SOLUTION: please show me the way you solve this problem. i am almost there. How many gallons of 5% acid solution should be mixed with 20 gallons of a 10% acid solution to obtain an 8% acid s

Question 945690: please show me the way you solve this problem. i am almost there. How many gallons of 5% acid solution should be mixed with 20 gallons of a 10% acid solution to obtain an 8% acid solution?

Found 3 solutions by lwsshak3, josmiceli, KMST:
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
please show me the way you solve this problem. i am almost there. How many gallons of 5% acid solution should be mixed with 20 gallons of a 10% acid solution to obtain an 8% acid solution?
***
let x=amt of 5% solution to mix
x+20=amt of combined 8% solution
..
5%x+10%*20=8%(x+20)
.05x+2=.08x+1.6
.03x=0.4
x=13 1/3
amt of 5% solution to mix=13 1/3 gallon
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = gallons of 5% acid solution needed
= gallons of acid in 5% acid solution
= gallons of acid in 10% acid solution
----------------------------------------------

13.333 gallons of 5% acid solution are needed
-------------
check:

OK

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
A CHEMIST"S NOTE: Be careful with acids. Do not use them or mix them unless you know exactly what they are, and what will or may happen when you mix them.
I have tablets that are mostly ascorbic acid (vitamin C) an others that are almost pure acetylsalicilic acid (aspirin) in the medicine cabinet section of my kitchen at home. Most people can swallow one of those tablets without ill effects.
In the lab, in a vented cabinet under the fume hood, I have liquids labeled sulfuric acid, nitric acid, glacial acetic acid, trifluoroacetic acid, and hydrochloric acid. The last one is a 36%w/w solution of hydrogen chloride gas in water. Do not ingest those.
I also have a lot of solids in my lab shelves with labeled names that include the word acid. The labels tell you about their dangers.

According to math teachers who never learned enough chemistry:
1) "Acid" is a term that is descriptive enough.
2) "A 10% solution" is a phrase with an unequivocal meaning.
3) When you mix volumes of liquids, the volume of the resulting mixture is the sum of the volumes mixed.
In the real world, none of that is true, but in the math teachers' world it works just fine.
In both worlds, we all agree that the amount of "acid" in the mixture is the sum of the amounts of "acid" that were in the solutions that were mixed.

= gallons of 5% acid solution that we need to mix with 20 gallons of a 10% acid solution to obtain an 8% acid solution.
Your teacher believes that 100 gallons an "8% solution of acid" contains 8 gallons of some liquid called "acid". I would describe that solution as an 8% (v/v) solution, where the "(v/v)" means volume in volume.
Your teacher believes that 100 gallons a "5% solution of acid" contains 5 gallons of some liquid called "acid". So, gallons of that solution contain gallons of acid.
Your teacher also believes that 100 gallons a "10% solution of acid" contains 10 gallons of some liquid called "acid". So, gallons of that solution contain gallons of "acid".
When you mix something containing gallons of acid with something containing gallons of acid,
you get a mixture containing gallons,
That mixture is expected to be an "8% solution of acid", and
since your teacher believes that 100 gallons an "8% solution of acid" contains 8 gallons of some liquid called "acid",
gallons of that solution contain
gallons of "acid".
So our equation is

gallons (rounded).
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