text{Fe}^{3+} \) in the mixture is \( 3:2 \).