Concentrated aqueous solution of sulphuric acid is `98 %` by mass and has density of `1.80 "g mL"^(-1)`. What is the volume of acid required to make one liter `0.1 M H_(2)SO_(4)` solution ?

Options

A. 16.65 mL
B. 22.20 mL
C. 5.55 mL
D. 11.10 mL

Answer

To solve the problem of finding the volume of concentrated sulfuric acid required to prepare 1 liter of a 0.1 M H₂SO₄ solution, we can follow these steps:

### Step 1: Calculate the molar mass of H₂SO₄
The molar mass of sulfuric acid (H₂SO₄) can be calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Sulfur (S): 32 g/mol × 1 = 32 g/mol
- Oxygen (O): 16 g/mol × 4 = 64 g/mol

Adding these together:
\[ \text{Molar mass of H₂SO₄} = 2 + 32 + 64 = 98 \, \text{g/mol} \]

### Step 2: Calculate the molarity of the concentrated sulfuric acid solution
We know the mass percentage and density of the concentrated sulfuric acid solution:
- Mass percentage = 98%
- Density = 1.80 g/mL

Using the formula for molarity (M):
\[ M = \left( \frac{\text{mass percentage} \times \text{density} \times 10}{\text{molar mass}} \right) \]

Substituting the values:
\[ M = \left( \frac{98 \times 1.80 \times 10}{98} \right) \]
\[ M = 18 \, \text{M} \]

### Step 3: Use the dilution equation to find the volume of concentrated acid needed
We can use the dilution equation:
\[ M_1 V_1 = M_2 V_2 \]
Where:
- \( M_1 \) = molarity of concentrated solution = 18 M
- \( V_1 \) = volume of concentrated solution (what we are trying to find)
- \( M_2 \) = molarity of diluted solution = 0.1 M
- \( V_2 \) = volume of diluted solution = 1 L = 1000 mL

Substituting the known values into the equation:
\[ 18 \, V_1 = 0.1 \times 1000 \]
\[ 18 \, V_1 = 100 \]
\[ V_1 = \frac{100}{18} \]
\[ V_1 \approx 5.56 \, \text{mL} \]

### Final Answer
The volume of concentrated sulfuric acid required to make 1 liter of a 0.1 M H₂SO₄ solution is approximately **5.56 mL**.

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