mathematics of dilution?

how do i learn to make different dilution numbers? for instance 1:30 or 1:100

 

how do i learn the math of dilutions? the package for dektol i believe tells you

to dilute 1:30, but i don't know how. how do i learn this stuff?

 

i know 1:1 is 1 part water and 1 part developer, if your tank is 20oz thats 10

and 10, thats as far as my knowledge goes.

You add the total amount of parts 1:30 will be 31 you divide your tank volume (20) through that and know how much developer you'll need: 0.6452oz - Happy eyedropping or Insulin-siringing

Ok, you are more advanced than you might think ...

 

Yes, a 1:1 is one part of A and one part of B.

 

same for 1:30 ...

 

one part of A and 30 parts of B ... one part developer 30 parts water.

 

Note that 1 plus 30 is 31 ... so, if you need 20oz (twenty oz), you calculate the size or weight of one part by dividing the 20oz by the number of parts (31) ... so ...

 

one part is: 20/31 oz (= 0.65 oz)

 

thirty parts are: 30*20/31 oz (= 19.35 oz)

 

same calculation for 20 oz of a 1:100 dilution:

 

one part is 20/101 oz

 

hundret parts are 100*20/101 oz

Hi Justin,

 

Pretty straightforward:

 

1:30 = 1 part concentrate, 30 parts water,

 

1:100 = 1 part concentrate, 100 parts water, etc.

 

/Clay

Sorry Justin,

I have to get new glasses, didn't see that part about

a 20 oz. tank ! The above advice is correct.

 

/Clay

A more interesting mathematical question is if something needs to be diluted 1:X for use, and you partially dilute it at 1:Y, what dilution ratio is needed to get this new solution to 1:X ?

Or:

If something needs to be diluted 1:X for use, and you want to mix an in-between solution that must be diluted at 1:Z in order to create a 1:X dilution, what is the ratio needed to get the in-between solution?

Transform a 1:X dilution into a 1:Y dilution:

 

case 1) X is smaller than Y: Example one liter of 1:10 -> 1:20

 

the liter of 1:10 contains 1000/11 = 91gr "stuff" (and 909gr water)

 

to make a 1:20 dilution of 91gr stuff, I need 20*91gr water = 1820gr.

The 1:10 dilution already contains 909gr water, so I need to add 1820-909 = 911gr of water to change from 1:10 to 1:20 ... I'll then have 1911gr of 1:20 dilution.

 

case 2) X is bigger than Y: Example one liter of 1:10 -> 1:5

 

One liter of 1:10 contains 1000*10/11=909gr water. To make a 1:5 dilution with 909gr water, the dilution needs to contain 909/5=182gr "stuff" ... 91gr stuff is already in the dilution, so I need to add another 91gr "stuff to it, and the dilution ratio will be 1:5.

I saw a lot of ppl using the meaning 1:30 meaning 1 part of A and 30 equal parts of B. Say 100ml of A then add 3000ml or 30 parts of B. But isn't the version 1:30 (just arbitrary numbers) but isn't that Ratio which is differnt? Which is actually I think explained correctly in the above post.

Reason I bring this up is cause most of the chemicals I use don't say 1:9 or 1:19, they say 1+9 or 1+19 for dilution and mixing. If a bottle, say my stop I use, Ilford Stop, says to dilute 1+19, so if I use 50ml of concentrate stop, then I would add 950ml of water right (50mlx19=950)?

Or my developer says to dilute 1+9, so 100ml of dev and 900ml of water right?

 

I have gotten kinda confused latley at the different labels one saying 1:4 and one saying 1+4, the (:) symbol indicates a ratio to proportion and the (+) symbol just means adding that much equal part of each.

If I remember from math, ratios are calculated differnt due to the proportion being made, but simple 1+4 is just diluting using equal parts to make a proper working solution no matter what the end quantity is, where a ratio is a soulution mixed for a specific proportion of product right?

