50 ml of '20 V' `H_(2)O_(2)` is mixed with 200 ml, '10 V' `H_(2)O_(2).` The volume strength of resulting solution is:

Answer

To solve the problem of finding the volume strength of the resulting solution when mixing two different concentrations of hydrogen peroxide (H₂O₂), we can follow these steps:

### Step 1: Understand the Volume Strength
Volume strength (V) of a solution indicates how many milliliters of oxygen gas (O₂) are produced by one milliliter of the solution at standard conditions. For hydrogen peroxide, a '20 V' solution means that 1 mL of the solution will produce 20 mL of O₂.

### Step 2: Identify Given Values
We have:
- Volume strength of solution 1 (V₁) = 20 V
- Volume of solution 1 (V₁) = 50 mL
- Volume strength of solution 2 (V₂) = 10 V
- Volume of solution 2 (V₂) = 200 mL

### Step 3: Calculate Total Volume of the Mixture
The total volume (V₃) of the resulting solution after mixing is:
\[ V₃ = V₁ + V₂ = 50 \, \text{mL} + 200 \, \text{mL} = 250 \, \text{mL} \]

### Step 4: Use the Volume Strength Formula
The formula to find the volume strength of the resulting solution (V₃) is given by:
\[ V₁ \times \text{Volume of solution 1} + V₂ \times \text{Volume of solution 2} = V₃ \times \text{Total Volume} \]

Substituting the known values:
\[ (20 \times 50) + (10 \times 200) = V₃ \times 250 \]

### Step 5: Calculate the Left Side of the Equation
Calculating the left side:
\[ 20 \times 50 = 1000 \]
\[ 10 \times 200 = 2000 \]
So,
\[ 1000 + 2000 = 3000 \]

### Step 6: Set Up the Equation
Now we have:
\[ 3000 = V₃ \times 250 \]

### Step 7: Solve for Volume Strength of Resulting Solution
To find \( V₃ \), we rearrange the equation:
\[ V₃ = \frac{3000}{250} \]

Calculating this gives:
\[ V₃ = 12 \]

### Final Answer
The volume strength of the resulting solution is **12 V**.

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