A little Math Help Please

[Dutchelm05]

Can anyone provide the formula for this.

I have X IPA (volume) and Y water (volume) = % IPA
I want to increase my water to get various IPA concentrations.

Example:

91% IPA, 9% water

I want 85% IPA. How much water do I need to add
Now I want 82% IPA. How much water do I add.

I tryed a few formulas and they didn't look right.
Anyone have a excel spread sheet or website or old fashion easy way of doing this.

Thanks
Tony

[Joe Farina]

Tony, here are a couple pages from the Mayer book which may be helpful.

[Ed Wesly]

What you are dealing with is a class of problems called inverse proportions. I just covered some of these things when I taught MAT 099 this summer. (Don’t forget I am the Math/Science Department of Harrington College of Design’s Digital Photography Department!)

If you want me to go totally math teacher anal and derive this formula, I would, but rather not. Here’s what you need to do:

To solve as a proportion: original percentage/new percentage = new volume/original volume
or to cut to the chase:

(original percentage/new percentage) * original volume = new volume

Need to subtract original volume from new volume to get the amount to add.

Example: Starting with 100 ml of 90% IPA, how much water needs to be added to get an 85% solution?
(90/85) * 100 = 105.8823529, so 5.8823259 ml need to be added, which rounds to 6 ml, unless you have a graduated cylinder that reads to the picoLiter!

Proof: the 90% solution means that 90 of the 100 ml are IPA. Adding the ~6 ml of H2O means you have 90 mL of IPA in 106 mL solution, with 90/106 = .849056604, close enough to 85% for Art School or holographic spec’s! (To be crazily exact, 90/105.8823529 does = exactly 85%)

Hope this helps!

After writing this and then reading the pages from the book, this is equivalent to the Artist’s Handbook p. 622 example 1.

[JohnFP]

Tony, I keep it simple. Alcohol comes in 70% and 91% off the shelf. So I think of both numbers, the alchol and the water. SO...

70 ml alcohol ..........30 ml water

For a 50% add 40 ml water to 100ml of 70% alcohol to have 70/70. (I really don't use this one)

For a 33% add 110ml water to 100 ml of 70% to have 70/140. ( I actually just add 100ml water to make it reall easy to remember, thus my baths are 33 - 35%, 70% (stock), 91%(stock) and 100%(stock)).

With these numbers you have 33%, 50%, 70%, 91% and 100% without using up your good stuff to make lower concentrations.

But we all know with a few uses these numbers go down as water is extracted out of the plate. To really conserve, I got a hydrometer. After a session of 10 or so plates I would measure each concentration and down it one. That is, ditch the 33%. Use the 70% to make 33%, use the 91% to make 70% and the 100% to make the 91%. This isn't too hard with the hydrometer but does take a little time. Just add a little water, stir and measure.

I know this doesn't directly answer you question as Ed did, but it was my way of keeping it simple to remember.

[Ed Wesly]

But it's identical to my method by intuition! Good thinking!

[Dutchelm05]

Wow thanks guys,
I knew you would come through.
You are the guys who messed up the curve for me when I was in school

I added Ed's and Joe's formula into excel

Thanks
Tony

[BobH]

If I remember correctly, alcohol dilution isn't straight forward. In other words, when you put 50mL of alcohol into 50mL of water, you get something less than100mL of solution. Might not be significant, but that's what I remember.

[Ed Wesly]

Yeah, I was thinking that myself, like the little H2O's fit in between the bigger bulkier IPA's, but chose to ignore it. But if that is so, then the specific gravity solution in the cut and paste above would be the safer way to go, but I wonder how significant the difference is.

Thanks a lot for making life so much more difficult! I thought I was the only party-pooper around here!

[BobH]

No Ed, I too love to poop on a good party. It's the technician in me. You gotta' know what's wrong before you can fix it! In any case, that little factoid and Avogadro's number (go figure) are about the only things I remember from high school chemistry.

[JohnFP]

LOL. You guys are the best.