Find out the volume of 98% w/w `H_(2)SO_(4)` (density = 1.8 gm/ml), must be diluted to prepare 2.6 litres of 2.0 M sulphuric acid solution

Answer

To solve the problem of finding the volume of 98% w/w H₂SO₄ needed to prepare 2.6 liters of a 2.0 M sulfuric acid solution, we will follow these steps:

### Step 1: Calculate the mass of sulfuric acid needed for the desired solution.
We know that molarity (M) is defined as moles of solute per liter of solution. Therefore, we can calculate the number of moles of H₂SO₄ required for a 2.0 M solution.

\[ \text{Moles of } H_2SO_4 = \text{Molarity} \times \text{Volume (L)} = 2.0 \, \text{M} \times 2.6 \, \text{L} = 5.2 \, \text{moles} \]

### Step 2: Calculate the mass of H₂SO₄ required using its molar mass.
The molar mass of H₂SO₄ is approximately 98 g/mol. Therefore, the mass of H₂SO₄ needed is:

\[ \text{Mass of } H_2SO_4 = \text{Moles} \times \text{Molar Mass} = 5.2 \, \text{moles} \times 98 \, \text{g/mol} = 509.6 \, \text{g} \]

### Step 3: Calculate the mass of the 98% w/w H₂SO₄ solution needed to obtain the required mass of H₂SO₄.
Since the solution is 98% w/w, this means that 98 grams of H₂SO₄ are present in 100 grams of the solution. We can set up a proportion to find the mass of the solution needed:

\[ \text{Let } x \text{ be the mass of the solution required.} \]
\[ 0.98x = 509.6 \, \text{g} \]
\[ x = \frac{509.6 \, \text{g}}{0.98} \approx 520.4 \, \text{g} \]

### Step 4: Calculate the volume of the 98% w/w H₂SO₄ solution using its density.
We know the density of the solution is 1.8 g/mL. We can use this to find the volume:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{520.4 \, \text{g}}{1.8 \, \text{g/mL}} \approx 289.1 \, \text{mL} \]

### Step 5: Convert the volume from mL to L.
Since the final answer is typically expressed in liters:

\[ \text{Volume in L} = \frac{289.1 \, \text{mL}}{1000} \approx 0.289 \, \text{L} \]

### Final Answer:
The volume of 98% w/w H₂SO₄ needed to prepare 2.6 liters of a 2.0 M sulfuric acid solution is approximately **0.289 liters** or **289.1 mL**.

---