The density (in g `ml^(−1)` ) of a 3.60M sulphuric acid solution having 30% `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 contains 30% \( H_2SO_4 \) by mass, we can follow these steps:

### Step 1: Understand the mass percentage
The mass percentage of \( H_2SO_4 \) in the solution is given as 30%. This means that in 100 grams of the solution, there are 30 grams of \( H_2SO_4 \).

### Step 2: Calculate the number of moles of \( H_2SO_4 \)
To find the number of moles of \( H_2SO_4 \), we use the formula:
\[ \text{Moles of } H_2SO_4 = \frac{\text{mass of } H_2SO_4}{\text{molar mass of } H_2SO_4} \]
Given that the molar mass of \( H_2SO_4 \) is 98 g/mol:
\[ \text{Moles of } H_2SO_4 = \frac{30 \text{ g}}{98 \text{ g/mol}} \approx 0.306 \text{ mol} \]

### Step 3: Use the molarity formula
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
We know the molarity is 3.60 M, so we can set up the equation:
\[ 3.60 = \frac{0.306}{V} \]
Where \( V \) is the volume of the solution in liters. Rearranging gives:
\[ V = \frac{0.306}{3.60} \approx 0.085 \text{ L} = 85 \text{ mL} \]

### Step 4: Calculate the mass of the solution
The total mass of the solution can be calculated as:
\[ \text{Mass of solution} = \text{mass of } H_2SO_4 + \text{mass of solvent} \]
The mass of the solvent can be calculated as:
\[ \text{Mass of solvent} = \text{mass of solution} - \text{mass of } H_2SO_4 = 100 \text{ g} - 30 \text{ g} = 70 \text{ g} \]
Thus, the total mass of the solution is:
\[ \text{Mass of solution} = 30 \text{ g} + 70 \text{ g} = 100 \text{ g} \]

### Step 5: Calculate the density of the solution
Density (\( D \)) is defined as mass per unit volume:
\[ D = \frac{\text{mass of solution}}{\text{volume of solution in mL}} \]
Substituting the values we have:
\[ D = \frac{100 \text{ g}}{85 \text{ mL}} \approx 1.176 \text{ g/mL} \]

### Final Answer
The density of the 3.60 M sulfuric acid solution is approximately **1.176 g/mL**.

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