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 find the molar concentration (molarity) of a solution from its molality, we need to use the relationship between molality, molarity, and density.
Given:
- Molality (m) = 5.25 mol/kg
- Density (d) = 1.266 g/mL
- The molar mass of H2SO4 = 98.08 g/mol
Step 1: Convert density from g/mL to g/L
The density is given in g/mL, but we need it in g/L to match the molarity units (mol/L). Since there are 1000 mL in 1 L, we multiply the density by 1000:Density (g/L)=1.266 g/mL×1000=1266 g/L\text{Density (g/L)} = 1.266 \, \text{g/mL} \times 1000 = 1266 \, \text{g/L}Density (g/L)=1.266g/mL×1000=1266g/L
Step 2: Convert molality to moles of solute per kilogram of solvent
Molality is defined as moles of solute per kilogram of solvent. We know that:Molality=moles of solutemass of solvent (kg)\text{Molality} = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}Molality=mass of solvent (kg)moles of solute
This gives us the number of moles of H2SO4 per kilogram of water.
Step 3: Convert mass of solution from g to kg
The mass of the solution can be calculated by the density and volume. Assuming 1 L of solution:Mass of solution=1266 g (since we are considering 1 L of solution)\text{Mass of solution} = 1266 \, \text{g} \, \text{(since we are considering 1 L of solution)}Mass of solution=1266g(since we are considering 1 L of solution)
Step 4: Calculate the mass of the solvent (water)
The mass of the solvent (water) can be found by subtracting the mass of the solute (H2SO4) from the total mass of the solution.
First, calculate the moles of H2SO4 in the solution:moles of H2SO4=5.25 mol/kg×1 kg=5.25 mol\text{moles of H2SO4} = 5.25 \, \text{mol/kg} \times 1 \, \text{kg} = 5.25 \, \text{mol}moles of H2SO4=5.25mol/kg×1kg=5.25mol
Then, calculate the mass of H2SO4:Mass of H2SO4=5.25 mol×98.08 g/mol=514.92 g\text{Mass of H2SO4} = 5.25 \, \text{mol} \times 98.08 \, \text{g/mol} = 514.92 \, \text{g}Mass of H2SO4=5.25mol×98.08g/mol=514.92g
Now, the mass of the solvent (water) is:Mass of water=1266 g−514.92 g=751.08 g=0.751 kg\text{Mass of water} = 1266 \, \text{g} – 514.92 \, \text{g} = 751.08 \, \text{g} = 0.751 \, \text{kg}Mass of water=1266g−514.92g=751.08g=0.751kg
Step 5: Calculate molarity (M)
Molarity is defined as moles of solute per liter of solution. We already know the number of moles of H2SO4 (5.25 mol) and the volume of the solution (1 L):Molarity=moles of H2SO4volume of solution (L)=5.25 mol1 L=5.25 M\text{Molarity} = \frac{\text{moles of H2SO4}}{\text{volume of solution (L)}} = \frac{5.25 \, \text{mol}}{1 \, \text{L}} = 5.25 \, \text{M}Molarity=volume of solution (L)moles of H2SO4=1L5.25mol=5.25M
Thus, the molar concentration of the H2SO4 solution is 5.25 M.
