How many liters of a \(0.25 \%(\mathrm{v} / \mathrm{v})\) oil of wintergreen solution can you prepare if you have only \(7.35 \mathrm{~mL}\) of oil of wintergreen on hand?

Understanding how to prepare chemical solutions is an important skill in chemistry. In our context, solution preparation involves combining a precise volume of solute, which is the oil of wintergreen, with a solvent to achieve a desired concentration. The process requires meticulous measurement and often involves the use of volumetric flasks and pipettes to ensure accuracy.

When preparing a solution, always first clarify the desired concentration and the total quantity of solute available. In this case, we are working towards a final solution that has a 0.25% volume-to-volume concentration, and we have 7.35 mL of the solute. Starting with the known amount of solute, the next step is to calculate the volume of solvent needed to achieve the desired concentration, which requires using the volume percent concentration formula.

Concentration calculations play a vital role in chemistry, as they allow scientists and students alike to determine the amount of substance present in a given volume of solution. The volume percent concentration formula is a simple relation that helps us solve for the necessary components of a solution. It is expressed as:
\[% (v/v) = \frac{volume \, of \, solute}{volume \, of \, solution} \times 100\]In our exercise, we are given a volume percent concentration \(0.25\% (v/v)\) and the amount of solute \(7.35\,mL\). By rearranging the formula to solve for the total volume of the solution and substituting in the known values, we can calculate the quantity of solution that can be made. Understanding how to manipulate this formula is key to many laboratory preparations and analyses.

Problem-solving in chemistry often requires a methodical approach: defining the problem, determining the required formula, substitifying known values, and performing calculations. When faced with a question such as determining the amount of solution we can make with a given quantity of solute and a fixed concentration, this strategy becomes evident. Using a step-by-step methodology helps to avoid errors and ensures we comprehend the underlying chemical principles.

For our current problem, we've defined the desired concentration and quantity of solute. We have identified the appropriate formula, substituted the known values to calculate the total volume of the solution, and now, the final step will be to make the unit conversion to match the units requested in the question.