 

Just curious cause in school I remember for most of the new photo students they put up a little sign over each tray, we used D-76 dev and the chart would say, add 200ml of developer and add 1800ml of water to the tray being a 1+9 like the bottle says. Is that correct?

 

I can't quite remember how to calculate ratio and proportion, but I think it is more like dividing and cross multipying to get the correct dilution for a specific end quantity as explained in the above post right?

Justin - first things first. When you mix Dektol per the package instructions you get what is commonly known as a "stock solution". Kodak recommends you dilute the stock solution 1:2 for use in developing your prints not 1:30 as you indicated. An example: dilution 1:24 Total solution needed 300ml (ounces or whatever). Sum of dilution 1 + 24 = 25. 300ml divided by 25 = 12ml (amount of concentrate or stock solution needed). 300ml - 12ml = 288ml (amount of water needed). Add 12ml stock or concentrate to 288ml water and you have 300ml of solution mixed 1:24. Just what everyone else is saying but in different words.

If we have 20 cookies and we divide them 1:4 between Jack and Jill, that means Jill gets four times as many as Jack. We have to add the two numbers together (1+4=5), and divide the number of cookies with that (20/5=4). Jack gets one time this number (1x4=4), and Jill gets four times this number (4x4=16).

 

Let's see another example. We've got 20 oz of soup that we need to sink our film in. Developer gets one part, and water gets 30 part (to stick with your example), so that's 1:30. Add them up (30+1=31), and divide the total amount by this number (20/31=0.65). Developer is one time this much (1x0.65=0.65 oz), and water is 30 times as much (30x0.65=19.5 oz).

 

If you check it, 19.5 and 0.65 do not add up to 20, but that's because 0.65 was an approximation. For all practical purposes, it really doesn't matter if you are using 20 oz or 20.15 oz of soup. If it bothers you, you can dump 0.15 oz of the final mix and you are there.

Justin: consistency is the key. Just do it the same way every time.It doesn't make that much difference if it's is 1:30 or 1:29. Or, even 1:2 or 1:3. You will end up tweaking those published development times anyway to get what works for you. You don't think those development times are cast in stone do you?

. . . or take the easy way out and add 1 ounce of "A" to 100 ounces of "B" then mix well and pour into 20 ounce container. It's easier to maintain the temperatures on larger quantities of liquid too! Now James Bond would have shaken it, not stirred! :-)

Luke, your question has come up a couple of times. If you ask chemists, they will say 1:30 dilution is 1 part developer and 29 parts water. However, manufacturers of photography chemicals normally mean 1+30 by that. It's incorrect, but apparently that's what it is. In practice, though, 1+30 and 1+29 are really not that different for our purposes.

My experience shows that there are so many possible's when you work in a Darkroom, you would drive yourself potty, trying to take it all in.!

Things like chemical dilution,are pretty straight forward though.

My B+W stock normally suggests x+y ie say 1oz chemical to 9oz of H2O, the total solution being 10oz.If you need an odd total amount of solution, say 15oz for you tank,then just add 1/2oz of chemical to another 4.5oz of Water, add in the 10oz you have already made up.

Another way is 1+1/2oz chemistry,plus 13.5oz Water, total is 15oz.!

Try to keep things as simple as poss,and be consistent,make notes.!

Basic chemistry math that always helps (it's very simple but good to fully understand, as it is fundamental to how processing solutions are mixed).

 

This formula describes concentrations and volumes in chemistry:

 

C x V = C' x V'

 

where C and V are the concentration and volume, respectively, of your solution BEFORE dilution, and C' and V' refer to the concentration and volume AFTER dilution. Usually you know C, C' and V', but not V, so you can solve the equation for V.

 

An example: say you need 500 ml of HC-110 working solution at 1:31 dilution, and you need to know how much of the HC-110 concentrate to use. We don't know exactly what C and C' are, but we do know that C is 32 times larger than C' (we are diluting 1 part of concentrate with 31 parts water). And we know the final volume, V', should be 500 ml. We need to find V. Plug in the formula:

 

C x V = C' x V'

32 x C' x V = C' x 500 ml

 

Divide both sides by C':

 

32 * V = 500 ml

V = 15.6 ml

 

Therefore, you need 15.6 ml of HC-110 concentrate to make 500 ml of HC-110 working solution at the 1:31 dilution.

