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 find the molar concentration of the sulfuric acid (H₂SO₄) solution, we need to use the information given:
- Molality (m) = 2.24 mol/kg
- Density (ρ) = 1.135 g/mL
- Molar mass of H₂SO₄ = 98.08 g/mol
Step-by-Step Solution:
- Convert molality to moles of H₂SO₄:
Molality (m) is defined as the number of moles of solute (H₂SO₄) per kilogram of solvent. Since we have a 2.24 molal solution, this means there are 2.24 moles of H₂SO₄ in every 1 kilogram (1000 grams) of solvent. - Find the mass of the solution:
The density of the solution is given as 1.135 g/mL, which means there are 1.135 grams of solution per 1 milliliter of solution. To calculate the mass of 1 liter (1000 mL) of solution, we multiply: Mass of 1 liter of solution=1.135 g/mL×1000 mL=1135 g\text{Mass of 1 liter of solution} = 1.135 \, \text{g/mL} \times 1000 \, \text{mL} = 1135 \, \text{g}Mass of 1 liter of solution=1.135g/mL×1000mL=1135g So, the mass of 1 liter of solution is 1135 grams. - Find the mass of solvent (water):
Since the solution contains H₂SO₄ dissolved in water, the mass of the solvent (water) is the mass of the solution minus the mass of the H₂SO₄. First, find the mass of H₂SO₄: Mass of H₂SO₄=molality×mass of solvent=2.24 mol/kg×1 kg=2.24 mol\text{Mass of H₂SO₄} = \text{molality} \times \text{mass of solvent} = 2.24 \, \text{mol/kg} \times 1 \, \text{kg} = 2.24 \, \text{mol} Mass of H₂SO₄=molality×mass of solvent=2.24mol/kg×1kg=2.24mol Now, multiply by the molar mass of H₂SO₄ to get the mass of H₂SO₄: Mass of H₂SO₄=2.24 mol×98.08 g/mol=219.79 g\text{Mass of H₂SO₄} = 2.24 \, \text{mol} \times 98.08 \, \text{g/mol} = 219.79 \, \text{g}Mass of H₂SO₄=2.24mol×98.08g/mol=219.79g Thus, the mass of the solvent (water) is: Mass of water=1135 g−219.79 g=915.21 g≈0.915 kg\text{Mass of water} = 1135 \, \text{g} – 219.79 \, \text{g} = 915.21 \, \text{g} \approx 0.915 \, \text{kg}Mass of water=1135g−219.79g=915.21g≈0.915kg - Calculate the moles of H₂SO₄ in 1 liter of solution:
From the molality, we already know that 2.24 moles of H₂SO₄ are in 1 kilogram of water. Since the mass of water in 1 liter of solution is 0.915 kg, the number of moles of H₂SO₄ in 1 liter is: Moles of H₂SO₄=2.24 mol/kg×0.915 kg=2.05 mol\text{Moles of H₂SO₄} = 2.24 \, \text{mol/kg} \times 0.915 \, \text{kg} = 2.05 \, \text{mol}Moles of H₂SO₄=2.24mol/kg×0.915kg=2.05mol - Calculate the molar concentration (M):
Molarity (M) is defined as the number of moles of solute per liter of solution. So, the molar concentration is: Molar concentration=Moles of H₂SO₄Volume of solution in liters=2.05 mol1 L=2.05 M\text{Molar concentration} = \frac{\text{Moles of H₂SO₄}}{\text{Volume of solution in liters}} = \frac{2.05 \, \text{mol}}{1 \, \text{L}} = 2.05 \, \text{M}Molar concentration=Volume of solution in litersMoles of H₂SO₄=1L2.05mol=2.05M
Conclusion:
The molar concentration of the solution is 2.05 M.
This means the solution contains 2.05 moles of H₂SO₄ per liter of solution.
