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# Thread: Help for the Math-Impaired

1. Originally Posted by Ole
NO!!!!!

1:1 = 1+0, no water added!!!

Some manufacturers insist on writing 1:1 when they mean 1+1. We should not believe that this is correct, but try to find out what they really mean. 1+1 is unambiguous, 1:1 is (sadly) ambiguous.

I am not a chemist so strictly speaking I can not say that you are right on wrong in this, but what I can say for fact is that much of the photographic literature establishes equivalency between 1:1 and 1+1 when describing the mixing of solutions. And I don't just refer to the literature by people who are not scientists but also to the literature written by trained research scientists. See, for example, Chapter 7 - Photographic Solutions of Grant Haist's Modern Photographic Processing, Volume 1. On page 345, for example, in describing mixing a 1:3 solution of Kodak D-76 working solution from a stock solution, Haist writes: "For the 1:3 dilution, take 250 ml (one part) of the stock solution and add it to 750 ml (three parts of water) . . . "

There is something strongly counter intuitive in the statement that “1:50 is the same as 1+49, so that makes 10ml concentrate to 490ml water, or that 1:100 = 1+99.” I personally find a great deal of linguistic ambiguity in this statement, even if in fact it is correct scientific terminology, if for no other reason the fact that the common defiition of *ratio* is far from completely unambiguous.

Now, if we talking about percent solutions this makes sense, because a one/half percent solution would indeed be one/half part of something in water (or some other solution) to make 100 total parts, or one part of something to to make a total of 100 parts.

But the basic point is that most photographic texts, and much if not all of Kodak literature, establish an equivalency between solutions that are expressed as 1:2:100 and one part A + two parts B + 100 parts C.

Sandy

2. Thanks, Shyguy and Ole. I agree, Ole, the the "plusses should be used. And, to "split hairs" your latter statement (1+2+97) is more precise.

3. Originally Posted by sanking
There is something strongly counter intuitive in the statement that “1:50 is the same as 1+49, so that makes 10ml concentrate to 490ml water, or that 1:100 = 1+99.” A rational person should certainly see a great deal of ambiguity in this kind of description, even if it scientific terminology.
Yes, and the amibuity does come from the irrational (really incorrect) use of ratios. The ":" sign indicates a ratio. Kodak uses it as a plus sign. That's the irrational part. "1:50" should be read as one part taken to a final volume of 50 parts, hence the equivalence to 1 part + 49 parts = 50 parts.

The "part plus parts" system really does make the most sense. Have you noticed that you never see anyone asking questions about "if I take 1 part of this and add it to 99 parts of that, how many parts do I have?"

Despite the usage by Haist and even Kodak today, it really is too bad that Kodak and others promote this expression today.

Originally Posted by sanking
Now, if we talking about percent solutions this would sense to me, because a 1/2% solution would indeed be one part of something in water (or some other solution) to make 50 total parts, or a 1% solution would be one part of something in 99 parts of water to make a total of 100 parts.
Sandy, I'm sure you meant that a 1/2% solution would be 1 part into a final volume of 200 parts, not 50 parts, as that makes a 2% solution.

Anyway, I'm just glad they don't use normal (N) concentrations. Molar, I could live with that...

4. Originally Posted by Kirk Keyes

Sandy, I'm sure you meant that a 1/2% solution would be 1 part into a final volume of 200 parts, not 50 parts, as that makes a 2% solution.
Hi Kirk,

Thanks. I corrected the statement. At least I think it was corrected!

Sandy

5. Thanks for the interest and the info, everyone. I've attached the spreadsheet that I started that got me wondering if my brain had gone south on me... It just didn't look right and seemed that my conversion factor wasn't correct. I inserted some numbers, etc and pasted a copy below. My main concern was to accurately build 500ml working solutions to test what would become concentrates if they worked. It had dawned on me that the concentrates go so far that things that don't work seem wasteful and I was becoming less quick to try experments because of that. I think this is right, now but I'd welcome corrections. It seemed easier to apply to a spreadsheet when I converted my thinking to parts/L and go from there.

Sheet

6. Craig, it's much, much simpler, at least for spreadsheet purposes, if you just include the number of grams or ml of component X and enough water to dissolve the components, and finish with "water to make 1 liter". Then for 500 ml, you use X/2 and water to make 500 ml. And for a concentrate, if you're making it yourself, you'd decide if you want 50 ml concentrate and water to make 500 ml (what I think of as 1:9, but by Ole's nomenclature would correctly be 1+9), or if you'd find it easier to use 45.5 ml concentrate and water to make 500 ml (1+10). For my money, if working in metric, 1+9 is about the simplest dilution you can possibly use.

Of course, different systems give advantages different places. Back around 1967, Kodak picked 1+31 (or 1:31, as they call it) for HC-110 Dilution B because it was one ounce concentrate per quart of working solution (and then they complicated the whole situation by recommending you mix the whole bottle of concentrate into stock solution, 1+3, and then use the stock solution at 1+7 -- it's tricky to get into the right mental viewing angle for that combination to add up the same as 1+31).

Now, just to bollix the works a bit, if you're mixing your own chemisty, the simple way is to make up packets of dry chemicals containing the premeasured amount of each ingredient to make 500 ml of working solution, and if you need a liter, use two packets. The only time there's a significant disadvantage to doing this is if a) you have a formula that is difficult to dissolve (has a lot of borax or sodium sulfite, for instance), or b) you have an ingredient that doesn't keep well in dry form, such as glycin. If you routinely use several different size batches, however, and have a concentrate that keeps well (say, dissolved in TEA or glycol, so the alkali isn't ionized and thus the phenidone doesn't deteriorate), then a concentrate will be easier than using the correct number of small-batch packets or keeping several packet sizes on hand; this is also the case if your formula is difficult to fully dissolve at room temperature.

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