 

Any questions about this, just e-mail me.

1:4 is 1+3 every where in the modern world except in photography. It is evidenced by the posts at the top of this page which all say 1:4 refers to 1 part stock + 4 parts diluent. In modern chemistry if you make a 1:4 stock solution and then dilute it 1:8 and then dilute it 1:8 again, what is the final concentration of the substance you started diluting? 4 X 8 X 8 = 256. The concentrate has been diluted 1:256. When 1:4 means 1 in a total of 4, 1:8 means 1 in a total of 8, it is very easy to compute compound dilutions. When you try to figure compound dilutions using the 1:4 is 1+4 definition, it becomes very difficult to make a series of dilutions and know the resulting concentration. A great example is HC-110. Kodak suggests you make a 1:4 stock solution, then dilute accordingly for B, C, D etc. You can dilute the stock 1:8 for dilution B or 1:16 for the unofficial dilution H. Let?s see, 4X8 is 32 or 4X16 is 64. According to people that say 1:4 is 1+4, the stock solution is 1:3 and Dilution B is 1:7 from the stock and dilution H is 1:15 from stock. There is no mathematical relationship between the 3 and the 7 and the 15 to understand the final dilution of the concentrate. That is why in the 1950's dilution ratios were standardized to indicate the concentration of the substance in the total volume. You will notice HERE most use the plus sign to end the confusion. That is why you see 1+9 and 1+7 because there is so much confusion in photography when the colon is used to denote dilutions.

 

Paul

Thanks Paul,

 

I'm an engineer, not a chemist and I wondered about that myself.

Not having to practice chemistry execpt in the darkroom, I was

happy to go with the Kodak instructions, but always felt

'something' was wrong. Yeah, makes sense 1:4= 1+3 ha !

/Clay

The A:B like 1:2 in Kodak literature; even the pre WW2 stuff is clear; its "a parts ratio". Its parts of stock solution one adds to parts water to create a diluted developer; stop; or fixer etc. The confusion with the non Kodak chemists is they assumed; didnt buy any of the zillion Kodak books! :). <BR><BR>Cooking uses writing like this too; or even washing clothes; even paint. <BR><BR>A new 2007 Clorox HE bottle says add 1/4 cup (stock solution) to 1 gallon water to pretreat stains. <BR><BR This type of "marking/instructions" is as old as dirt; beasts caught in a kill were divided up in parts in the cave man days. <BR><BRTypically in the 1950's in 4H club we fixed up stock solutions 1 or 5 gallons of Dektol, D76, DK50 and stored in sealed brown gallon, quart and pint bottles. One then only used and fixed what was required; thus maximizing ones money. To mix up a batch of D76 1:2; one used one part stock D76 with two parts water. <BR><BR>The 1920's and 1930's Kodak books show one this too.; its like mixing up raw concrete or mortar; so many parts x; so many parts Y; or mixing up gunpowder in the 1200's. Or is like flower pot mix of 2 part sand; 1 part clay; 1 part manure. There cane be more than two parts too !<BR><BR>As a practical matter the old outboard 2 cycle oil mix might be 1:16 . Our 1947 Mongomery Wards manual says to add 1 oz oil; for every 16oz of gasoline. Its a "parts ratio"; one really has 1oz oil in 17 fluid oz. A "parts ratio" is done for practical reasons; one fills up a 1 1/2 or 2 gallon gas container with 1 gallon of gas; then adds 128/16 oz oil; ie 8 oz. <BR><BR>A "parts ratio" is used because folks physically have a scoup; container, or laddle in their hand; and are making soap in 1600, using clorox in 1913; making cement in old Egypt BC. A parts ratio is done because one might be making a receipe in 2000BC; or mixing a punch drink for Thanksgiving next week; its practical; it works, NO MATH IS REQUIRED. <BR><BR>A parts ratio allows folks to make KoolAid, mix developer, cook, clean the toilet, make a can of soup. Many of us have made soup with one part ie the can; and another the can filled with water. Even chemists probably can do this without a Mettler balance or simple math:) Its like figuring two beers per worker at job finish. There is an integral number of whole beers and guys too.<BR><BR>If one wants to fight with old Campbells; just try to get them to make label that requires alot of math!

