80 mL of `M/24 K_(2)Cr_(2)O_(7)` oxidises 22.4 mL `H_(2)O_(2)` solution. Find volume strength of `H_(2)O_(2)` solution.

Explanation

To solve the problem, we need to find the volume strength of the hydrogen peroxide (H₂O₂) solution that is oxidized by the potassium dichromate (K₂Cr₂O₇). Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Reaction
The reaction between potassium dichromate and hydrogen peroxide can be represented as follows:
\[ \text{H}_2\text{O}_2 + 2 \text{H}^+ + \text{Cr}_2\text{O}_7^{2-} \rightarrow 2 \text{Cr}^{3+} + 2 \text{H}_2\text{O} + \text{O}_2 \]

From this equation, we can see that 1 mole of H₂O₂ produces 0.5 moles of O₂.

### Step 2: Calculate the Moles of K₂Cr₂O₇
Given:
- Volume of K₂Cr₂O₇ = 80 mL
- Molarity of K₂Cr₂O₇ = \( \frac{1}{24} \) M

To find the number of moles of K₂Cr₂O₇:
\[ \text{Moles of K}_2\text{Cr}_2\text{O}_7 = \text{Molarity} \times \text{Volume (in L)} = \frac{1}{24} \times \frac{80}{1000} = \frac{80}{24000} = \frac{1}{300} \text{ moles} \]

### Step 3: Calculate the Equivalent of K₂Cr₂O₇
The number of equivalents of K₂Cr₂O₇ can be calculated using its valency factor. The valency factor for K₂Cr₂O₇ in this reaction is 6 (because it can oxidize 6 moles of electrons).
\[ \text{Equivalents of K}_2\text{Cr}_2\text{O}_7 = \text{Moles} \times \text{Valency Factor} = \frac{1}{300} \times 6 = \frac{6}{300} = \frac{1}{50} \]

### Step 4: Calculate the Equivalents of H₂O₂
Since the equivalents of K₂Cr₂O₇ are equal to the equivalents of H₂O₂ in the reaction:
\[ \text{Equivalents of H}_2\text{O}_2 = \frac{1}{50} \]

### Step 5: Calculate the Moles of H₂O₂
Given:
- Volume of H₂O₂ = 22.4 mL

To find the number of moles of H₂O₂:
\[ \text{Equivalents of H}_2\text{O}_2 = \text{Moles} \times \text{Valency Factor} \]
The valency factor for H₂O₂ is 1 (since it gives 1 mole of O₂).
Thus,
\[ \frac{1}{50} = \text{Moles of H}_2\text{O}_2 \times 1 \implies \text{Moles of H}_2\text{O}_2 = \frac{1}{50} \]

### Step 6: Calculate the Molarity of H₂O₂
To find the molarity of H₂O₂:
\[ \text{Molarity} = \frac{\text{Moles}}{\text{Volume (in L)}} = \frac{\frac{1}{50}}{\frac{22.4}{1000}} = \frac{1}{50} \times \frac{1000}{22.4} = \frac{20}{22.4} \approx 0.8929 \text{ M} \]

### Step 7: Calculate the Volume Strength of H₂O₂
The volume strength of H₂O₂ is defined as the volume of O₂ produced by 1 liter of H₂O₂ at STP. Since 1 mole of H₂O₂ produces 0.5 moles of O₂, we can use the molarity to find the volume strength:
\[ \text{Volume Strength} = \text{Molarity} \times 11.2 \text{ L} = 0.8929 \times 11.2 \approx 10 \text{ V} \]

### Final Answer
The volume strength of the H₂O₂ solution is approximately **10 V**.

---