A solution of H
SO
(aq) with a molal concentration of 2.24 m has a density of 1.135 g/mL. What is the molar concentration of this solution? molar concentration:
The Correct Answer and Explanation is:
To calculate the molar concentration of a solution, we need to use the relationship between molality, density, and molar concentration. Here’s how you can do it step by step:
Given:
- Molality (m) of the solution = 2.24 mol/kg
- Density (ρ) of the solution = 1.135 g/mL
- The solvent in this case is water (H₂SO₄ is dissolved in water).
Step 1: Convert molality to moles of solute per kilogram of solvent.
Molality (m) is defined as the number of moles of solute (H₂SO₄) per kilogram of solvent. So, the molality (2.24 mol/kg) means there are 2.24 moles of H₂SO₄ per 1 kilogram of water.
Step 2: Determine the mass of the solution.
Density (ρ) is given as 1.135 g/mL. To convert this to kilograms per liter (kg/L), we multiply by 1000 (since 1 g/mL = 1000 kg/L):1.135 g/mL=1135 g/L=1.135 kg/L.1.135 \, \text{g/mL} = 1135 \, \text{g/L} = 1.135 \, \text{kg/L}.1.135g/mL=1135g/L=1.135kg/L.
Step 3: Find the mass of 1 liter of solution.
1 liter of solution weighs 1.135 kg.
Step 4: Use molality to calculate moles of solute in 1 liter of solution.
Since 2.24 mol of H₂SO₄ are dissolved in 1 kg of water, and the mass of the solution is 1.135 kg, we can figure out the moles of H₂SO₄ in 1 liter of solution.
- Mass of solvent (water) in 1 liter of solution = 1.135 kg (total solution mass) – 1 kg (mass of water) = 0.135 kg of water.
- The molality gives the amount of H₂SO₄ per kilogram of water:
Moles of H₂SO₄=2.24 mol/kg×0.135 kg=0.3024 mol.\text{Moles of H₂SO₄} = 2.24 \, \text{mol/kg} \times 0.135 \, \text{kg} = 0.3024 \, \text{mol}.Moles of H₂SO₄=2.24mol/kg×0.135kg=0.3024mol.
Step 5: Calculate the molar concentration.
Molar concentration is the number of moles of solute per liter of solution. Since we have 0.3024 moles of H₂SO₄ in 1 liter of solution, the molar concentration is:Molar concentration=0.3024 mol/L.\text{Molar concentration} = 0.3024 \, \text{mol/L}.Molar concentration=0.3024mol/L.
Thus, the molar concentration of the solution is 0.302 mol/L.
Conclusion:
By understanding the relationship between molality, density, and volume, we can determine that the molar concentration of the H₂SO₄ solution is 0.302 mol/L.
