Peroxides are basic in nature and they form hydrogen peroxides on treatment with acid. What volume of 0.5 M `H_(2)SO_(4)` solution is required to neutralise a solution containing 7.2 g of `CaO_(2)` ?

Options

A. 400 ml
B. 300 ml
C. 200 ml
D. 100 ml

Answer

To solve the problem, we need to determine the volume of 0.5 M H₂SO₄ required to neutralize a solution containing 7.2 g of CaO₂ (calcium peroxide). Here’s a step-by-step solution:

### Step 1: Calculate the Molar Mass of CaO₂
The molar mass of calcium peroxide (CaO₂) can be calculated as follows:
- Atomic mass of Calcium (Ca) = 40 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol

Molar mass of CaO₂ = 40 + (2 × 16) = 40 + 32 = 72 g/mol

### Step 2: Calculate the Number of Moles of CaO₂
Using the mass of CaO₂ given (7.2 g), we can calculate the number of moles:
\[ \text{Number of moles of CaO₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{7.2 \text{ g}}{72 \text{ g/mol}} = 0.1 \text{ mol} \]

### Step 3: Determine the Equivalent Weight of CaO₂
The equivalent weight of CaO₂ can be calculated using its molar mass and the n-factor. The n-factor for CaO₂ is 2 (since it can donate two moles of H⁺ ions when reacting with an acid).
\[ \text{Equivalent weight of CaO₂} = \frac{\text{Molar mass}}{\text{n-factor}} = \frac{72 \text{ g/mol}}{2} = 36 \text{ g/equiv} \]

### Step 4: Calculate the Number of Gram Equivalents of CaO₂
Using the equivalent weight calculated, we can find the number of gram equivalents of CaO₂:
\[ \text{Number of gram equivalents of CaO₂} = \frac{\text{mass}}{\text{equivalent weight}} = \frac{7.2 \text{ g}}{36 \text{ g/equiv}} = 0.2 \text{ equiv} \]

### Step 5: Calculate the Normality of H₂SO₄
The normality (N) of H₂SO₄ is given as 0.5 M. Since H₂SO₄ has an n-factor of 2 (it can donate 2 H⁺ ions), the normality is:
\[ \text{Normality of H₂SO₄} = \text{Molarity} \times \text{n-factor} = 0.5 \text{ M} \times 2 = 1 \text{ N} \]

### Step 6: Use the Neutralization Equation
According to the neutralization reaction, the number of equivalents of H₂SO₄ will equal the number of equivalents of CaO₂:
\[ N_1V_1 = N_2V_2 \]
Where:
- \(N_1\) = Normality of H₂SO₄ = 1 N
- \(V_1\) = Volume of H₂SO₄ (in liters) = ?
- \(N_2\) = Number of gram equivalents of CaO₂ = 0.2 equiv

Substituting the known values:
\[ 1 \times V_1 = 0.2 \]
Thus,
\[ V_1 = 0.2 \text{ L} \]

### Step 7: Convert Volume to Milliliters
To convert liters to milliliters:
\[ V_1 = 0.2 \text{ L} \times 1000 \text{ mL/L} = 200 \text{ mL} \]

### Final Answer
The volume of 0.5 M H₂SO₄ required to neutralize 7.2 g of CaO₂ is **200 mL**.

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