What volume of `3` molar `HNO_(3)` is needed to oxidise `8 g` of `Fe^(3+)`, `HNO_(3)` gets converted to `NO` ?

Options

A. 8 ml
B. 16 ml
C. 32 ml
D. 64 ml

Answer

To solve the problem of determining the volume of 3 molar HNO₃ needed to oxidize 8 g of Fe³⁺, where HNO₃ is converted to NO, we can follow these steps:

### Step 1: Determine the moles of Fe³⁺
First, we need to calculate the number of moles of Fe³⁺ in 8 g of iron. The molar mass of iron (Fe) is approximately 56 g/mol.

\[ \text{Moles of Fe}^{3+} = \frac{\text{mass}}{\text{molar mass}} = \frac{8 \text{ g}}{56 \text{ g/mol}} = \frac{1}{7} \text{ mol} \approx 0.143 \text{ mol} \]

### Step 2: Identify the oxidation states and the reaction
In the reaction, HNO₃ (with nitrogen in the +5 oxidation state) is reduced to NO (with nitrogen in the +2 oxidation state). This means that each mole of HNO₃ reduces to NO, and in the process, it can oxidize iron from Fe²⁺ to Fe³⁺.

### Step 3: Determine the stoichiometry of the reaction
From the balanced reaction, we can see that:
- 1 mole of Fe²⁺ is oxidized to 1 mole of Fe³⁺.
- 2 moles of HNO₃ are required to oxidize 1 mole of Fe²⁺ to Fe³⁺.

Thus, the stoichiometric ratio is:
\[ \text{Fe}^{2+} : \text{HNO}_3 = 1 : 2 \]

### Step 4: Calculate the moles of HNO₃ needed
Since we have approximately 0.143 moles of Fe²⁺, we will need double that amount of HNO₃ to oxidize it.

\[ \text{Moles of HNO}_3 = 2 \times \text{Moles of Fe}^{2+} = 2 \times 0.143 \text{ mol} \approx 0.286 \text{ mol} \]

### Step 5: Calculate the volume of HNO₃ needed
We know the molarity (M) of HNO₃ is 3 mol/L. We can use the formula:

\[ \text{Molarity} = \frac{\text{moles}}{\text{volume (L)}} \]

Rearranging this gives us:

\[ \text{Volume (L)} = \frac{\text{moles}}{\text{Molarity}} = \frac{0.286 \text{ mol}}{3 \text{ mol/L}} \approx 0.0953 \text{ L} \]

To convert this to milliliters:

\[ \text{Volume (mL)} = 0.0953 \text{ L} \times 1000 \text{ mL/L} \approx 95.3 \text{ mL} \]

### Final Answer
The volume of 3 molar HNO₃ needed to oxidize 8 g of Fe³⁺ is approximately **95.3 mL**.

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