Calculate the volume strength of `H_(2)O_(2)` solution if `50 mL` of `H_(2)O_(2)` solution is diluted with `50 mL` of `H_(2)O. 20 mL of this diluted solution required 40 mL of `M//60 K_(2)Cr_(2)O_(7)` solution in presence of `H_(2)O_(2)` for complete reaction.

Explanation

To calculate the volume strength of the `H2O2` solution, we will follow these steps:

### Step 1: Understand the Reaction
Hydrogen peroxide (`H2O2`) acts as a reducing agent and will react with potassium dichromate (`K2Cr2O7`). The relevant half-reactions are:
- For `H2O2`:
\[ 2H^+ + O_2 + 2e^- \quad (n \text{ factor} = 2) \]
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