From: roger.kockaerts (roger.kockaerts@chello.be)
Date: 04/19/01-08:28:01 AM Z
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De : Alberto Novo <alnovo@inwind.it>
À : alt-photo-process-l@skyway.usask.ca
Objet : CONCENTRATIONS
Date : Sam 24 mars 2001 17:12
I have noted some confusion, or misunderstanding, among photographers
regarding the conversion among concentrations.
So I prepared some notes on it, and if at the end something is not yet
clear, please tell me why.
Concentration is the amount of a substance contained in a mixture, expressed
as a ratio or a percentage.
The ways one can express this ratio can vary.
The best way for a chemist is the molar ratio, i.e., m.r = (moles of a
substance) / (total moles in the mixture). This ratio varies from 0 to 1
(the pure substance) and deals directly with the interaction among the
molecules.
The m.r. can be used with every type of substance, and is independent on
temperature and pressure. In particular, for the gases it coincides with the
partial pressure. But this is chemistry....
More pragmatically, usually we use concentration as the ratio of a weight to
a certain total amount of.... and here the confusion begins. Leaving apart
some other typical ways in which the chemists define the concentrations, the
main popular ones are:
1) by weight (weight/weight, w/w)
2) by volume (weight/volume, w/v)
3) by alcoholic degree (volume/volume)
4) by volumes (volume/weight)
What is important in the common life is the simplest way to dissolve
something in a solute, and this is why we have so much definitions of
concentration.
The third, for example, has its origin because to measure the amount alcohol
in a spirit it is very practical to use a densimeter (and not a
densitometer...). This was calibrated against known solutions, prepared
mixing known volumes of alcohol and water, that are more easier measured as
liquids than weights.
The fourth is used, as I know, only for hydrogen peroxyde. I will deal with
this for last.
The two common ways are the first two. The confusion arises because the only
*stable* unit is the w/w. In fact, changing the temperature, the volume of
the mixture changes accordingly, and so also the ratio weight/volume.
When preparing a solution in water, instead, it is simpler to dissolve a
weighted amount into a volume of solvent. I want here to remember that cubic
centimetres and milliliters are not exactly the same amount; the latter is
usually referred to a temperature of 25°C, while the former is independent
from temperature.
Suppose we read: prepare a 30% solution of sodium thiosulphate...
We can:
1) dissolve 30 g of hypo and add 100 g of water (or, the same, dissolve ...
in 100 g of water)
2) " " " 100 cc "
3) " " " 70 g "
4) " " " in a few water and fill a graduated bottle or
cylinder up to the final volume of 100 cc
Only the last two meet the definition of 30%: the third as w/w (the total
weight of that solution is 100g), the fourth as w/v (there are 30 g of hypo
in 100 cc of total solution).
NOTE: if we dissolved hypo in hot water (but I don't suggest...), we will
also need to refrigerate the solution to be sure that the final volume is
measured at 25°C, otherwise, once cooled, it will be something less than
100cc.
The conversion between w/w and w/v is made knowing the density of the
solution. The density is the ratio of the weight of a body to its volume,
and the same is valid for a solution. NOTE: at different temperatures the
volume of a body changes, so that it is needed to declare the temperature at
which the density is referred.
Specific gravity is not the same of density, as it is the ratio of the
weight of a body to the volume displaced when immersed in water. It depends
double from the temperature, because this changes both the volume of the
body as well as the density of the water.
Suppose we need to prepare a 30% solution of sulphuric acid, starting with a
98% w/w sol. of H2SO4 (the commercial concentrated sulphuric acid).
Well, this time it seems more practical to measure the amount of H2SO4 as a
volume. But 30 g are not 30 cc!. The density of 98% H2SO4 is about 1.96
kg/dm3, and 30 g of pure H2SO4 are in 30/0.98=about 30.61 g of solution,
that is in 30.61/1.96=about 15.62 cc of 98% H2SO4.
After having determined how to keep 30 g of pure H2SO4, proceed as 3) or 4).
NOTE: the volume/weight concentration of a 98% (w/w) solution of H2SO4 is
98*1.96=192.1% (192 grams of H2SO4 in 100 cc of solution!)
Finally, the concentration of hydrogen peroxyde was expressed as volumes of
oxygen developped from one volume of solution. I don't know why this units
were introduced instead simply of %; probablily because to measure the
amount of H2O2 in a solution it was decomposed and the resulting volume of
oxygen was measured.
However, also in the case of H2O2 we have to deal with density. In fact the
commercial percentages are expressed as w/w, while the vols are expressed as
vol(oxygen)/vol, and the density varies with concentration.
To convert vols into % what is needed is the density of H2O2 at that
concentration, and this is not ever simple.
>From a manufacturer of H2O2 I have this table: 10%=34.03 vol, 20%=71.19 vol,
30%=110.96 vol, 40%=153.68 vol (the relation is not linear as the density
increases with concentration).
By means of a simple proportion (for example, 10:34.03=x:20, x=10*20/34.03)
one can obtain all the conversions he needs.
All the best
Alberto Novo
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