To calculate the molarity and molality of an H2SO4 solution with a density of 1.198 g/cm³ and containing 27% by mass of H2SO4, we will follow these steps:
### Step 1: Determine the mass of the solution for 1 liter
Given that the density is 1.198 g/cm³ and we are considering 1 liter (1000 cm³) of the solution:
[tex]\[
\text{Mass of the solution} = \text{Density} \times \text{Volume} = 1.198 \, \text{g/cm}^3 \times 1000 \, \text{cm}^3 = 1198 \, \text{g}
\][/tex]
### Step 2: Calculate the mass of the solute (H2SO4) in the solution
The solution contains 27% by mass of H2SO4:
[tex]\[
\text{Mass of solute (H2SO4)} = 27\% \times \text{Mass of the solution} = 0.27 \times 1198 \, \text{g} = 323.46 \, \text{g}
\][/tex]
### Step 3: Calculate the mass of the solvent (water) in the solution
The mass of the solvent is the total mass of the solution minus the mass of the solute:
[tex]\[
\text{Mass of solvent (water)} = \text{Mass of the solution} - \text{Mass of solute} = 1198 \, \text{g} - 323.46 \, \text{g} = 874.54 \, \text{g}
\][/tex]
### Step 4: Calculate the number of moles of H2SO4
To find the number of moles of H2SO4, we use its molar mass. The molar mass of H2SO4 is 98.079 g/mol:
[tex]\[
\text{Number of moles of H2SO4} = \frac{\text{Mass of H2SO4}}{\text{Molar mass of H2SO4}} = \frac{323.46 \, \text{g}}{98.079 \, \text{g/mol}} = 3.298 \, \text{mol}
\][/tex]
### Step 5: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution. Since we are considering 1 liter of the solution:
[tex]\[
\text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} = \frac{3.298 \, \text{mol}}{1 \, \text{L}} = 3.298 \, \text{M}
\][/tex]
### Step 6: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent. First, we convert the mass of the solvent (water) to kilograms:
[tex]\[
\text{Mass of solvent in kg} = \frac{874.54 \, \text{g}}{1000} = 0.875 \, \text{kg}
\][/tex]
Then we use the number of moles of solute and the mass of solvent in kilograms to find the molality:
[tex]\[
\text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} = \frac{3.298 \, \text{mol}}{0.875 \, \text{kg}} = 3.771 \, \text{m}
\][/tex]
### Summary
- Mass of the solution: 1198.0 g
- Mass of the solute (H2SO4): 323.46 g
- Mass of the solvent (water): 874.54 g
- Moles of H2SO4: 3.298 mol
- Molarity (M): 3.298 M
- Molality (m): 3.771 m
