Need some math assistance here.
If I have 32 oz of phosphoric acid 85% concentration, how do I calculate the amount of water to dilute the 85% to some other percentage?
I’m having a brain cramp here!
assuming we are talking about volumetric %
85% of 32 is 27.2. (Total Volume X %pa) = volume pa)
if you want 75% you need to have
Total Volume X .75 = 27.2
so total volume = 27.2/.75
so 36.266
so add 4.266 oz water and you have 75% concentration.
volume A x concentration A = volume B x concentration B
Say you want to make 10 mL of a 8.5% concentration:
10 * 8.5 = x * 85 - solve for x
(10 * 8.5)*85 = x
You would need 1 mL of your concentrated solution to make 10mL of your dilute solution.
You math guys! My problem is once I have solved for X, I don’t have a container with the gradients needed!
what’s the trouble? are you trying to measure out tenths of a ml? you can probably find an appropriately graduated syringe at the drug store.
Just kidding - but 4.266 ounces is just going to have to be a heavy 4.25 ounces!
ahh yes. well we do the best we can. easier if you use metric.
Generally chemicals when indicated as being a certain % concentration are in weight %. ABV is somewhat of an aberration.
Thus
mass A x conc A = mass B x conc B.
You can measure water by weight too. 4.26 oz (weight) = 4.26 oz (volume)
only at 39*f
Only at 4°C, and only if we’re talking about avoirdupois fluid ounces. At 20°C one US customary fluid ounce of water has a mass of 1.041 avoirdupois ounces.
Anyway, the problem with solutions is that mass/volume don’t usually scale linearly with concentration. If it’s important to get a precise result, you’ll need to look up a table for that particular solute/solvent.
Yeah, what he said.
I checked the CRC handbook. I have gravity and other properties up to 80% lactic acid. D’Oh! Anyway the gravity at 85% should be 1.19 g/l based on interpolation of 80% lactic acid and pure lactic acid.
Eh, it’s an art.
That’s what you always say! 
Thanks for the solutions!
Always fun to see the responses from the homebrewing mathematicians and scientists among us!