A 250-milliliter solution of hand sanitizer contains 150 milliliters of propan-2-ol. What is the percentage concentration by volume of propan-2-ol in this solution? Give your answer to the nearest whole percentage.
This bottle of hand sanitizer has a total volume of 250 milliliters. Of the 250 milliliters of hand sanitizer, 150 milliliters are propan-2-ol, the active ingredient. The additional 100 milliliters are made up of inactive ingredients such as fillers, binders, and fragrances. We want to determine the percentage concentration by volume of propan-2-ol in the hand sanitizer. We can calculate a percentage by taking the part that we want to know about, dividing it by the whole, and multiplying by 100 percent.
For example, if I wanted to know what percentage of the dots are pink, I would need to know that there are four pink dots and 12 total dots. I would substitute the four pink dots for the part in the percentage equation and the 12 total dots for the whole to determine the percentage of pink dots to be 33.3 percent.
Now let’s go back to the hand sanitizer. We want to determine the percentage concentration by volume of propan-2-ol, not the inactive ingredients. This means that propan-2-ol will be the part in our percentage equation and the hand sanitizer will be the whole. Furthermore, we are solving for the percentage concentration by volume. This is frequently written as v slash v. This means that the part and whole must have units of volume. We can substitute the volume of propan-2-ol and the total volume of hand sanitizer into the equation. Always make sure that the volume units match before solving. We perform the calculation and determine that the percentage concentration by volume of propan-2-ol is 60 percent volume by volume.