Main Answer
To find the total volume of solvent required for a 5ml bottle of perfume with a fragrance oil to total volume ratio of 3:20, we can use the following formula:Total volume = (Fragrance oil volume) / (Fragrance oil concentration) (Total volume concentration).
Substituting the given values, we get:
Total volume = (3 ml) / (0.15) (20 ml)
Total volume ≈ 120 ml.
Explanation:
The formula used to calculate the total volume is derived from the concept of dilution, which is the process of adding a smaller amount of a substance (the solute) to a larger amount of another substance (the solvent) to obtain a solution.
In this case, we're trying to find the total amount of solvent required to dilute a certain amount of fragrance oil to a specific concentration. The formula involves two concentration ratios: one for the fragrance oil and one for the total solution.
The first ratio, fragrance oil concentration, is the amount of fragrance oil in milliliters divided by the total volume in milliliters. In our case, this ratio is 3:20, which means that there are 3 milliliters of fragrance oil in every 20 milliliters of total solution.
The second ratio, total volume concentration, is the total volume in milliliters divided by the total volume in milliliters. This ratio is always equal to 1, since by definition, the total volume is the entire solution.
By multiplying the fragrance oil concentration by the total volume concentration and then dividing by the fragrance oil concentration, we can find the total volume required to achieve a certain concentration.
In our case, we're using this formula to find out how much solvent is needed to dilute 3 milliliters of fragrance oil to a concentration of 0.15 in a 20 ml bottle.
This calculation assumes that there are no other factors influencing the dilution process besides the initial concentrations and volumes. In reality, there may be other variables such as temperature or impurities that could affect the dilution process.
However, for our purposes here, we're simplifying things to illustrate how these variables interact with each other in this context.