How many milliliters of concentrated sulphuric acid, 94.5% (g/100 g solution), density 1.831 g/cm3, are required to prepare 1 litre of a 0.15 M solution

Answer 1

To determine the volume of concentrated sulfuric acid (H₂SO₄) required to prepare 1 liter (1000 mL) of a 0.15 M solution, follow these steps:

### Step-by-Step Calculation

1. **Calculate moles of H₂SO₄ needed:**
$$\text{Moles of H₂SO₄}=\text{Molarity}\times \text{Volume (in L)}$$
$$\text{Moles of H₂SO₄}=0.15M\times 1\text{L}$$
$$\text{Moles of H₂SO₄}=0.15\text{moles}$$

2. **Calculate mass of H₂SO₄ needed (using molar mass of H₂SO₄, which is 98.08 g/mol):**
$$\text{Mass of H₂SO₄ (in grams)}=\text{Moles}\times \text{Molar Mass}$$
$$\text{Mass of H₂SO₄ (in grams)}=0.15\text{moles}\times 98.08\frac{\text{g}}{\text{mol}}$$
$$\text{Mass of H₂SO₄ (in grams)}=14.712\text{g}$$

3. **Calculate the mass of concentrated solution required:**
Given that the concentrated sulfuric acid solution is 94.5% H₂SO₄ by mass:
$$\text{Mass of solution (required)}=\frac{\text{Mass of H₂SO₄}}{\text{Fraction of H₂SO₄ in solution}}$$
$$\text{Mass of solution (required)}=\frac{14.712\text{g}}{0.945}$$
$$\text{Mass of solution (required)}\approx 15.56\text{g}$$

4. **Convert mass of the solution to volume:**
Using the density provided (1.831 g/cm³ or 1.831 g/mL):
$$\text{Volume}=\frac{\text{Mass}}{\text{Density}}$$
$$\text{Volume}=\frac{15.56\text{g}}{1.831\text{g/mL}}$$
$$\text{Volume}\approx 8.50\text{mL}$$

### Final Answer
You need approximately 8.50 mL of the concentrated sulfuric acid solution to prepare 1 liter of a 0.15 M H₂SO₄ solution.