Answer :
Final answer:
To dilute a 65% isopropyl alcohol solution to a 50% concentration by adding sterile water, the person needs to add around 0.3 gallons of water. This is calculated by setting up the proportion of isopropyl alcohol to the total solution as equal to 50%, and solving the resulting equation.
Explanation:
The task involves diluting a 65% isopropyl alcohol solution to a 50% solution by adding sterile water. We know that a gallon of the initial solution contains 0.65 gal of isopropyl alcohol, because 65% of 1 gal is 0.65.
In order to attain a 50% solution by adding water, the total volume of the solution should be such that the isopropyl alcohol portion equals 50%. Consequently, you can use the following proportion to solve this problem:
isopropyl alcohol / total solution = 50%
So, 0.65 / (1 + x) = 0.50
Where x is the volume of sterile water to be added in gallons. Solving this equation for x yields approximately 0.3 gallons.
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