Figuring dilution

[Ulophot]

With some trepidation that there will be conflicting responses to this just as there are regarding the calculation of lighting ratios, I'll take the risk.

I recently mixed up some stronger selenium toner than my usual, for an experiment. My usual is what I thought to be 1:19, and this was, I thought, 2:9 (1:4.5). I may not have further use for the stronger, and thought I'd calculate how to dilute it to 1:19. Since math tends to make my eyes glaze over, I tried to figure it out but eventually performed a web search, where I discovered that, respecting dilution ratios, 1:19 does not mean 1 part toner and 19 water, but 1 part toner and 18 water; likewise, 2:9 is only nine parts in total, not eleven. So, my 2:9 is actually... well, some amount weaker than I thought, not that that makes much difference at the moment.

However, I remain at a loss to arrive at how much water I need to add to my "2:9" to convert it to my "1:19". If it helps, I could start with, say, 32 oz. of "2:9".

I will be grateful for guidance.

[Doremus Scudder]

Philip,

I've posted this before, but it bears posting again. Here's an easy way to figure dilutions. Don't be put off by the algebraic-looking equation; it's very easy.


Q1/Q2 :: C2/C1 or… Q1 x C1 = Q2 x C2 (Note: the "::" means "is proportional to.")

Where
Q1 = quantity 1, Q2 = Quantity 2, C1 = Concentration 1 (%), C2 = Concentration 2

So, using your example:

Q1 = however much you want to dilute, lets say 100ml
C1 = 2:9 which is the same as 2+9 or 2 parts in 11 parts total or, converted to percent by dividing the total amount by the smaller amount, approx.18% ((2/11) x 100 = 18.1818...)

and you want 1:19 or 1+19, or 1 part in 20 total, so dividing total by smaller we get: (1/20) x 100 = 5%, so...
C2 = 5%
Q2 is what you're trying to find, so it's "X"

So, using our formula above,
Q1 x C1 is 100 x 18 = 1800
Q2 x C2 = X x 5 or better, 5X

Now we make our equation:
1800 = 5X

Divide both sides by 5 to get X alone and we get:
1800/5 = 360

So just add water to 100ml of your 2:9 solution to bring it up to 360ml and you're done. (Because of the approximating we did above, you're actually about 3.5ml short, but that shouldn't matter much; you can do the math more precisely if you want.)

The formula works for any standard w/v type of dilution and for most v/v things as well. It only fails when mixing two volumes of different things results in a different volume than the sum of the two parts, which is relatively rare with photo chemicals and aqueous solutions.

You could also work the formula backward, deciding how much of Q2 you wanted and have Q1 be your unknown. It's the same math.

However:
Now I'm going to tell you you're wasting your time toning your prints in a given dilution for a given amount of time.

You simply will not get the same result over time doing this. Every print through the toner weakens it somewhat. As more prints go through, the activity decreases. After 10 or so prints through a normal amount of toning solution, print 10 is not nearly as fully-toned as print one in the same amount of time.

The actual amount of toning is what matters, and that is only practically controllable by visually evaluating your prints. Keep in mind, that if you're not getting any visible tone change or any perceptible change in densities, you're not toning, or you're toning so little as to make no difference.

My advice: Tone till you get the desired image change. If toning times are too fast, dilute your working solution till times are more comfortable and vice-versa. Keep an untoned print wet and easily viewable under the same lighting so you can monitor the progress of the toning. Tone till you get what you want and note the time. You can use this time for the next couple of prints to get the same effect for prints of the same image on the same paper, but don't think you can use it for many more than that or for prints of other images.

Every print has a different distribution of densities and tones differently visually. Some prints need a bit more toning, some a bit less to "feel right."

If you're toning for "permanence," forget it. It's been fairly-well established that any degree of protection that selenium toning gives is proportional to the amount of toning. Toning for X minutes in a 1:X dilution and getting no visible change gives you zero protection. And, not many of us want to fully-tone a print in selenium; we usually just want a hint of that purplish-red to counteract the unpleasant tone of the paper or to lend the print a little warmth. Not many want to see bright red or fully light-brown prints. So, we're only getting partial protection anyway. The best way to ensure the longevity of your prints is proper fixation and washing.

I've got two jugs of toner, one labeled "weak" and one labeled "strong." I'm not sure what the actual dilutions are, just that some papers tone rather quickly and I can work more comfortably with weaker toner and some papers need a rather strong toner to get any reaction in a reasonable amount of time. When my toning times get too long, I add some concentrate to the working solution replenish it and boost its activity.

If you haven't seen all (or some) of my posts on replenishing and reusing selenium toner, do a search on my name and the site and you'll find them easily.

Best,

Doremus

[Oren Grad]

...I tried to figure it out but eventually performed a web search, where I discovered that, respecting dilution ratios, 1:19 does not mean 1 part toner and 19 water, but 1 part toner and 18 water; likewise, 2:9 is only nine parts in total, not eleven.

...except that would mean that "D-76 1:1" is undiluted D-76, which is never how that notation has been used. This kind of confusion is why many of us prefer the X+Y notation rather than X:Y.

