Question

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

[AI-generated answer — Bot GPT-4o]

To determine how many milliliters of concentrated sulfuric acid are needed to prepare 1 liter of a 0.15 M solution, we need to follow a series of steps involving calculations of moles, mass, and volume. Let's break it down step-by-step.

### Step 1: Calculate the moles of \( H_2SO_4 \) required for 1 liter of 0.15 M solution

Molarity (M) is defined as moles of solute per liter of solution. So, for a 0.15 M \( H_2SO_4 \) solution in 1 liter:

\[ \text{Moles of } H_2SO_4 = Molarity \times Volume \]
\[ \text{Moles of } H_2SO_4 = 0.15 \, \text{M} \times 1 \, \text{L} \]
\[ \text{Moles of } H_2SO_4 = 0.15 \, \text{moles} \]

### Step 2: Convert moles to grams

The molar mass of \( H_2SO_4 \) (sulfuric acid) is approximately:
\[ (2 \times 1.01) + 32.07 + (4 \times 16.00) \approx 98.09 \, \text{g/mol} \]

So, the mass of \( H_2SO_4 \) required is:

\[ \text{Mass of } H_2SO_4 = \text{Moles} \times \text{Molar mass} \]
\[ \text{Mass of } H_2SO_4 = 0.15 \, \text{moles} \times 98.09 \, \text{g/mol} \]
\[ \text{Mass of } H_2SO_4 \approx 14.7135 \, \text{g} \]

### Step 3: Determine the mass of the concentrated \( H_2SO_4 \) solution needed

The concentrated sulfuric acid solution is 94.5% \( H_2SO_4 \) by weight. Let's denote the mass of the concentrated solution required as \( m \).

\[ \text{Mass of } H_2SO_4 = \frac{94.5}{100} \times m \]
\[ 14.7135 \, \text{g} = 0.945 \times m \]
\[ m = \frac{14.7135 \, \text{g}}{0.945} \]
\[ m \approx 15.566 \, \text{g} \]

### Step 4: Convert the mass of the concentrated solution to volume

Using the density of the concentrated sulfuric acid solution (1.831 g/cm³):

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
\[ \text{Volume} = \frac{15.566 \, \text{g}}{1.831 \, \text{g/cm}^3} \]
\[ \text{Volume} \approx 8.50 \, \text{cm}^3 \]

Since 1 cm³ = 1 mL, the volume:
\[ \text{Volume} \approx 8.50 \, \text{mL} \]

### Conclusion

To prepare 1 liter of a 0.15 M \( H_2SO_4 \) solution, you need approximately 8.50 milliliters of the concentrated 94.5% sulfuric acid solution.