- Is Beer a mixture, a compound, or an element?
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- How to become a Good Modern Spectroscopist (GMS)?
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Prior to ANYTHING: Think - AND NEVER STOP in case they are YOUR Thoughts!
Second: I can give you ONLY ONE recipe; Maybe the .... !:
- ) Start to study the "Special Beer-Lambert-Bouguer Law" and thereafter the "General Beer-Lambert-Bouguer Law". Don't
ask me later: Why you had to study first the "Special" !!! My Answer must be: It's the easiest and "most fecund" kind
of learning: From the mistakes of all others, because otherwise you have to do all the mistakes by yourself - What a pity !!
- ) Now it's the highest time to study the spectroscopy (The reliable one!!) AND to realise,
that except "the real first days" it should NEVER be allowed to make Single Wavelength Measurements,
only/again AND for not every sample AND without The Consequences.
IF you don't believe, study next step anyway; it's a second chance to realise.
- ) It's time to do some more sophisticated, after you had an ample training in the laboratory:
Real Multi Component Analysis (MCA) — Don't forget: It's absolutely normal ...
("MCA - It's absolutely normal spectroscopy; only 'She' never forgets a mistake you do !!"P.F.)
Real Multi Component Analysis (MCA/MKA) IS ONLY the consequent application of the General Beer-Lambert-Bouguer Law
to the field of spectroscopy (AND Single Wavelength Measurements!) !!!
But there is another big advantage: Real Multi Component Analysis (MCA/MKA) is THE easiest, cheapest, and "most
perfect" entry ticket to the discipline called:
Trustworthily (Trustable) Chemometrics (T'CHM).
- ) Now, after you have studied and reformed the 'Chemometrics', your biggest problem arises:
You need 'somebody' who "is able" to certify — "Your - Master of Science".
Please, when (not if!) you have climbed the Olymp, take care AND patient for your students.
Add. References:
Beer-Lambert Law
General Beer-Lambert Law/Linearity
MCA/MKA |
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- Do you know what's The BEST Combination in .... ? (G&G)!
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- What's the definition of the Beer's Law and Lambert Law?
- What's the Definition of the Beer-Lambert-Bouguer Law?
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Mr. J.H. Lambert: (1728 - 1777)
He worked out the relationship between "pathlength" and attenuation for:
(conc. = const.).
Mr. P. Bouguer: (1698 - 1758)
He did already similar work about 30 years before. But knowledge got lost.
Mr. A. Beer: (1825 - 1863)
He worked out the relationship between concentration and attenuation for:
("pathl." = const.).
(I believe, a hard work, because "our" spectrometers were not known at that time!) |
 |
| |
El. Lamp: 1850/1860[2] |
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But you have to remember, only the combination and the final translation to Absorptions gave us this two so handy and so
easily interpretable Laws:
General Beer-Lambert Law &
Special Beer-Lambert Law |
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- What's the Definition of 'Species' in the Beer-Lambert-Bouguer Law?
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It seems: Not the same for Special Beer-Lambert Law and for General Beer-Lambert Law !!
The adequate Definition for the General Beer-Lambert Law !!:
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Definition: A "SPECIES" in Spectroscopy (for a good modern Spectroscopist!) is defined as
a Compound, an Atom, or parts of them, or "Clusters" of them, which are the SINGLE CAUSE of an UNIQUE ABSORBANCE
SPECTRUM in a WELL DEFINED "ENVIRONMENT" for IT !!! |
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A little simpler (not so complete) Definition for most Spectroscopist may be: |
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Definition: "SPECIES", in the spectroscopic sense, are different MANIFESTATIONs of the
IDENTICAL MATTER (Molecule/Compound/../etc.) in Solution! |
The Definition for the Special Beer-Lambert Law !!:
Sorry, but that cannot be my job/responsibility !! Maybe there are some, or quite a lot !!
But keep in mind:
1.) It is allowed to define what ever you like !!
2.) Definitions can only be qualified and be proofed to make sense and to be adequate !!
