20 ml of `20 vol` `H_(2)O_(2)` solution is diluted to 80 ml. The final volume strength of solution is

Options

A. 80 vol'
B. 25 vol'
C. 5 vol'
D. 8 vol'

Answer

To solve the problem, we need to find the final volume strength of the hydrogen peroxide (H₂O₂) solution after dilution. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Given Data
- Initial volume (V₁) = 20 ml
- Initial volume strength (S₁) = 20 vol
- Final volume (V₂) = 80 ml
- Final volume strength (S₂) = ?

### Step 2: Use the Volume Strength Formula
The relationship between the initial and final conditions can be expressed as:
\[ V₁ \times S₁ = V₂ \times S₂ \]
Where:
- V₁ = initial volume
- S₁ = initial volume strength
- V₂ = final volume
- S₂ = final volume strength

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ 20 \, \text{ml} \times 20 \, \text{vol} = 80 \, \text{ml} \times S₂ \]

### Step 4: Calculate the Left Side
Calculate the left side of the equation:
\[ 20 \times 20 = 400 \]

### Step 5: Set Up the Equation
Now, we have:
\[ 400 = 80 \times S₂ \]

### Step 6: Solve for S₂
To find S₂, divide both sides by 80:
\[ S₂ = \frac{400}{80} \]
\[ S₂ = 5 \, \text{vol} \]

### Conclusion
The final volume strength of the solution is **5 vol**.