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:**
\[ \text{Moles of H₂SO₄} = \text{Molarity} \times \text{Volume (in L)} \]
\[ \text{Moles of H₂SO₄} = 0.15 \, M \times 1 \, \text{L} \]
\[ \text{Moles of H₂SO₄} = 0.15 \, \text{moles} \]

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.