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If you got the whole message, then you know now, why almost every spectroscopist (!! NOT ANY GMS !!) is so keen to tell you about:
EXCEPTIONS & LIMITS & DEVIATIONS & 'NOT OBEYED' & 'PROBLEMS' of:
The Beer-Lambert-Bouguer-law? |
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- Why are there TWO of the Beer-Lambert Laws (Beer's Law)?
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Of course: Mother Nature knows only one 'Beer-Lambert-Bouguer Law' !!!!
So, why we have a 'Special Beer-Lambert Law' (you may have learned) and a 'General Beer-Lambert Law'
(you will/must know/use for the future), and which of both is correct?
I think you know already the correct answers. Otherwise respond to both of my simple questions:
- By which of both "EveryBody" is taking about:
Nonlinearities, Deviations, Not Obeyed, Not Valid, Problems, Exceptions, Lacks, etc. ?
- Why have you not any chance to do the same by the other?
And: What's about the consequences from all of them?
Add. References:
General Beer-Lambert Law
Linearity
Special Beer-Lambert Law |
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- Why is the Beer-Lambert Law (Beer's Law) only correct for monochromatic light?
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Because: IT IS NOT TRUE, - not at all ! Why you don't think by yourself?
Do you know, what's so nice about?:
It's such an easy game to play, to show you the evidence of THE ABSOLUTE CONTRARY !!:
And do you know, How it can "best" be demonstrated?: Use TWO monochromatic light sources!
- Nice, isn't it?
But real the Best: I, and thousands of others use it since more then 21 years!, almost every workday!
Let's start the experiment: - if your monochromatic (mostly gray) matter is ready for:
| 1.) |
Prepare a cuvette with a sample solution, that meets all the requirements for the use of the Special Beer-Lambert Law
(S'BLBL), because it's a little bit simpler for the required maths. |
| 2.) |
Adjust your two monochromatic light sources to two different wavelength, not overlapping
their slit functions, but so, that you still measure an absorbance of your sample in the cuvette. |
| 3.) |
Adjust also the geometry of both beams in such a kind, that both bring the information of the same number of
Species to the detector. You remember, for what is the product: cn*d in the the Beer-Lambert-Bouguer Law
standing? |
| 4.) |
Now trim your monochromatic light sources to nearly the highest possible
monochromaticy, but without losing to much energy to do comfortable measurements. |
| 5.) |
It's time to start the ceremony: Turn on one of the light sources. What do you have ?
Exactly - an absolutely normal spectrometer, adjusted to a single wavelength. And you know, that you can
do all measurements at the wavelength, you do normally without any additional limitations, like Linearity (as you
do it, not I), concentrations, etc., according to the Special Beer-Lambert Law:
A(λ1) = ε(λ1)* c * d |
| 6.) |
Turn the beam off and the other on! What have you now?
Precise - exactly the same situation as under 5.), only another wavelength. So the Special Beer-Lambert Law
looks this time:
A(λ2) = ε(λ2)* c * d
The only thing you have to do is to recalibrate your Linearity for the new wavelength, because only the
ε is, and can be influenced in this situation. |
| 7.) |
And so we turn the other monochromatic light sources on, too. What has now changed for your measuring?
Of course, it can't be as easy as in the situations before! — Why ?:
A(λ1,λ2) = A(λ1)
+ A(λ2)
= ε(λ1)* c * d +
ε(λ2)* c * d
= (ε(λ1) + ε(λ2))
* c * d
From the last line it is for everybody absolutely obvious, that must be true what he already feels; it could not
be possible, that in this case the absorbance's would be additive, because as both results from the identical species.
But regardless, the last equations is only a double step from heaven:
Guide a "f" in front of the left parentheses, - and metamorphose the plus sign into a comma:
You arrived on Olympus (but only on the small) and may now remove the red colour from the Equation!! - Well done!
A(λ1,λ2) =
f(ε(λ1), ε(λ2))
* c * d
In case you like to substitute, you may use:
ε(λ1,λ2) =
f(ε(λ1)
, ε(λ2))
- and you're right back where you always started: the Special Beer-Lambert Law.
Of course, no surprise!
But is it allowed, all we did? Of course, again!!
