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Changing a Percentage Solution

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I don't know how many of you have run into this little problem before, but if you have then this is formula is tops! i have run into the problem in the past of needing something, such as an acid solution, that needed a certain percentage or concentration of the chemical. Say for example you want to etch a pattern in a knife but the etching solution (we will say an acid solution for example purposes) is a 25% solution, but you want it a little more dilute to have better control over the etching rate. How do you calculate how much water do you mix with the acid you have to make it a 15% solution? This little formula works like a charm and gives you very accurate results.It is a simple little subtraction formula that anyone can do.

To begin with write down the following letters on a sheet of paper.

(To make it simpler to use write the letters across the page rather than down as shown in this post.Keep a good separation between the letters)

To figure out a percentage dilution:

1.Place the percentage strength of the solution to be diluted at A
2.Put the percentage of the diluting solution at B (water should be entered as 0 )
3.Place the desired percentage at D
4.Subtract D from A and place the answer at Y
5.Subtract B from D and place the answer at X

Then mix X parts of A with Y parts of B to make the percent solution listed at D.

Example 1
Using the numbers from above ( 25% solution, needing 15% solution) using water to dilute:
A - 25
B - 0
D - 15
X - 15
Y - 10

Following steps 1 to 5 from above you would mix 15 parts of 25% acid solution with 10 parts water to get a 15% acid solution.

Example 2
You have a 25% solution of acid and a 10% solution of acid but you want an 18% solution of acid.In this case we will be using the weaker acid to dilute the stronger one down to the percentage req'd. Using this same formula:

A - 25.
B - 10
D - 18
X - 8
Y - 7

Again following steps 1 through 5 above you would mix 7 parts of 25% acid with 8 parts of 10% acid to make a 18% solution of acid.

This seems a little confusing when you first start to use it but after you have done it a couple of times it is really quite simple to do.Just use the numbers I provided in the examples and work it out yourselves a couple of times then work in your own numbers for practice. It is surprising how easy it becomes to use it.


Always add acid to water, or a stronger acid to a weaker, to prevent splashing

Edited by mod07
edited typo for safety

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The simple formula we used to perform this dilution in the chemistry labs was:

C1V1 = C2V2

Where C=concentration and V=volume. A little algebra will help you calculate the unknown variable.

For example, you have 100ml of 25% acid that you want to make 15%.

25 X 100 = 15 X V2

(25 X 100) / 15 = V2

167 = V2 so you would have to add 67ml of water to the original 100 ml
of 25% acid to get 15% solution.

As a note for acid dilutions ALWAYS add water to concentrated acid, NEVER add concentrated acid to water.

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