Strength of 10 volume hydrogen peroxide solution means

Options

A. `30.36 gL^(-1)`
B. `17 gL^(-1)`
C. `34 gL^(-1)`
D. `68 gL^(-1)`

Explanation

To determine the strength of a 10 volume hydrogen peroxide (H2O2) solution, we can follow these steps:

### Step 1: Understand the Concept of Volume Strength
The term "10 volume" means that 1 liter of the hydrogen peroxide solution can produce 10 liters of oxygen gas (O2) at normal temperature and pressure (NTP).

### Step 2: Write the Reaction Equation
The decomposition of hydrogen peroxide can be represented by the following balanced chemical equation:
\[ 2 \, \text{H}_2\text{O}_2 \rightarrow 2 \, \text{H}_2\text{O} + \text{O}_2 \]

### Step 3: Determine Moles of H2O2 Required
From the balanced equation, we see that 2 moles of H2O2 produce 1 mole of O2. Therefore, to produce 10 liters of O2, we need to calculate how many moles of H2O2 are required.

### Step 4: Calculate Moles of O2
At NTP, 1 mole of gas occupies 22.4 liters. Therefore, the number of moles of O2 produced from 10 liters is:
\[ \text{Moles of O2} = \frac{10 \, \text{liters}}{22.4 \, \text{liters/mole}} \approx 0.4464 \, \text{moles} \]

### Step 5: Calculate Moles of H2O2 Required
Since 2 moles of H2O2 produce 1 mole of O2, the moles of H2O2 required to produce 0.4464 moles of O2 is:
\[ \text{Moles of H2O2} = 2 \times 0.4464 \approx 0.8928 \, \text{moles} \]

### Step 6: Calculate Mass of H2O2
The molar mass of H2O2 is calculated as follows:
- Hydrogen (H) = 1 g/mol, so for 2 H: \(2 \times 1 = 2 \, \text{g/mol}\)
- Oxygen (O) = 16 g/mol, so for 2 O: \(2 \times 16 = 32 \, \text{g/mol}\)
- Total molar mass of H2O2 = \(2 + 32 = 34 \, \text{g/mol}\)

Now, we can calculate the mass of H2O2 required:
\[ \text{Mass of H2O2} = \text{Moles} \times \text{Molar Mass} = 0.8928 \, \text{moles} \times 34 \, \text{g/mol} \approx 30.36 \, \text{grams} \]

### Step 7: Determine Strength of the Solution
Since the strength of the solution is expressed in grams per liter, we conclude that the strength of a 10 volume hydrogen peroxide solution is:
\[ \text{Strength} = 30.36 \, \text{grams per liter} \]

### Final Answer
The strength of a 10 volume hydrogen peroxide solution is **30.36 grams per liter**.

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