Potassium permanganate can be used as a disinfectant. How would you prepare \(25.0 \mathrm{~L}\) of a solution that is \(15.0 \% \mathrm{KMnO}_{4}\) by mass if the resulting solution has a density of \(1.08 \mathrm{~g} / \mathrm{mL}\) ? What is the molarity of the resulting solution?

Understanding solution concentration is key in chemistry, especially when preparing a specific solution like potassium permanganate, which can be used as a disinfectant. Concentration describes how much of a substance is present in a certain amount of solvent. There are several ways to express this, but the most common is by mass percent (mass %), volume percent, molarity, and molality.

For mass percent, this indicates the mass of solute (in this case, KMnO₄) present per 100 grams of the solution. The provided problem states that we want to prepare a solution with a mass percent of 15.0%. It means that for every 100 grams of our potassium permanganate solution, 15 grams will be KMnO₄, and the remaining 85 grams will be water or other solvents present.

When dealing with solutions, molarity is an essential concept to grasp. It measures the concentration of a solution by describing the number of moles of solute per liter of solution. The formula to calculate molarity is:
\[ M = \frac{n}{V} \]
where \( M \) is the molarity, \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. In the exercise, we already determined the number of moles of KMnO₄ and the volume of the solution required. By dividing the number of moles by the volume, we can calculate the molarity of the potassium permanganate solution. This step is critical for various applications where a precise concentration is necessary, such as in lab settings, industrial processes, or medical treatments.

Preparing a solution based on mass percent involves calculating the exact weight of the solute and solvent required to reach the desired concentration. The process involves multiple steps that must be meticulously followed to ensure accuracy. To prepare a 15.0% KMnO₄ solution by mass, first, we need to find the total mass of the solution using the given density and desired volume. Then, we calculate 15.0% of this total mass to determine the mass of KMnO₄ we need to weigh out.

To further clarify, if we have 27,000 grams of our final solution and we want a 15.0% concentration, we need to calculate 15.0% of 27,000 grams, which is 4,050 grams of KMnO₄. The remaining mass will be the mass of the water or other components of the solution. It's important to ensure that all equipment used for measurement is calibrated and that temperature, which can affect density, is considered during preparation.