`5.0 cm^(3)` of `H_(2)O_(2)` liberates 0.508 g of iodine from an acidified KI solution. The strength of `H_(2)O_(2)` solution in terms of volume strenth at STP is

Options

A. 6.48 volumes
B. 4.48 volumes
C. 7.68 volumes
D. none of these

Explanation

To find the strength of the `H2O2` solution in terms of volume strength at STP, we will follow these steps:

### Step 1: Calculate moles of iodine (I2) produced
We start by calculating the number of moles of iodine produced from the given mass.

\[ \text{Moles of I}_2 = \frac{\text{mass of I}_2}{\text{molar mass of I}_2} \]

Given:
- Mass of iodine (I2) = 0.508 g
- Molar mass of iodine (I2) = 254 g/mol

\[ \text{Moles of I}_2 = \frac{0.508 \, \text{g}}{254 \, \text{g/mol}} = 0.002 \, \text{mol} \]

### Step 2: Use the stoichiometry of the reaction
The balanced chemical reaction for the reaction between `H2O2` and `I-` is:

\[ \text{H}_2\text{O}_2 + 2\text{I}^- + 2\text{H}^+ \rightarrow 2\text{H}_2\text{O} + \text{I}_2 \]

From the reaction, we see that 1 mole of `H2O2` produces 1 mole of `I2`. Therefore, the moles of `H2O2` used will also be 0.002 mol.

### Step 3: Calculate the molarity of `H2O2`
We know the volume of `H2O2` used is 5.0 cm³, which is equivalent to 0.005 L.

Using the formula for molarity:

\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in L}} \]

\[ \text{Molarity of H}_2\text{O}_2 = \frac{0.002 \, \text{mol}}{0.005 \, \text{L}} = 0.4 \, \text{M} \]

### Step 4: Calculate the normality of `H2O2`
The n-factor for `H2O2` in this reaction is 2 (since it reacts with 2 moles of `I-`).

\[ \text{Normality (N)} = \text{Molarity (M)} \times \text{n-factor} \]

\[ \text{Normality of H}_2\text{O}_2 = 0.4 \, \text{M} \times 2 = 0.8 \, \text{N} \]

### Step 5: Calculate the volume strength of `H2O2`
The volume strength of a solution is calculated using the formula:

\[ \text{Volume Strength} = \text{Normality} \times 5.6 \]

\[ \text{Volume Strength of H}_2\text{O}_2 = 0.8 \, \text{N} \times 5.6 = 4.48 \, \text{volumes} \]

### Final Answer
The strength of the `H2O2` solution in terms of volume strength at STP is **4.48 volumes**.

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