A solution of 49.0% H2SO4 by mass has a density of 1.39 g/cm³ at 293 K. A 25.0-cm³ sample of this solution is mixed with enough water to increase the volume of the solution to 99.8 cm³. Find the molarity of sulfuric acid in this solution.

Verified step by step guidance

1. Calculate the mass of the 25.0 cm³ sample using the density: \( \text{mass} = \text{density} \times \text{volume} \).
2. Determine the mass of \( \text{H}_2\text{SO}_4 \) in the sample using the percentage by mass: \( \text{mass of } \text{H}_2\text{SO}_4 = \text{total mass} \times 0.49 \).
3. Convert the mass of \( \text{H}_2\text{SO}_4 \) to moles using its molar mass: \( \text{moles of } \text{H}_2\text{SO}_4 = \frac{\text{mass of } \text{H}_2\text{SO}_4}{\text{molar mass of } \text{H}_2\text{SO}_4} \).
4. Calculate the molarity of the \( \text{H}_2\text{SO}_4 \) solution by dividing the moles of \( \text{H}_2\text{SO}_4 \) by the final volume of the solution in liters: \( \text{Molarity} = \frac{\text{moles of } \text{H}_2\text{SO}_4}{\text{volume in liters}} \).
5. Convert the final volume from cm³ to liters by dividing by 1000.

Key Concepts

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for understanding how much solute is present in a given volume of solution. To calculate molarity, one must know the amount of solute in moles and the total volume of the solution in liters.

Density

Density is the mass of a substance per unit volume, typically expressed in grams per cubic centimeter (g/cm³). In this context, the density of the sulfuric acid solution allows us to convert between mass and volume, which is essential for determining the mass of sulfuric acid in the solution. Understanding density helps in calculating how much solute is present when given a percentage by mass.

Dilution

Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. The dilution equation, M1V1 = M2V2, relates the molarity and volume of the concentrated solution (M1, V1) to the molarity and volume of the diluted solution (M2, V2). In this problem, knowing how to apply dilution principles is key to finding the final molarity after mixing the sulfuric acid solution with water.