Do you need a few arguments? Ok, ok, of course, again!:
a.) c * d we never changed, kept constant, so they was never involved.
b.) For each wavelength the Linearity is given. (see: 1.) ... meets the requirements ...)
c.) The number of species never changed. (see: 3.) .... geometry ....)
d.) From a.), b.), and c.), and the Special Beer-Lambert Law follows:
- only the ε's are left!,
and must be the cause for the changes we found!
e.) ε(λ1) and ε(λ2) are constants for their given Linearities.
f.) The next step of conclusion you may do by yourself:
- What can a linear function produce, if you feed it with only two constants?
Do you need any additional argument? Oh, you are very clever: You mean, the population of the ground (or starting)
states are not the same with one or two beams! Yes that's right, that has to be by nature law. And now?
What does a small change to a constant?: It results in a 'small changed constant', and now?
You know, you have to calibrate it anyway, so - what's the matter??
But let's go ahead |
| 8.) |
You can now repeat this game again, and again, and bring each time both wavelength closer together, till their slit
function meet (start to overlap), and as you now know, you will find all the time congruent results.
But now!!, Now it must be different! - Yes, of course, now it's different - but what?
The only thing that changes in real is, every 'slit' spends a little bit energy to the neighbour 'slit' and eats (measures)
a little bit gras from 'him' therefore. What's now the conclusion?::: You have to calibrate anyway! So, why you
have to care about, if in this situation the combination function changes a little bit?
But now my Question: What will happen, if finally both wavelength are identical and thus results in absolutely
congruent slit functions?
And a Remark: What is it, if both wavelength are identical? - Do you think so? - You're right!
It's just another starting point to answer the initial Question, too. |
Finally the only conclusion that's left, is:
There is as good as "Never" a requirement for monochromatic light !!
Oh, Sorry, the "more then 21 years, workday for workday":
Do you know PDA's ? NO? — PDA's are Photo Diode Array Spectrometers
PDA's are some times also called DAD's : Diode Array Detectors (The Best you can choose today!)
PDA's sends not monochromatic light through the cuvette to the detector!
PDA's sends not oligochromatic light through the cuvette to the detector!
PDA's sends polychromatic light through the cuvette to
thousands of detectors!
If you see, how PDA's work on the "Diode Array Spectrometer" page, you will realise:
Monochromatic light can never be a requirement for S'BLBL and G'BLBL!
NO, Sorry, — Don't ask me: Why since more then 21 years,
workday for workday, almost every professor for Chemistry, for Physics, for Others (Biology, etc.) tells
his students a different story, and still believes himselves the most?
Add. References:
S'Beer-Lambert Law
General Beer-Lambert Law/Linearity
PDA/DAD |
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- Why is the Beer-Lambert Law (Beer's Law) an empiric law?
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Radio Yerevan: "Because the WRONG POINT OF VIEW !!"
At least from now, till the end of every and the last day, it is IMPERMISSIBLE to call even
the smallest 'Stroke of a Feather' of the "General Beer-Lambert Law" to be of any Empiric Nature,
without having himself/yourself disqualified in the most dramatic of all possible Ways !!!
You are easy able to verify this natural Fact of NON-Empiry by your self:
But set the following headline in front of every Argumentation:
| Everybody is self disqualifying, who "is not able"/"does not" distinguish between Absorption and Scattering!! |
Argumentation:
| 1.) |
It's obvious that only the "General Beer-Lambert-Bouguer Law" can be used
for all Discussions!:
A(λ) = Σ ε(λ, n) *
c(n) * d |
| 2.) |
That we have to be complete in the sense of "Sigma" (Σ) to be able
to distinguish between Empiricism and "Absolute" needs no discussion, but we have to dispute
the terms:
ε(λ, n) the molar absorption;
c(n) the Concentration of the Species n;
d the pathlength, the thickness of observation; AND the
ominous and objectionable "Deviation"/"Not obeyed"/"Nonlinearity"/"etc." |
| 3.) |
ε(λ, n) The molar absorption/absorptivity:
Since more then 30 (thirty !!) years, Since is able to calculate Spectra for nearly every substance:
 |
With only the known Configuration, and Conformation, with Dipole moment and a few
other parameters, you are able today, to determine the spectrum of a substance before it is
ever synthesised for the first time (SCF-PPP; CNDO/2; INDO; MINDO; CNDO/S;
etc).
