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.

Understanding sulfuric acid solutions is essential for many chemistry applications. Sulfuric acid ((H_2SO_4)) is a strong acid commonly used in industrial processes and laboratory settings. When dissolved in water, it dissociates into hydrogen ions (H^+) and sulfate ions (SO_4^{2-}), thus contributing to its high acidity. The concentration of (H_2SO_4) in a solution is critical for determining how it will react with other substances. Concentration is typically expressed as molarity, which is the number of moles of solute per liter of solution, but it can also be expressed as a mass percent, indicating the mass of the solute as a percentage of the total solution mass.

When creating or analyzing sulfuric acid solutions, it's important to note that handling this acid requires strict safety protocols due to its highly corrosive nature.

The mass percent concentration is a way of expressing the composition of a mixture or solution. It is calculated by taking the mass of the solute and dividing it by the total mass of the solution, then multiplying by 100 to get a percentage. This concept allows chemists to quantify how much of a certain substance is present in a mixture.

For example, in our exercise, the 49.0% mass percent concentration of the sulfuric acid solution means that in a 100 gram sample of the solution, there are 49 grams of (H_2SO_4) and 51 grams of water and other components. This measure is useful when mixing solutions to achieve a desired concentration or when diluting a concentrated solution with water.

Molar mass is a key concept in chemistry that corresponds to the weight of one mole (Avogadro's number, 6.022 x (10^{23})) of molecules or atoms of a substance. This value is expressed in grams per mole ((g/mol)). The molar mass of (H_2SO_4) can be calculated by summing the atomic masses of the constituent elements from the periodic table: the molar mass of (H_2SO_4) is 2 times the atomic mass of hydrogen (H) plus the atomic mass of sulfur (S) plus 4 times the atomic mass of oxygen (O).

The exact calculation is: M_{H_2SO_4} = 2(M_H) + M_S + 4(M_O) where (M_H), (M_S), and (M_O) are the molar masses of hydrogen, sulfur, and oxygen, respectively. Understanding molar mass is essential for converting between the mass of a substance and the number of moles.

The term 'moles of solute' refers to the amount of a substance present in a solution. A mole is a unit of measurement used in chemistry to express amounts of a chemical substance. It allows chemists to count particles (like atoms or molecules) by weighing them. We use the mole because dealing with atomic-scale particles individually is impractical due to their small size and large numbers.

To calculate the moles of the solute, you should divide the mass of the solute by its molar mass. This calculation gives you the number of moles of (H_2SO_4) in the sample, which can then be used to determine the molarity of the solution. For instance, with the mass of (H_2SO_4) obtained from the mass percent concentration, dividing by the molar mass yields the moles of (H_2SO_4) in our sample.

Solution dilution involves adding more solvent (like water) to a solution to decrease the concentration of the solute (like (H_2SO_4)). When diluting a solution, the amount of solute remains the same, but the overall volume of the solution increases, resulting in a lower concentration.

Mathematically, the initial and final concentrations of the solution can be related by the dilution equation (M_1V_1 = M_2V_2), where (M_1) and (M_2) are the initial and final molarities respectively, and (V_1) and (V_2) are the initial and final volumes. In the context of our problem, once we have mixed the sulfuric acid with water, we need to adjust our calculations to account for the increased volume of the solution to find its new molarity.