The density (in g `ml^(−1)` ) of a 3.60M sulphuric acid solution having 50% `H_2SO_4`[molar mass =98g `mol^(−1)`] by mass, will be:

Answer

To find the density of a 3.60 M sulfuric acid solution that is 50% H₂SO₄ by mass, we can follow these steps:

### Step 1: Understand the given information
- Molarity (M) = 3.60 M
- Mass percentage of H₂SO₄ = 50%
- 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 50%, in 100 g of the solution, there will be:
\[ \text{Mass of H₂SO₄} = 50\% \text{ of } 100 \text{ g} = 50 \text{ g} \]

### Step 3: Calculate the number of moles of H₂SO₄
Using the molar mass of H₂SO₄, we can find the number of moles:
\[ \text{Moles of H₂SO₄} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{50 \text{ g}}{98 \text{ g/mol}} \]
\[ \text{Moles of H₂SO₄} = 0.5102 \text{ mol} \]

### Step 4: Use the molarity formula to find the volume of the solution
Molarity (M) is defined as:
\[ M = \frac{\text{Moles of solute}}{\text{Volume of solution in L}} \]
Rearranging the formula to find the volume:
\[ \text{Volume of solution in L} = \frac{\text{Moles of solute}}{M} \]
Substituting the values:
\[ \text{Volume of solution in L} = \frac{0.5102 \text{ mol}}{3.60 \text{ M}} = 0.1412 \text{ L} \]
Convert to mL:
\[ \text{Volume of solution in mL} = 0.1412 \text{ L} \times 1000 = 141.2 \text{ mL} \]

### 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 (as we assumed 100 g of solution initially).
Substituting the values:
\[ D = \frac{100 \text{ g}}{141.2 \text{ mL}} \]
\[ D = 0.707 \text{ g/mL} \]

### Final Answer
The density of the 3.60 M sulfuric acid solution is approximately:
\[ \text{Density} \approx 0.707 \text{ g/mL} \]

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