So there is nothing left empiric at the molar absorption coefficient.
(Calculations with SCF-PPP-CI method:
H. Hartmann and J.Fabian;
Ber. Bunsenges. physik. Chem. 73 (1969), 107) |
|
| 4.) |
c(n) The Concentration of the Species n:
As I already told earlier on this Site and on this Page: It would be the most
stupid mistake we are able to do, if we use the isolated "Concentration Term" for any judgment/appreciation,
because only the Term: c(n) * d is of relevance
in this "game"!
Only the product of c(n) with d of every individual Species gives you the
"absolute number" of the absorbing "particles" of the observed
Species inside your measuring beam. That's even true, when you
usually do, in contrary, a correlation for method calibration in spectroscopy.
|
| 5.) |
"Deviation"/"Not obeyed"/"Nonlinearity"/"etc."
Under this topic is already more then enough written on this particular Page and on this particular
Site. It is not coming more true, if I repeat it again, and again. |
| 6.) |
When we now final summarise, so we was/are not able to find anything with
even a marginal suspicion of Empiricism or similar. We found the absolute contrary is true.
NOT more, — NOT less !
(We have to learn to think not only one-dimensional!, if we prefer to understand mother nature!) |
Add. References:
"Corrected" Beer-Lambert Law
General Beer-Lambert Law/Linearity |
Back to FAQ's Index
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- How to calculate % Transmittance (%T) from Absorbance?
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Back to FAQ's Index
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- What's the practical use of the Beer-Lambert-Bouguer Law (Beer's Law)?
(17.November 2006 20.21 GMT)
| |
A very good Question !! Difficult
to answer for me, IF - I would like to be complete!
So, I can you offer only a short list of Applications/Examples.
- Let's hope, it's inspiring enough!:
| |
| a.) | Concentration determination: - For example see:
Linearity, Spectroscopy,
NNIR, And quite a lot more .... |
| b.) | Content determination: - For example, as in:
Tablets, Powders, Capsules, Ampullae, Suppositories,
Salves, Flasks, ..., - also in:
Kettles (Production), Mills, Tanks/Silos, Barrels,
- and so on, and on, and ...
For example see the Internet, but also: ARGUS. |
| c.) | Product/Educt Identification: - For example, as with:
MCA/MKA, PCA/PCR/PLS, SIMCA/Clusters, Patter, FA, and ...
See: Multi Component Analysis (MCA / MKA) OR
Chemometrics. |
| d.) | Production Guiding/Controlling: - For example, as in:
Kettle charging, Reaction Controlling, Reaction Correction,
Reaction Termination, ..., AND
Reaction mechanism determination AND Reaction Forensics AND
...
Sure, the most powerful Tools: MCA/MKA with the RFE!,
(ARGUS)
Quite seldom, but in addition: PCA & FA (Chemometrics). |
| e.) |
Quality Control: - As it is absolutely required (also) for:
Production, Registration, Specifications, Selling,
Stability, Warranty, ....
Typical Tasks for Beer-Lambert-Bouguer are:
Content, CU, Identification, DR, Purity, Colour, Nuance, ....
Quality Control - It's the perfect
Combination of: a.)/b.) with c.) !!!
The unbeatable Tool, -yet: MCA/MKA and RFE!
combined with: SST:
(ARGUS). |
| f.) | Determination of ..................... - For example, as: |
| g.) | Determination of .............. - For example, as with: |
| h.) | |
Add. References:
MCA / MKA
Chemometrics
System Suitability Test (SST:) |
Back to FAQ's Index
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- How do we use the Beer-Lambert-Bouguer Law (Beer's Law)?
| |
Correct !! NO - It's not a joke!!
Most people, and specially spectroscopists, do it the other way!
Most people use the Beer-Lambert Law to measure/calculate concentration of a sample. And that's quite less enough!
