Calculate the strenght of 5 volumes `H_(2)O_(2)` solution.

Explanation

To calculate the strength of a 5 volumes H₂O₂ (hydrogen peroxide) solution, we can follow these steps:

### Step 1: Understand the Concept of "Volumes"
The term "5 volumes" means that 1 liter of the H₂O₂ solution can produce 5 liters of oxygen gas (O₂) at standard temperature and pressure (STP).

### Step 2: Write the Decomposition Reaction of H₂O₂
The decomposition of hydrogen peroxide can be represented by the following balanced chemical equation:
\[ 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \]
This indicates that 2 moles of H₂O₂ decompose to produce 1 mole of O₂.

### Step 3: Calculate the Molar Mass of H₂O₂
The molar mass of H₂O₂ can be calculated as follows:
- Hydrogen (H) = 1 g/mol, and there are 2 H atoms: \( 2 \times 1 = 2 \) g/mol
- Oxygen (O) = 16 g/mol, and there are 2 O atoms: \( 2 \times 16 = 32 \) g/mol
- Therefore, the molar mass of H₂O₂ = \( 2 + 32 = 34 \) g/mol

### Step 4: Determine the Amount of H₂O₂ Required to Produce 5 Liters of O₂
At STP, 1 mole of any gas occupies 22.4 liters. Therefore, to find out how many moles of H₂O₂ are needed to produce 5 liters of O₂:
- Since 2 moles of H₂O₂ produce 1 mole of O₂, we need:
\[ \text{Moles of O}_2 = \frac{5 \text{ liters}}{22.4 \text{ liters/mole}} \approx 0.223 \text{ moles} \]
- Thus, the moles of H₂O₂ required:
\[ \text{Moles of H}_2\text{O}_2 = 2 \times 0.223 \approx 0.446 \text{ moles} \]

### Step 5: Calculate the Mass of H₂O₂ Required
Now, we can convert moles of H₂O₂ to grams:
\[ \text{Mass of H}_2\text{O}_2 = 0.446 \text{ moles} \times 34 \text{ g/mol} \approx 15.164 \text{ grams} \]

### Step 6: Calculate the Strength of the H₂O₂ Solution
The strength of the solution is defined as the mass of solute (H₂O₂) per liter of solution. Since we have calculated that 1 liter of the 5 volumes H₂O₂ solution contains approximately 15.164 grams of H₂O₂, we can express the strength as:
\[ \text{Strength} = 15.164 \text{ g/L} \]

### Step 7: Calculate the Percentage Strength
To find the percentage strength of the H₂O₂ solution:
\[ \text{Percentage Strength} = \left( \frac{\text{mass of solute (g)}}{\text{volume of solution (mL)}} \right) \times 100 \]
\[ \text{Percentage Strength} = \left( \frac{15.164 \text{ g}}{1000 \text{ mL}} \right) \times 100 \approx 1.5164\% \]

### Final Answer
- The strength of the 5 volumes H₂O₂ solution is approximately **15.164 g/L**.
- The percentage strength is approximately **1.52%**.