Ok math guys/gals, need help with dilution calculations

Discussion in 'B&W: Film, Paper, Chemistry' started by Eric Rose, Oct 22, 2003.

  1. Eric Rose

    Eric Rose Subscriber

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    Barnbaum now uses the following dilutions for TriX 320 rated at asa 160.

    First he makes a stock solution of 1:3. Then he takes that and further cuts it to 1:12.5.

    If you were just going from the concentrate to the final dilution what would it be? Would it be 1:37.5? I just have a mental block when it comes to ratios and dilutions etc. Duh!!
     
  2. jbj

    jbj Member

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    first: 1:3 is equal to 1 part in 4 parts total, or 1/4 =25% v/v

    1:12.5 is equal to 1 part in 13.5 parts total, or 1/13.5= approx 7.4% v/v

    multiply 0.074 * 0.25 = 0.0185 or 1.85% v/v or approx 1.9% v/v

    then to see what the overall dilution factor is:

    solve the equation for x

    1/(x+1) = 0.019 x = 51.6

    so overall this is equivalent to approximately 1:51.6 dilution

    hope this helps,
    JBJ
     
  3. Eric Rose

    Eric Rose Subscriber

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    I stand in awe.

    As defined:

    A mixed emotion of reverence, respect, dread, and wonder inspired by authority, genius, great beauty, sublimity, or might.

    So if I want to make up 1000ml of working solution would I say 1:52 so that would be 53 parts in total. So 1000 / 53 = about 19ml. So 19ml of concentrate and the rest water to make up 1000ml?

    Geez this stuff drives me nuts!!
     
  4. jbj

    jbj Member

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    The main reason to do it in two successive dilutions is that it is (usually) more accurate to say dilute both 25 ml + 75 ml (1:3) and also 1:12.5 than to add simply add 18.5mL + 980.5 mL = 1:53 (999mL total)

    This is more accurate than what I posted the first time, remember I rounded up in my first post from 0.0185 to 0.019. So to be more accurate is a 1:53 dilution, or 1 part in 54 total (18.5 + 980.5).

    Another issue is the rate at which these solutions deteriorate. A concentrated stock solution will oxidize/deteriorate much slower than a dilute solution in which the pH is not as well buffered and more aeration has taken place (mixing fresh oxygen-rich water with concentrated developer).

    But to answer the original question:

    1:53 dilution is really close. That would be 18.5mL + 980.5 mL. 999mL total. I assume you have graduated cylinders that can measure an accurate half mL increment?

    good luck,

    JBJ
     
  5. Jorge Oliveira

    Jorge Oliveira Member

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    From a strictly practical view from someone tha have used HC-110 higly dilluted for a long time;

    If you use 19ml + 1liter water, it will be VERY much OK.

    I've never been able to tell the difference between 5ml concentrate to 295 or 300 ml water.

    Jorge O
     
  6. ann

    ann Subscriber

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    Darn! I still confused and I mix from scratch all the time. Surely I am not the only one who is still lost? (And I am not even using that combination)
     
  7. Ole

    Ole Moderator Staff Member Moderator

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    Funny, these rounding-off errors...

    1:3 gives 1/4 concentrate. So the next step is: 1/4 : 12.5, multiply both sides by 4 to get 1:50.

    Why make it more complicated than it is?
     
  8. jbj

    jbj Member

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    As Jorge pointed out, for practical use it probably doesnt matter that much for this particular developer/film combination. I don't use HC-110 so I cannot comment on that.

    However I do use D76 and TMX sheet and roll films. My experience with this combination, and what I have read from others, is that tight control over all aspects is important (temperature, agitation, concentration, time, age of developer, etc.)

    But, with respect, in strictly technical terms 1:3 further diluted 1:12.5 is not the same as 1:50

    (1/4) * (1/13.5) = 1/54 not 1/50
     
  9. fhovie

    fhovie Subscriber

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    Beautiful Mind??
    Governing Dynamics?

    .... sorry -- I live near Hollywood
     
  10. Ole

    Ole Moderator Staff Member Moderator

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    It ends up as 1+50, not 1/50 concentration. The final ratio is 1/51... Which is what I dislike about the convention of writing 1:12.5 when what is really meant is 1 part A plus 12.5 parts B.
     
  11. MJD800

    MJD800 Member

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    What developer is it Eric? I have a chemistry friend who may be able to tell us whether it is critical to dilute 1:3 then 1: .. or can you just go strainght in to the final dilution. Some compounds dissociate into their constituents if you don't maintain the buffer level, he told me one night when we were both pretty drunk and very young and foolish. He grew out of it. I am still working on all 3.
     
  12. Eric Rose

    Eric Rose Subscriber

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    Using HC 110. Actually as an update just developed some TX rated at 200asa with a 1:53 dilution (19ml of HC110 with water to 1000ml). Came out really good, but before tipping a glass of wine I will need to do some prints. That will have to wait until later Nov. However the tonal range seemed very wide and the grain was very subdued.