Let's give a short/simple recipe how most people do it: (with the Special Beer-Lambert Law)
| |
| 1.) | You have to rearrange the Beer-Lambert Law to isolate the Concentration (letter c) on the left side. |
| 2.) | So you have defined the Letters c as the Concentration you have to 'measure' and to calculate. |
| 3.) | In the same way you have to define the other Letters and you will end in:
A is the absorption of the sample you measure,
b is the path length of your cuvette, and
ε is the molar absorption of your sample compound. (or how ever you cal it) |
| 4.) | The only problem left is the determination of ε and this procedure is called Calibration.
Now you have to select one of the options:
A) If you prefer the molar absorption from the literature, please continue with:
Is it wise to use molar absorptivity values from the literature?
B) If you prefer to calibrate by yourself, please continue later with:
How to determine/find molar absorptivity/absorbance/extinction coefficients?
Selecting option B has a couple of advantages:
a) Your calibration is congruent to your later analysis.
b) You know exactly what you have.
c) From your Calibration you know the range your method will work.
d) You know the precision and the accuracy for your method from your Calibration.
e) You know, that's all time reproducible, for everybody.
f) I'm sure, there are several more.
|
Using the General Beer-Lambert Law instead, gives you four times as much advantages.
Good Luck !! |
Back to FAQ's Index
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- Is the Beer-Lambert-Bouguer Law (Beer's Law) additive?
| |
Radio Yerevan: "In principle: All times!!, — but All times more then what you will prefer !!!"
As you know, Linearity can never be true, if not Additivity is given/valid, because Linearity is only Additivity
for the identical homogenous Species.
But what you have to think about, and maybe that's the cause of your question, that it is VERY, very often happen,
that two different "substances" "react inside" your cuvette!!!
To understand, what I'm talking about, you must use a much more comprehensive reaction term than the traditional chemistry defines!
And as if it would not be enough, the Linearity as you know it, can easily be influenced in a absolutely uncontradicted way!
But don't fear, the whole 'thing' can be handled quite easy, with:
The G'BLBL.
That The G'BLBL, absolutely additive is explained on MCA/MKA Page.
Add. References:
General Beer-Lambert Law
It's real Linear
Linearity |
Back to FAQ's Index
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- What's the linear range in %T of the Beer-Lambert Law (Beer's Law)?
| |
Sorry: 0.000 %T till 100.000 %T Do you know anything else ?
If you measure any time more as 100.000 %T, - then you have to accept, that it must be the result of a personal
mistake!, OR: The next Nobel Prize in Chemistry will be for YOU,
for sure ('perpetuum mobile second order/kind') !!
Of course:
If Fluorescence or Phosphorescence is present, the situation seems to look different, but never in real !!
Definition must be Definition! — Why? (How you measure Transmittance?)
Add. References:
Beer-Lambert-Bouguer Law |
Back to FAQ's Index
|
- Why / When can Beer-Lambert Law (Beer's Law) become nonlinear?
- Why does Beer-Lambert Law (Beer's Law) become nonlinear at high Concentrations?
- Why is the Beer-Lambert Law (Beer's Law) NOT VALID for high Concentrations?
- Why the Beer-Lambert Law (Beer's Law) doesn't work at high Concentrations?
- Why is the Beer-Lambert Law NOT TRUE at high Concentrations?
- What is the Problem with the Beer-Lambert Law at high Concentrations?
| |
That's NOT TRUE !!!!
The Beer-Lambert Law does NOT become non-linear at high Concentrations!
TRUE IS: Beer-Lambert Law is almost EVERY TIME TRUE/VALID,
also at high Concentrations, too!
Do you know somebody with such Problems?
The common problems are: Nobody is doing the correct measuring's, and nobody is doing the correct calculations and that
results in "wrong" graphs, which nobody is able to read. — Such easy!
If you really would like to solve your problem, start studying Discussion
1[3] and take the required consequences from the MCA Page.
Add. References:
General Beer-Lambert Law
It's real Linear
Linearity |
Back to FAQ's Index
|
- What are the Deviations of the Beer-Lambert Law (Beer's Law)?
