Question 877862
"I have one gallon of acid 30% solution"


So you have 1*0.30 = 0.30 gallons of pure acid.


-------------------------------------------------------


This means


(amount of pure acid)/(total amount of solution) = (0.30)/(1) = 0.30


which points back to the 30% acid solution


-------------------------------------------------------


Let x = amount of water to add (amount in gallons)


If you add x gallons of water to the solution, you get 1+x total gallons (acid + water)


so we now have


(amount of pure acid)/(total amount of solution) = (0.30)/(1+x)


You then take (0.30)/(1+x) and set that equal to 0.05 because you want to force the final solution to be 5% acid.


So,


(0.30)/(1+x) = 0.05


Now solve for x


(0.30)/(1+x) = 0.05
0.30 = 0.05(1+x)
0.30 = 0.05+0.05x
0.30-0.05 = 0.05x
0.25 = 0.05x
0.25/0.05 = x
5 = x
x = 5



You need to add <font color="red">5 gallons</font> of pure water to dilute the 30% acid solution to a 5% acid solution.