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. (a)`16.65 mL`
B. (b)`22.20 mL`
C. (c )`5.55 mL`
D. (d)`11.10 mL`

Explanation

To solve this problem, we need to determine the volume of concentrated sulfuric acid (H₂SO₄) required to prepare 1 liter of a 0.1 M H₂SO₄ solution. Let's break down the solution step by step:

### Step 1: Calculate the volume of the concentrated H₂SO₄ solution
Given:
- Concentrated H₂SO₄ solution is 98% by mass.
- Density of the concentrated H₂SO₄ solution is 1.80 g/mL.

First, we need to find the volume of the concentrated H₂SO₄ solution that contains 98 grams of H₂SO₄.

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

Since the solution is 98% H₂SO₄ by mass, 100 grams of the solution contains 98 grams of H₂SO₄.

\[ \text{Volume of solution} = \frac{100 \text{ g}}{1.80 \text{ g/mL}} = 55.56 \text{ mL} \]

Convert this volume to liters:

\[ 55.56 \text{ mL} = 0.05556 \text{ L} \]

### Step 2: Calculate the molarity of the concentrated H₂SO₄ solution
Molarity (M) is defined as the number of moles of solute per liter of solution.

First, calculate the number of moles of H₂SO₄ in 98 grams:

\[ \text{Molar mass of H₂SO₄} = 2 \times 1 + 32 + 4 \times 16 = 98 \text{ g/mol} \]

\[ \text{Number of moles} = \frac{98 \text{ g}}{98 \text{ g/mol}} = 1 \text{ mole} \]

Now, calculate the molarity of the concentrated solution:

\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} = \frac{1 \text{ mole}}{0.05556 \text{ L}} = 18.02 \text{ M} \]

### Step 3: Use the dilution formula to find the required volume
We need to prepare 1 liter of a 0.1 M H₂SO₄ solution using the concentrated 18.02 M H₂SO₄ solution. We use the dilution formula:

\[ M_1 V_1 = M_2 V_2 \]

Where:
- \( M_1 \) = 18.02 M (molarity of concentrated solution)
- \( V_1 \) = volume of concentrated solution needed
- \( M_2 \) = 0.1 M (molarity of the desired solution)
- \( V_2 \) = 1 L (volume of the desired solution)

Rearrange to solve for \( V_1 \):

\[ V_1 = \frac{M_2 V_2}{M_1} = \frac{0.1 \text{ M} \times 1 \text{ L}}{18.02 \text{ M}} = 0.00555 \text{ L} \]

Convert this volume to milliliters:

\[ 0.00555 \text{ L} = 5.55 \text{ mL} \]

### Final Answer:
The volume of concentrated H₂SO₄ required to make 1 liter of a 0.1 M H₂SO₄ solution is **5.55 mL**.