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If have a container with a capacity of 5,000 cubic inches, how do I calculate the ratio of 50 ppm? I would describe the problem as,

1.) statements,

a/b = 50/1,000,000
a = ?
b = 5,000

2.) show your work,

Establish the ratio of the ppm ratio and "to be scaled"* volume

50/1,000,000 = a/5,000

Cross multiply,

a1,000,000 = 50*5,000
a = .25

3.) the full answer,

The fraction of liquid (a) to liquid (b) is 
0.25 cu. in. of liquid (a), to 5,000 cu. in. of liquid (b).

4.) Check my work,

(0.25/5,000) = 0.00005 = (50/1,000,000)

Is this correct? Is there a simpler way?


* I'm making this ratio fraction problem simple and not using the "total" volume.

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1 Answer

Ah, but you are using the "total" volume, and in fact, what you have called $B$ is this total volume, and it is not, as you seem to be thinking, the volume of the second liquid. If it is, then you now have a total liquid volume in the container of 5000.25 cu.in., and have apparently have spilled a little.

However, I think your overall approach is correct, you've just mis-interpreted your results. There are 0.25 cu.in. of liquid $A$, 4999.75 cu.in of liquid $B$, for a total volume of 5000 cu.in (with liquid A occupying 50 ppm.)

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Yes! spilled very little but how much? (^_^) +1 for "spilled a little" –  xtiansimon Sep 27 '11 at 15:53
    
Of course were referring to the Dilution ratio: "For example, a 1:5 dilution (verbalize as "1 to 5" dilution) entails combining 1 unit volume of solute (the material to be diluted) + 4 unit volumes (approximately) of the solvent to give 5 units of the total volume. (Some solutions and mixtures take up slightly less volume than their components.)" –  xtiansimon Sep 27 '11 at 19:19
    
And yet my confusion is not unfounded since there is also this example of a simple ratio where the total is not included in ratio notation but is the total of the two values... –  xtiansimon Sep 27 '11 at 19:46
    
The Parts-Per Wikipedia page mentions "Parts-per notation is often used describing dilute solutions in chemistry", and describes PPM as a fraction. Thus the fractional definition would represent the Dilution ratio, and not what I call the simple ratio or Odds ratio "Odds (as in gambling) are expressed as a ratio. For example, odds of "7 to 3 against" (7:3) mean that there are seven chances that the event will not happen to every three chances that it will happen." For a total of 10 chances! –  xtiansimon Sep 27 '11 at 19:51
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