`H_(2)O_(2)` is used as bleaching reagent because on dissociation it gives oxygen
`(H_(2)O_(2) to H_(2)O+(1)/(2)O_(2))`
"Chachi420" used `H_(2)O_(2)` solution to bleach her hair and she required `2.24L O_(2)` gas at 1atm and 273K. She has a `H_(2)O_(2)` solution labelled '5.6V' then what volume of such solution must she required to bleach her hair?

Options

A. 200mL
B. 300mL
C. 400mL
D. 500mL

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the dissociation of H₂O₂
The dissociation of hydrogen peroxide (H₂O₂) can be represented by the equation:
\[ \text{H}_2\text{O}_2 \rightarrow \text{H}_2\text{O} + \frac{1}{2}\text{O}_2 \]
This means that 1 mole of H₂O₂ produces 0.5 moles of O₂.

### Step 2: Calculate the number of moles of O₂ required
We are given that Chachi420 requires 2.24 L of O₂ at standard temperature and pressure (STP: 1 atm and 273 K). At STP, 1 mole of any gas occupies 22.4 L. Therefore, we can calculate the number of moles of O₂ required:
\[ \text{Number of moles of O}_2 = \frac{\text{Volume of O}_2}{\text{Molar volume at STP}} = \frac{2.24 \, \text{L}}{22.4 \, \text{L/mol}} = 0.1 \, \text{mol} \]

### Step 3: Determine the moles of H₂O₂ needed
From the stoichiometry of the dissociation reaction, we know that:
- 1 mole of H₂O₂ produces 0.5 moles of O₂.
- Therefore, to produce 0.1 moles of O₂, we need:
\[ \text{Moles of H}_2\text{O}_2 = 2 \times \text{Moles of O}_2 = 2 \times 0.1 \, \text{mol} = 0.2 \, \text{mol} \]

### Step 4: Calculate the molarity of the H₂O₂ solution
The H₂O₂ solution is labeled as '5.6 V', which means that 1 mL of H₂O₂ produces 5.6 mL of O₂. To find the molarity, we can use the relationship between volume strength and molarity:
\[ \text{Volume strength} = 11.2 \times \text{Molarity} \]
Given that the volume strength is 5.6 V, we can rearrange the equation to find the molarity:
\[ \text{Molarity} = \frac{5.6}{11.2} = 0.5 \, \text{mol/L} \]

### Step 5: Calculate the volume of H₂O₂ solution required
We have the number of moles of H₂O₂ needed (0.2 mol) and the molarity of the solution (0.5 mol/L). We can use the formula for molarity to find the volume:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]
Rearranging gives:
\[ \text{Volume in liters} = \frac{\text{Number of moles}}{\text{Molarity}} = \frac{0.2 \, \text{mol}}{0.5 \, \text{mol/L}} = 0.4 \, \text{L} \]
Converting this to milliliters:
\[ 0.4 \, \text{L} = 0.4 \times 1000 \, \text{mL} = 400 \, \text{mL} \]

### Final Answer
Chachi420 will require **400 mL** of the H₂O₂ solution to bleach her hair.

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