Let's make the arithmetic concrete. Suppose you've mixed a total of 110 ml of diluted toner as two parts toner plus nine parts water (2+9). That means you've used 20 ml of toner plus 90 ml of water. To make the overall dilution 1+19 instead, you'd need to have 19 times as much water as toner, or 19 * 20 = 380 ml of water. So you'd add another 290 ml of water to your original 90 ml and end up with a total of 400 ml of toner diluted at 1+19. (20 ml of toner concentrate + 90 ml of water that you initially added + 290 ml of additional water that you subsequently added.)

Your 32 oz example results in messier arithmetic, but we can do that too. 5.8 oz of toner concentrate plus 26.2 oz of water gives you 32 oz of toner at 2+9. (Note that I've rounded up to tenths of an ounce, so the ratio isn't *exactly* 2+9.) To make the overall dilution 1+19 instead, you'd need 19 * 5.8 = 110.2 ounces of water, or an additional 110.2 - 26.2 = 84 ounces, to give you a total quantity of 116 oz of toner diluted 1+19.

[Tin Can]

I consider many mix are insane, starting with dilution h

[Doremus Scudder]

...I tried to figure it out but eventually performed a web search, where I discovered that, respecting dilution ratios, 1:19 does not mean 1 part toner and 19 water, but 1 part toner and 18 water...

Philip,

I missed this on first reading and calculated incorrectly the first time (it's always setting up the problem that gets you ).

As far as Kodak is concerned, 1:19 and 1+19 are exactly the same thing. Really, the use of the colon here is ambiguous and should be either qualified or replaced.

Personally, I like 1+x. As for my response to your question, I've recalculated and corrected to reflect that 1:x and 1+x mean the same, which is what Kodak means and how most photo chemicals are mixed and how I should have done it in the first place. Sorry for any confusion.

Best,

Doremus

[Tin Can]

I should add the entire world was taught fractions with different rules and nomenclature

I will bow out

sorry to interrupt

[tgtaylor]

https://en.wikipedia.org/wiki/Ratio

[Wayne]

This one is fun every time.

[Ulophot]

Thanks for the assistance. I'll work on the math you have variously provided.

I have always understood a plus for the colon, after all these decades of mixing chemistry. Seeing the contrary on whatever site it was that I found, made me suddenly assume that I had been doing it wrong all this time -- exactly the kind of propitiation of arbitrary "authority" against which the great philosophers and scientists have always warned. I should know better!

Doremus, I have seen your posts on toning and have returned to that well-reasoned approach. The 1:19 starting point has been my standard since the days of printing my Portriga portfolio for college back in 1971, and all through numerous graded and VC papers since. The 2:9 had emerged as an option from tests a couple of years ago as I was returning to the darkroom and looking for a stronger toning for some images. I tested down to 1:3, finding -- correctly or not as the case may be -- that the tendency for split toning, with more toning of lower values than high, tended to increase in the middle dilutions (e.g., 1:9, 1:14) with Ilford MG; I now use the Warmtone almost exclusively. In the 1:3, 2:9 range, I was able to get more toning in the high values, but only with significant brown in the lows.

My impression is that split-toning in non-bleach/redevelop toners is a drawback of variable contrast papers in general. The graded papers of yore did not seem to evidence the problem, judging from many prints of masters. Strand and Rosenblum, for instance, achieved a onsistent warm color from high to low with a gold toning solution, for instance, and I have seen the same consistency with selenium on graded papers.

I have more testing to do. I used a rather warm fresh 2:9 toning bath a couple of weeks ago and got too much red, rather than brown. Its possible that a temperature closer to 70 is what I used in my earlier tests to achieve the brown.

Well, why lead a boring life?

[sharktooth]

I discovered that, respecting dilution ratios, 1:19 does not mean 1 part toner and 19 water, but 1 part toner and 18 water; likewise, 2:9 is only nine parts in total, not eleven. So, my 2:9 is actually... well, some amount weaker than I thought, not that that makes much difference at the moment.

Your discovery was incorrect, or rather, you got dilution ratio confused with dilution factor. Your original assumption was correct, the dilution ratio 1:19 does mean 1 part toner to 19 parts water. This jives with what everyone else has said.

Here is another approach to solve the problem, that may or may not be any easier to understand. In your example you asked to start with 32 oz of 2:9, so that's what I'll describe.

for 32 oz of 2:9 solution you have 2 parts concentrate to 9 parts water. This means you have 11 parts total. If you take your 32 oz solution and divide it by 11, you get 2.909 oz per part. That means you have 2.909 x 2 (5.818 oz) of concentrate in the 32 oz of solution.

For a 1:19 solution, you already have 5.818 oz of concentrate, but you need 19 x 5.818 (110.54 oz) of water. Combined, that gives you a total of 5.818 + 110.54 (116.358 oz) total solution. That means you need to add water to bring the total volume to 116.358 oz.

In short, take your 32 oz of 2:9 solution and add another 84.358 oz of water to bring the total volume to 116.358 oz.