(a) How much water must be added to concentrated sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right)(17.8 \mathrm{M})\) to prepare \(8.4 \mathrm{~L}\) of \(1.5 \mathrm{M}\) sulfuric acid solution? (b) How many moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) are in each milliliter of the original concentrate? (c) How many moles are in each milliliter of the diluted solution?

Understanding the process of dilution is fundamental in chemistry, especially when preparing specific concentrations of solutions for experiments or industrial processes. Dilution involves adding more solvent to a solution without altering the amount of solute present. This process results in a decrease in the concentration of the solute in the solution. A key formula used in this context is the dilution equation: \( C1 \times V1 = C2 \times V2 \), where \( C1 \) and \( C2 \) represent the concentrations (molarity) of the original and final solutions, respectively, while \( V1 \) and \( V2 \) are the corresponding volumes.

Applying this to our exercise, we begin with a highly concentrated sulfuric acid and aim to achieve a less concentrated one by adding a certain volume of water. The dilution formula helps us determine the precise volume of concentrated solution needed before water addition, to end up with our desired concentrated final solution.

The mole is a fundamental unit in chemistry that quantifies the amount of substance. When calculating moles, we often use the molarity equation: \( \text{Molarity} (M) = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}} \). The manipulation of this formula allows us to solve for the unknown variable, dependent on the values provided.

In the context of our exercise, once we determined the molarity and volume of the diluted sulfuric acid solution, we rearranged the formula to solve for the moles of solute (sulfuric acid) required. By calculating moles in the context of a dilution, it ensures the final solution retains the same total number of moles of solute, even though its volume – and thus its concentration – changes.

The concentration of an acid, such as sulfuric acid in our example, plays a pivotal role in both the property of the acid and its application. Acid concentration is typically expressed in molarity (M), which is moles of solute per liter of solution. Higher molarity indicates a more concentrated acid, which can be more corrosive or reactive.

To tackle the parts of our exercise involving acid concentration, we used the concept of molarity to calculate both the starting and the desired concentrations of sulfuric acid. For example, the molarity of the original concentrated sulfuric acid is given as 17.8 M, while the desired concentration for the diluted solution is 1.5 M. By understanding how to manipulate the molarity equation, we calculated the moles of sulfuric acid per milliliter for both concentrated and diluted solutions, which is essential when precise measurements of acid concentration are required in various scientific and industrial applications.