The molarity of 20% (W/W) solution of sulphuric acid is 2.55 M. The density of the solution is :

Options

A. 1.25 g `cm^(-3)`
B. 0.125 g `L^(-1)`
C. 2.25 g `cm^(-3)`
D. unpredictable

Explanation

To find the density of a 20% (W/W) solution of sulfuric acid given that its molarity is 2.55 M, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Molarity (M) = 2.55 M
- Weight/Weight percentage (W/W) = 20%
- Assume the weight of the solution = 100 g for simplicity.

2. **Calculate the Weight of the Solute:**
- Since it is a 20% (W/W) solution, the weight of the solute (H₂SO₄) in 100 g of solution is:
\[ \text{Weight of solute} = 20\% \text{ of } 100 \text{ g} = 20 \text{ g} \]

3. **Calculate the Molar Mass of Sulfuric Acid (H₂SO₄):**
- The molar mass of H₂SO₄ is 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
- Total = 2 + 32 + 64 = 98 g/mol

4. **Calculate the Number of Moles of Solute:**
- Using the weight of the solute and its molar mass, the number of moles of H₂SO₄ can be calculated:
\[ \text{Number of moles} = \frac{\text{Weight of solute}}{\text{Molar mass}} = \frac{20 \text{ g}}{98 \text{ g/mol}} \approx 0.2041 \text{ moles} \]

5. **Calculate the Volume of the Solution:**
- Molarity is defined as the number of moles of solute per liter of solution. Rearranging the formula gives:
\[ \text{Volume of solution (L)} = \frac{\text{Number of moles}}{\text{Molarity}} = \frac{0.2041 \text{ moles}}{2.55 \text{ M}} \approx 0.0800 \text{ L} \]
- Converting liters to milliliters:
\[ \text{Volume of solution (mL)} = 0.0800 \text{ L} \times 1000 \text{ mL/L} = 80.0 \text{ mL} \]

6. **Calculate the Density of the Solution:**
- Density is defined as mass per unit volume. Therefore:
\[ \text{Density} = \frac{\text{Weight of solution}}{\text{Volume of solution}} = \frac{100 \text{ g}}{80.0 \text{ mL}} = 1.25 \text{ g/mL} \]

### Final Answer:
The density of the 20% (W/W) solution of sulfuric acid is **1.25 g/mL**.