A solution of H2SO4 with a molal concentration of 5.25m has a density of 1.266 g/ml. what is the molar concentration of this solution?
The Correct Answer and Explanation is:
To calculate the molar concentration of the solution, we first need to understand the relationship between molality and molarity.
Step 1: Define the given values
- Molality (m): 5.25 mol/kg
- Density (d): 1.266 g/mL
- Molar mass of H2SO4: 98.079 g/mol
Step 2: Convert the density from g/mL to g/L
Since we are working with density in g/mL and molarity requires units in mol/L, we first convert the density:1.266 g/mL×1000 mL/L=1266 g/L1.266 \, \text{g/mL} \times 1000 \, \text{mL/L} = 1266 \, \text{g/L}1.266g/mL×1000mL/L=1266g/L
Step 3: Calculate the mass of the solution
Molality is defined as moles of solute per kilogram of solvent (mol/kg). To calculate molarity, we need to know the total volume of the solution. Let’s assume that we have 1 kg of solvent. Since molality is 5.25 mol/kg, this corresponds to 5.25 moles of H2SO4 in 1 kg of solvent.
Now, the mass of H2SO4 in 5.25 moles is:Mass of H2SO4=5.25 mol×98.079 g/mol=514.41675 g\text{Mass of H2SO4} = 5.25 \, \text{mol} \times 98.079 \, \text{g/mol} = 514.41675 \, \text{g}Mass of H2SO4=5.25mol×98.079g/mol=514.41675g
Thus, the total mass of the solution is the mass of the solvent (1000 g) plus the mass of H2SO4 (514.41675 g):Total mass of solution=1000 g+514.41675 g=1514.41675 g\text{Total mass of solution} = 1000 \, \text{g} + 514.41675 \, \text{g} = 1514.41675 \, \text{g}Total mass of solution=1000g+514.41675g=1514.41675g
Step 4: Calculate the volume of the solution
Using the density formula, we can calculate the volume of the solution:Volume of solution=Mass of solutionDensity=1514.41675 g1266 g/L=1.195 L\text{Volume of solution} = \frac{\text{Mass of solution}}{\text{Density}} = \frac{1514.41675 \, \text{g}}{1266 \, \text{g/L}} = 1.195 \, \text{L}Volume of solution=DensityMass of solution=1266g/L1514.41675g=1.195L
Step 5: Calculate the molarity
Finally, molarity (M) is defined as the number of moles of solute per liter of solution:Molarity=Moles of H2SO4Volume of solution=5.25 mol1.195 L=4.39 M\text{Molarity} = \frac{\text{Moles of H2SO4}}{\text{Volume of solution}} = \frac{5.25 \, \text{mol}}{1.195 \, \text{L}} = 4.39 \, \text{M}Molarity=Volume of solutionMoles of H2SO4=1.195L5.25mol=4.39M
Final Answer:
The molar concentration of the H2SO4 solution is 4.39 M.
