What volume of 96% `H_(2)SO_(4)` solution (density 1.83 g/mL) is required to prepare 4 litre of 3.0 M `H_(2)SO_(4)` solution ?

Options

A. 335 ml
B. 670 ml
C. 167.5 ml
D. 572 ml

Answer

To solve the problem of determining the volume of 96% H₂SO₄ solution needed to prepare 4 liters of a 3.0 M H₂SO₄ solution, we can follow these steps:

### Step 1: Calculate the number of moles of H₂SO₄ needed
We know that molarity (M) is defined as the number of moles of solute per liter of solution.

\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \]

Given:
- Molarity = 3.0 M
- Volume = 4 L

\[ \text{Number of moles} = 3.0 \, \text{mol/L} \times 4 \, \text{L} = 12 \, \text{moles} \]

### Step 2: Calculate the mass of H₂SO₄ required
Next, we need to calculate the mass of H₂SO₄ required using its molar mass. The molar mass of H₂SO₄ is approximately 98 g/mol.

\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]

\[ \text{Mass} = 12 \, \text{moles} \times 98 \, \text{g/mol} = 1176 \, \text{grams} \]

### Step 3: Calculate the mass of the 96% H₂SO₄ solution needed
Since we have a 96% solution, we need to find out how much of this solution contains the required mass of H₂SO₄.

Let \( X \) be the mass of the 96% solution. The mass of H₂SO₄ in this solution is 96% of \( X \).

\[ 0.96X = 1176 \, \text{grams} \]

Solving for \( X \):

\[ X = \frac{1176}{0.96} = 1225 \, \text{grams} \]

### Step 4: Calculate the volume of the 96% H₂SO₄ solution
Now that we have the mass of the 96% solution, we can find the volume using the density.

Given:
- Density = 1.83 g/mL

Using the formula for density:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Substituting the values:

\[ \text{Volume} = \frac{1225 \, \text{grams}}{1.83 \, \text{g/mL}} \approx 669.45 \, \text{mL} \]

### Step 5: Round the volume
Rounding this value gives us approximately:

\[ \text{Volume} \approx 670 \, \text{mL} \]

### Final Answer
The volume of 96% H₂SO₄ solution required to prepare 4 liters of a 3.0 M H₂SO₄ solution is approximately **670 mL**.

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