<h3><b>Sing and rerecord Surf City with:</h3></b><BR><BR><BR><i>Two girls for every boy<BR>You know we're goin' to Surf City, 'cause it's two to one<BR><BR>You know we're goin' to Surf City, gonna have some fun, now

Two girls for every boy<BR><BR>Yeah, and there's two swingin' honeys for every guy</i><BR><BR>Now change the lyrics to be confusing; maybe throwing in 2/3'ds girls; 67 percent; or maybe 1 girl per 1/2 a guy?:)

A Chemists Surf City recording might have a "solution of 2/3rds girls" and make the top 100 at the chemistry lab building PA; but might confuse Chef Spicoli.

With out old British Seagull 2HP for our sailboat; its calls out for a 1:10 oil:gas mixture; and to refrain from swearing at the motor too. Its 1:16 in the old 1947 outboard; and 1:50 in the weedeater and chainsaws. With the dinky weedeater I might just mix up a pint (16oz) of gas and 16/50 oz oil with a dinky calibrated 2 cycle helper measure. When killing weeds one might mix up 2 oz of round per gallon; or a heaver dose for tougher weeds. In the 1950's thru 1990's we use to use a slicker sticker additive of a few drops per gallon; and some alcohol to cut the wax off the weeds. Boatmakers would grind down pennies to add to paint to make the paint foul less.

With large ratio the parts to ratio error is not much. A part ratio of 1:50 means one has 1 part Ethol Blue developer to 50 parts water; ie now one has 51 total parts when mixed. With a 1:2 D76 or Surf City event; one guy has 2 girls; D76 stock has 2 parts water added. Saying to mix your D76 stock solution so its 1/3 full strength is valid too; you just have to solve for the number of parts. 1/(1+X) =1/3 ; 1+X =3 ; X=3-1 =2 parts.

Kelly,

 

You are absotuley correct! If you are discussion parts ratio as in the example of 1:2:1, it make perfect sense. . Practical non scientific uses of parts ratios works for the general public. And I noticed in your examples you also cited specific instructions which takes the mystery out of how to mix A and B substances; the instruction left nothing to chance.

 

Regarding Surf City, I am not going to hang my hat on a song to prove or disprove anything. The lyrics work for the song and the Beach boys were very successful. And being a California boy in the 60's those were great odds no matter how you interpreted them.

 

A number of years ago I had to mix equal volumes of Glacial Acetic Acid and Acetic Anhydride. To 900 ml of that mixture I had to add 100 ml of Sulfuric Acid. The final solution would measure Cholesterol in human serum. The formula was not in parts ratio because there is too much confusion and a mistake in these ratios can be dangerous. Photography comes under modern chemistry and the mixing of solutions and making dilutions has people from all walks of life; some scientific and some not. If two people read HC-110 Dilution B is a 1:32 dilution from concentrate, and 1 make his developer 1+31 and the other 1+32, there will be very little difference between the action of the two developers. But if these two people read D76 should be diluted 1:2 and 1 makes his developer 1+2 and the other 1+1, there will be a big difference between the action of the two developers. Science had the same problem 50 years ago that we are discussing here today. They settled on 1:4 should be a fraction; 1/4. Most suppliers of photographic solutions see the issue and have replaced the colon with a + sign; end of confusion on how to dilute your stock solution for a working solution. But when somebody ask how to compute dilutions and what do they mean as is the case in this specific question, I feel Justine deserves the best answer that conforms to modern photography, science and math.

 

Paul

Yes the "x:y" formulation is confusing. I much prefer this one "x+y".