What mass of `HNO_(3)` is needed to convert 5 gm of iodine into iodic acid according to the reaction?
`I_(2) + HNO_(3) rArr HIO_(3) + NO_(2) + H_(2)O`

Options

A. 12.4gm
B. 24.8gm
C. 0.248gm
D. 1.24gm

Answer

To determine the mass of `HNO₃` needed to convert 5 g of iodine into iodic acid according to the reaction:

\[ I_2 + 10 HNO_3 \rightarrow 2 HIO_3 + 10 NO_2 + 4 H_2O \]

we will follow these steps:

### Step 1: Write the balanced chemical equation
The balanced equation is already provided:

\[ I_2 + 10 HNO_3 \rightarrow 2 HIO_3 + 10 NO_2 + 4 H_2O \]

### Step 2: Calculate the moles of iodine (I₂)
To find the moles of iodine, we use the formula:

\[ \text{Moles of } I_2 = \frac{\text{mass of } I_2}{\text{molar mass of } I_2} \]

Given:
- Mass of iodine = 5 g
- Molar mass of iodine (I₂) = 2 × 126.9 g/mol = 253.8 g/mol (approximately 254 g/mol)

Calculating the moles:

\[ \text{Moles of } I_2 = \frac{5 \text{ g}}{254 \text{ g/mol}} \approx 0.0197 \text{ moles} \]

### Step 3: Determine the moles of `HNO₃` required
From the balanced equation, 1 mole of `I₂` reacts with 10 moles of `HNO₃`. Therefore, the moles of `HNO₃` required can be calculated as:

\[ \text{Moles of } HNO_3 = 10 \times \text{Moles of } I_2 \]

Calculating:

\[ \text{Moles of } HNO_3 = 10 \times 0.0197 \approx 0.197 \text{ moles} \]

### Step 4: Calculate the mass of `HNO₃`
To find the mass of `HNO₃`, we use the formula:

\[ \text{Mass of } HNO_3 = \text{Moles of } HNO_3 \times \text{Molar mass of } HNO_3 \]

Given:
- Molar mass of `HNO₃` = 63 g/mol

Calculating the mass:

\[ \text{Mass of } HNO_3 = 0.197 \text{ moles} \times 63 \text{ g/mol} \approx 12.41 \text{ g} \]

### Final Answer
The mass of `HNO₃` needed to convert 5 g of iodine into iodic acid is approximately **12.41 g**.

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