Calculate the strength of 5 volume `H_2O_2` solution. Round off answer in two digits

Explanation

To calculate the strength of a 5 volume H₂O₂ solution, we can follow these steps:

### Step 1: Understand the Meaning of "5 Volume"
The term "5 volume" means that 1 liter of the H₂O₂ solution will produce 5 liters of O₂ gas when it decomposes.

### Step 2: Write the Decomposition Reaction
The decomposition of hydrogen peroxide (H₂O₂) can be represented by the following balanced chemical equation:
\[ 2 \, H_2O_2 \, \rightarrow \, 2 \, H_2O + O_2 \]

### Step 3: Calculate the Volume of O₂ Produced
From the definition of "5 volume," we know that 1 liter of 5 volume H₂O₂ will produce 5 liters of O₂ at Normal Temperature and Pressure (NTP).

### Step 4: Use Molar Volume at NTP
At NTP, 1 mole of any gas occupies 22.4 liters. Therefore, to find how many moles of O₂ are produced, we can use the volume of O₂ produced:
\[ \text{Moles of } O_2 = \frac{5 \, \text{liters}}{22.4 \, \text{liters/mole}} \approx 0.223 \, \text{moles} \]

### Step 5: Relate Moles of O₂ to Moles of H₂O₂
From the balanced equation, we see that 1 mole of O₂ is produced from 2 moles of H₂O₂. Therefore, the moles of H₂O₂ required to produce 0.223 moles of O₂ is:
\[ \text{Moles of } H_2O_2 = 2 \times 0.223 \approx 0.446 \, \text{moles} \]

### Step 6: Calculate the Mass of H₂O₂
The molar mass of H₂O₂ (hydrogen peroxide) is approximately 34 g/mol. Therefore, the mass of H₂O₂ in the solution is:
\[ \text{Mass of } H_2O_2 = 0.446 \, \text{moles} \times 34 \, \text{g/mol} \approx 15.16 \, \text{grams} \]

### Step 7: Calculate the Strength of the Solution
The strength of a solution is defined as the mass of solute (H₂O₂) in grams per liter of solution. Since we have 15.16 grams of H₂O₂ in 1 liter of solution, the strength is:
\[ \text{Strength} = \frac{15.16 \, \text{grams}}{1 \, \text{liter}} = 15.16 \, \text{g/L} \]

### Step 8: Round Off the Answer
Rounding off the strength to two decimal places, we get:
\[ \text{Strength} \approx 15.16 \, \text{g/L} \]

### Final Answer
The strength of the 5 volume H₂O₂ solution is approximately **15.16 g/L**.

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