Tom has 1 cup of a 5% vinegar-water solution, 2 cups of a 10% vinegar-water solution, and 3 cups of a 15% vinegar-water solution. He needs at least 8 cups of a 5% vinegar-water solution for his chemistry project. What is the number of cups of pure water he should add to the total of all his vinegar-water solutions to complete the project?

Another eight cups of pure water will be required.

Explanation:

Start by calculating the amount (in cups) of vinegar in these six cups:

Therefore, if these six cups of solutions were mixed, the mixture would contain cups of vinegar. Also, the mixture is supposed to have a volume of six cups. Therefore, the concentration of this six-cup mixture would be:

.

In other words, if these six cups of vinegar-water solutions are mixed, it would be necessary to dilute (by adding more water) before reaching the concentration of .

The goal is to dilute this solution with cups of vinegar to a concentration of . Consider: what would be the volume the solution after dilution?

The volume of a solution can be found from the quantity and concentration of its solute:

After dilution, the volume of this solution would be:

.

At this moment, this solution only has a volume of six cups. Therefore, cups of pure water will be required.

a electronegativity decreases beacuse the size of nucleus is bigger.