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 80 mL of M/24 potassium dichromate (K₂Cr₂O₇). Here's a step-by-step breakdown of the solution:

### Step 1: Write the balanced chemical reaction
The reaction between potassium dichromate and hydrogen peroxide can be represented as follows:

\[ K_2Cr_2O_7 + H_2O_2 \rightarrow Cr^{3+} + O_2 + H_2O \]

### Step 2: Determine the oxidation states
In K₂Cr₂O₇, the oxidation state of chromium (Cr) is +6. In the reaction, Cr is reduced to Cr³⁺, and H₂O₂ is oxidized to O₂.

### Step 3: Calculate the normality of K₂Cr₂O₇
The normality (N) of a solution can be calculated using the formula:

\[ N = n \times M \]

Where:
- \( n \) = number of electrons transferred (for K₂Cr₂O₇, n = 6)
- \( M \) = molarity of the solution

Given that the molarity of K₂Cr₂O₇ is \( \frac{1}{24} \) M, we can calculate the normality:

\[ N_{K_2Cr_2O_7} = 6 \times \frac{1}{24} = \frac{6}{24} = \frac{1}{4} \, \text{N} \]

### Step 4: Calculate the milli-equivalents of K₂Cr₂O₇
The milli-equivalents (meq) of K₂Cr₂O₇ can be calculated using the formula:

\[ \text{meq} = N \times V \]

Where:
- \( V \) = volume in liters

For K₂Cr₂O₇:

\[ \text{meq}_{K_2Cr_2O_7} = \frac{1}{4} \times 0.080 = 0.02 \, \text{meq} \]

### Step 5: Set up the equation for H₂O₂
Let \( V \) be the volume of H₂O₂ solution in liters. The normality of H₂O₂ is 2 (since it releases 2 electrons during oxidation). Therefore, we can write:

\[ \text{meq}_{H_2O_2} = N \times V = 2 \times V \]

### Step 6: Equate the milli-equivalents
Since the milli-equivalents of K₂Cr₂O₇ and H₂O₂ are equal, we can set up the equation:

\[ 0.02 = 2 \times V \]

### Step 7: Solve for V
Now, we can solve for \( V \):

\[ V = \frac{0.02}{2} = 0.01 \, \text{L} \]

Converting liters to milliliters:

\[ V = 0.01 \times 1000 = 10 \, \text{mL} \]

### Step 8: Calculate the volume strength of H₂O₂
Volume strength is defined as the volume of oxygen gas released at STP by 1 mL of H₂O₂ solution. Since 1 mole of H₂O₂ produces 0.5 moles of O₂, we can calculate the volume strength:

\[ \text{Volume strength} = \text{Volume of O₂ produced} \times 2 = 10 \, \text{mL} \times 2 = 20 \, \text{mL} \]

### Final Answer
The volume strength of the H₂O₂ solution is **20**.

---