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 calculate the molar concentration of a solution from its molal concentration, we need to follow a few steps, considering both the density and molality of the solution.
Step 1: Define the terms
- Molality (m) is the number of moles of solute per kilogram of solvent.
- Given molality = 8.01 mol/kg
- Density (ρ) is the mass of the solution per unit volume.
- Given density = 1.354 g/mL = 1354 g/L (since 1 mL = 1/1000 L)
Step 2: Set up the equation
The molar concentration (M), or molarity, is the number of moles of solute per liter of solution. We can relate molality and density to find the molarity.
- Molality is defined as: m=moles of solutemass of solvent (kg)m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}m=mass of solvent (kg)moles of solute
- Molarity is defined as: M=moles of solutevolume of solution (L)M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}M=volume of solution (L)moles of solute
From the molality, we can calculate the moles of solute, and from the density, we can determine the volume of the solution.
Step 3: Calculate the mass of solvent and total mass of solution
Let’s assume we have 1 kg of solvent (which makes the calculation simpler, since molality is given in mols per kg of solvent).
- For 1 kg of solvent, the number of moles of H2SO4 (sulfuric acid) is: moles of H2SO4=8.01 mol\text{moles of H2SO4} = 8.01 \text{ mol}moles of H2SO4=8.01 mol
- The mass of the solution is: mass of solution=mass of solvent+mass of solute\text{mass of solution} = \text{mass of solvent} + \text{mass of solute}mass of solution=mass of solvent+mass of solute The molar mass of H2SO4 is approximately 98.079 g/mol, so the mass of 8.01 moles of H2SO4 is: mass of H2SO4=8.01 mol×98.079 g/mol=785.26 g\text{mass of H2SO4} = 8.01 \text{ mol} \times 98.079 \text{ g/mol} = 785.26 \text{ g}mass of H2SO4=8.01 mol×98.079 g/mol=785.26 g Thus, the total mass of the solution is: mass of solution=1000 g+785.26 g=1785.26 g\text{mass of solution} = 1000 \text{ g} + 785.26 \text{ g} = 1785.26 \text{ g}mass of solution=1000 g+785.26 g=1785.26 g
Step 4: Calculate the volume of the solution
We know the density of the solution is 1.354 g/mL, which means:volume of solution=mass of solutiondensity=1785.26 g1354 g/L=1.318 L\text{volume of solution} = \frac{\text{mass of solution}}{\text{density}} = \frac{1785.26 \text{ g}}{1354 \text{ g/L}} = 1.318 \text{ L}volume of solution=densitymass of solution=1354 g/L1785.26 g=1.318 L
Step 5: Calculate molarity
Now, we can calculate the molarity by dividing the number of moles of solute by the volume of the solution in liters:M=moles of H2SO4volume of solution=8.01 mol1.318 L=6.08 MM = \frac{\text{moles of H2SO4}}{\text{volume of solution}} = \frac{8.01 \text{ mol}}{1.318 \text{ L}} = 6.08 \text{ M}M=volume of solutionmoles of H2SO4=1.318 L8.01 mol=6.08 M
Final Answer:
The molar concentration of the solution is 6.08 M.
Explanation:
The molality gives us the number of moles of H2SO4 per kilogram of solvent. Using the density, we can calculate the mass and volume of the solution, and finally determine the molarity. This process ensures that we account for the volume of the solution, which is crucial since molarity depends on the volume of the total solution, not just the solvent.
