The volume strength of `1*5` N `H_(2)O_(2)` solution is

Options

A. `4*8`
B. `5*2`
C. `8*8`
D. `8*4`.

Explanation

To find the volume strength of a 1.5 N solution of hydrogen peroxide (H₂O₂), we will follow these steps:

### Step 1: Understand Normality
Normality (N) is defined as the number of equivalents of solute per liter of solution. For hydrogen peroxide, the equivalent weight can be calculated based on its reaction in producing oxygen gas.

### Step 2: Calculate the Equivalent Weight of H₂O₂
The molecular weight of H₂O₂ is calculated as follows:
- H: 1 g/mol (2 H = 2 g/mol)
- O: 16 g/mol (2 O = 32 g/mol)
- Total molecular weight of H₂O₂ = 2 + 32 = 34 g/mol

In the reaction:
\[ 2 H_2O_2 \rightarrow 2 H_2O + O_2 \]
1 mole of H₂O₂ produces 0.5 moles of O₂. Therefore, the equivalent weight of H₂O₂ is:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{n} = \frac{34 \text{ g/mol}}{1} = 34 \text{ g/equiv} \]

### Step 3: Calculate the Weight of H₂O₂ in 1 L of 1.5 N Solution
Using the normality:
\[ \text{Normality} = \frac{\text{Number of equivalents}}{\text{Volume in liters}} \]
For a 1.5 N solution:
\[ \text{Number of equivalents in 1 L} = 1.5 \text{ equivalents} \]

The weight of H₂O₂ in 1 L of the solution can be calculated as:
\[ \text{Weight} = \text{Number of equivalents} \times \text{Equivalent weight} \]
\[ \text{Weight} = 1.5 \times 34 = 51 \text{ grams} \]

### Step 4: Calculate the Volume of O₂ Produced
From the reaction, 34 grams of H₂O₂ produce 16 grams of O₂. Thus, we can find the grams of O₂ produced from 51 grams of H₂O₂:
\[ \text{O}_2 \text{ produced} = \frac{16 \text{ g O}_2}{34 \text{ g H}_2O_2} \times 51 \text{ g H}_2O_2 \]
\[ \text{O}_2 \text{ produced} = \frac{16 \times 51}{34} = 24 \text{ grams} \]

### Step 5: Calculate the Volume of O₂ at STP
At standard temperature and pressure (STP), 1 mole of gas occupies 22,400 mL. The molecular weight of O₂ is 32 g/mol, so:
\[ \text{Number of moles of O}_2 = \frac{24 \text{ g}}{32 \text{ g/mol}} = 0.75 \text{ moles} \]

Now, calculate the volume of O₂ produced:
\[ \text{Volume of O}_2 = 0.75 \text{ moles} \times 22,400 \text{ mL/mole} = 16,800 \text{ mL} \]

### Step 6: Calculate the Volume Strength
The volume strength is defined as the volume of O₂ produced from 1 mL of H₂O₂ solution. Since we have calculated the volume of O₂ produced from 1 L (1000 mL) of solution:
\[ \text{Volume strength} = \frac{16,800 \text{ mL}}{1000 \text{ mL}} = 16.8 \]

### Final Answer
The volume strength of a 1.5 N H₂O₂ solution is **16.8**.

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