A solution of H2SO4 with a molal concentration of 8.01 mol/kg has a density of 1.354 g/mL. What is the molar concentration of this solution
The Correct Answer and Explanation is:
To find the molar concentration of the solution, we need to follow a few steps using the information provided:
Step 1: Understand what molal concentration is
Molality (m) is defined as the number of moles of solute (H₂SO₄ in this case) per kilogram of solvent. You are given that the solution has a molal concentration of 8.01 mol/kg. This means that for every 1 kg of solvent, there are 8.01 moles of H₂SO₄.
Step 2: Use the density to convert mass into volume
Next, we are given the density of the solution, which is 1.354 g/mL. The density formula is: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Rearranging this formula to solve for volume: Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass
Let’s say we have 1 kg of solvent (1000 g), and from the molality definition, there will be 8.01 moles of H₂SO₄. Now, calculate the mass of the solution.
- Mass of solution = Mass of solvent + Mass of solute (H₂SO₄).
The molar mass of H₂SO₄ is 98.079 g/mol. So:
- Mass of H₂SO₄ = 8.01 mol × 98.079 g/mol = 785.1 g.
Thus, the total mass of the solution is:
- Total mass = 1000 g (solvent) + 785.1 g (solute) = 1785.1 g.
Now, we can calculate the volume using the density: Volume=1785.1 g1.354 g/mL=1319.8 mL=1.3198 L.\text{Volume} = \frac{1785.1 \, \text{g}}{1.354 \, \text{g/mL}} = 1319.8 \, \text{mL} = 1.3198 \, \text{L}.Volume=1.354g/mL1785.1g=1319.8mL=1.3198L.
Step 3: Calculate molar concentration
Molar concentration (M) is the number of moles of solute per liter of solution. The number of moles of H₂SO₄ is 8.01 mol (as given), and the volume of the solution is 1.3198 L. Therefore, the molar concentration is: M=8.01 mol1.3198 L=6.07 mol/L.M = \frac{8.01 \, \text{mol}}{1.3198 \, \text{L}} = 6.07 \, \text{mol/L}.M=1.3198L8.01mol=6.07mol/L.
Conclusion:
The molar concentration of the solution is 6.07 mol/L.
