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# Concentration calculations allowing for dilution

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If I dilute 5ml of cola up to 100ml, then find that this solution contains 0.45ppm of caffeine, how do I calculate how much caffeine there is in say a litre of cola?

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Concentration calculations are not difficult when you get the hang of it.

in 5 ml of cola there are 0.45ppm of caffine.

in 1000 ml of cola there are ......... of caffine.

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No need to be condescending sebby. What is difficult to one is easy to another.

Joho, sebby felt that your confusion lied within the phrasing of the question. Is that the case, or do you seek some other sort of clarification?

Cheers. :cup:

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One problem : ppm is a weight on weight ratio, and your dilution is expressed in volumes. Of course, we can take it that the density is 1 (= 1g/ml), and in the case of diluted soda drinks we will not be far off.

0.45 ppm (parts per miollion), with a density of 1, would be 0.45 mg/l.

In 100 ml of dilute that would be 0.045 mg.

In 5 ml of undiluted cola that would be the same 0.045 mg.

0.045 mg / 5 ml or 0.045 g / 5 l would be 0.090 g/l.

If you do not have the density figure for your undilted cola, you should not convert this to ppm. 1 ppm equals 1 mg/kg, but not necessarily 1 mg/l.

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Thanks guys. I think something didn't come across right in my original question, or I've missed something:doh:

I think I can manage to work out how much there would be in 1000ml, if there is 0.45ppm in 5ml. No, it isn't that hard really.:naughty:

The instructions I was given were: "A stock solution of 100 ppm caffeine in mobile phase is provided. Use this stock solution to prepare standards containing 2, 4, 6, 8 and 10 ppm of caffeine by dilution with the mobile phase solution. Take 5 mL of the Coca Cola drink and dilute to 100 mL with the mobile phase solution (1 : 1 mixture of methanol and 1 % aqueous acetic acid). Analyse each of the standards and the soft drink samples. Build a calibration graph of peak area against concentration (ppm) with the caffeine standards. Verify that the detector response is linear with respect to the caffeine. Calculate the regression equation for the line of best fit. From the equation, find the concentration of caffeine in the diluted soft drink samples and, hence, in the original Cola drink."

It was from the regression equation that I calculated the 0.45ppm. Anyway, I did a factor of my original cola and how much it was diluted (5:100 or 1:20) so did 20 x 0.45ppm = 9ppm in the undiluted cola. If its wrong :( , If not :) .

Edit: I've just re-read my original post and realised how daft my original question seemed:lol: :eek2: :eek:

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One problem : ppm is a weight on weight ratio, and your dilution is expressed in volumes.

:naughty:

ppm - parts per million, it is exactly that and is not a weight ratio. Imagine if you had 1 ppm of a brick and feather solution (silly i know, but youll see where im going) that means for every million feathers you have 1 brick - Is that a weight ratio? I think not, that 1 brick is likely to weigh more than all the combined feathers :eek2:

ppm is a concentration calculated via the the pure amount of objects, in this case we need to know if it is unit masses, volumes, molecules.. etc.

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Yeah, I think alot of this is about what ppm really is. I didn't recognise it in my answer. I assumed it was some kind of weight unit. It's actually some kind of concentration unit.

What the f*** is it? I havn't a clue.

But I'm not sure you need to know to answer the question; some kind of unit of concentration is enough.

100ml of diluted coke contains 0.45 ppm.

5ml of undiluted coke contains x ppm.

1000ml = 1l of undiluted coke contains y ppm.

Simple sentences like that was the way I always did my working out.

So you should be able to find x and y.

Hope this helps.

[don't look at this.

x = 0.45 * 100 / 5 = 9ppm.

y = 9ppm, concentration does not increase simply because you use a greater volume]

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:)

ppm - parts per million, it is exactly that and is not a weight ratio. Imagine if you had 1 ppm of a brick and feather solution (silly i know, but youll see where im going) that means for every million feathers you have 1 brick - Is that a weight ratio? I think not, that 1 brick is likely to weigh more than all the combined feathers :)

ppm is a concentration calculated via the the pure amount of objects, in this case we need to know if it is unit masses, volumes, molecules.. etc.

What I wanted to indicate is that ppm can not be used as equal to mg/l. It may be approximately right in te case of (dilute) solutions in water, but not for concentrated solutions or with other solvents. In fact, we were taught to abstain from "ppm" and to work with "mg/l"; "% vol." was another of those "popular" units we were taught to avoid.

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Would I be being pedantic if I pointed out that a brick weighs about 5kg and a feather weights about 1 g. 1 million feathers will weigh a metric ton? So if the brick weighs more than all the combined feathers, it must be a very heavy brick indeed. :)

In fact, we were taught to abstain from "ppm" and to work with "mg/l"; "% vol." was another of those "popular" units we were taught to avoid.

Very sensible advice indeed. But if you can do it, you deserve extra credit in my view. But you should do both mg/l and ppm.

If you really wish to persue ppm then perhaps you could say exactly what 1 ppm means.

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Yes, ppm is an older unit, we now steer towards using SI units in schools such as g/L. But I do think you can have ppm of mg per L, sorry to stir things up :D

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So we all agree now that you can use ppm, but the question is, do you really want to?

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No the question is, what is required as an answer :phones:

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In my opinion, the answer can go and **** itself. If the question is worded badly as it uses units incompatible with the scientific community, then the person who wrote the question deserves a C, not you.

But if you want to be fly, then I think include both.

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Apparently it is one of these "problems" connected with the Americans going metric - inch by inch.

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