The density (in g `ml^(−1)` ) of a 3.60M sulphuric acid solution having 20% `H_2SO_4`[molar mass =98g `mol^(−1)`] by mass, will be:

Options

A. 4.47g/ml
B. 1.76g/ml
C. 6.14g/ml
D. 0.18g/ml

Explanation

To find the density of a 3.60 M sulfuric acid solution that is 20% H₂SO₄ by mass, we can follow these steps:

### Step 1: Understand the given information
- Molarity (M) of the solution = 3.60 M
- Mass percentage of H₂SO₄ = 20%
- Molar mass of H₂SO₄ = 98 g/mol

### Step 2: Calculate the mass of H₂SO₄ in 100 g of solution
Since the mass percentage of H₂SO₄ is 20%, in 100 g of the solution, the mass of H₂SO₄ is:
\[ \text{Mass of H₂SO₄} = 20\% \text{ of } 100 \text{ g} = 20 \text{ g} \]

### Step 3: Calculate the number of moles of H₂SO₄
Using the molar mass of H₂SO₄, we can calculate the number of moles:
\[ \text{Moles of H₂SO₄} = \frac{\text{Mass of H₂SO₄}}{\text{Molar mass of H₂SO₄}} = \frac{20 \text{ g}}{98 \text{ g/mol}} \approx 0.2041 \text{ mol} \]

### Step 4: Use the definition of molarity to find the volume of the solution
Molarity (M) is defined as:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
Rearranging this gives:
\[ \text{Volume of solution} = \frac{\text{moles of solute}}{M} \]
Substituting the values:
\[ \text{Volume of solution} = \frac{0.2041 \text{ mol}}{3.60 \text{ mol/L}} \approx 0.0567 \text{ L} = 56.7 \text{ mL} \]

### Step 5: Calculate the density of the solution
Density (d) is defined as:
\[ d = \frac{\text{mass of solution}}{\text{volume of solution}} \]
The mass of the solution is 100 g (from our initial assumption). Thus:
\[ d = \frac{100 \text{ g}}{56.7 \text{ mL}} \approx 1.76 \text{ g/mL} \]

### Final Answer
The density of the 3.60 M sulfuric acid solution is approximately **1.76 g/mL**.

---