- When is the Beer-Lambert Law not obeyed?
| |
There are NO (almost) Deviations given from mother nature !!!
The Beer-Lambert-Bouguer Law IS (almost) ALL TIME obeyed !!!
Till today, there is ONLY ONE REAL Deviation known, — if you are doing a Mistake!
Most common Mistakes:
A.) If you don't take care to stay all time inside the linear rang of your spectrometer!
B.) If you don't know what your actual cuvette really contains!
Otherwise I can only repeat:
If you really would like to solve your problem, start studying Discussion
1[3] and take the required consequences from the MCA Page.
Add. References:
General Beer-Lambert Law
It's real Linear
'SPECIES'
Linearity |
Back to FAQ's Index
|
- And: When is the Beer-Lambert Law obeyed?
- And: When is the Beer-Lambert Law strictly obeyed, -also
at high Concentrations?
| |
It's: Forever and a day !!! The General Beer-Lambert-Bouguer Law tells it!
( - and specially at high Concentrations !!).
So: If you find yourself in a situation, where you still think: "It's NOT TRUE", you have to accept,
that you must have made at least one mistake.
Help is not difficult to give, because the mistakes are so well known, as everybody is trying to bet every
other before, in doing exactly the same mistakes in his own special kind again, and again, and a..... .
If you really would like to have a helping hand, study all related Questions on this particular page !!!
Add. References:
General Beer-Lambert Law
It's real Linear
Linearity |
Back to FAQ's Index
|
- What's the high Limit of Detection of the Beer-Lambert Law (Beer's Law)?
- What's the upper Limit of Concentration of the Beer-Lambert Law (Beer's Law)?
| |
Radio Yerevan: "In principle yes, but you must know, what you prefer !!!"
Surprised? - But for once, it's absolutely true !
Before we start, please let me "kill" the ineradicable false doctrine:
The high/upper Limit of Detection/Concentration depends on the Spectrometer you use !
Especially, with a Doublemonochromator/Doublebeam Instrument, you can go higher ! |
Both are, as you will now learn, absolutely wrong !! (Because mother nature has told!)
But it is of the same true:
You are responsible to stay all times inside the linear range of your Instrument !
That's not only valid for Spectrometers!
Let's start:
Which of both Beer-Lambert Laws you need? — Of course there is a big difference!
If you need it for:
- a SINGLE SPECIES (NOT molecule; much more restrictive!!), use: Special Beer-Lambert Law!
- a SINGLE chemical COMPOUND; (mostly for concentration), use: General Beer-Lambert Law!
Why? What's the difference between: Compound, Molecule, and Species?
Ok!, Let's do it the simple way:
- Compound, in the chemical sense, is matter with a unique formula.
(not dealing with enantiomer, racemate, etc.)
- Molecules, we can use instead of Compound, in almost any case.
- Species, in the spectroscopic sense, are different manifestations of the identical Molecule/Compound in solution!
- Species, as a consequence, must all have different spectra and molar absorptivities!
And the final result:
The first ("Special") is really and only a very special case of the later ("General Beer-Lambert
Law").
| I will only discuss the later: |
(Please: Dear Professors and Teachers, don't "listen" ahead!) |
Because we now know,[3] that a Compound can manifest itself in
different species, so only the matrix and the concentration are the causes for this physical facts. In consideration of
this circumstances the maximal measurable concentration is the maximal concentration you are able to bring into the measuring
beam. And that's the solid body - what surprise !!!
Wrong! - Wrong! - Absolutely Wrong! You have not even understood the Beer Lambert Law!
Remember, for what is the term: cn* d in EVERY Beer Lambert Law standing? —
Ahhh ..., exactly!, I see it's coming back to you: cn* d is representing nothing else!, as
the number of the absorbing "particles" of the species(n) in the measuring beam!
And what have we to learn from this term? We have to learn, that we have to compensate the rise of the concentration over
hills and mountains by reducing the used pathlength to arrive back into the linear range of your spectrometer.
So you see, it's all only depending of the design of your experiment, and so it must be your fault, if something goes wrong.
But keep in mind: You will meet a lot of different species on your concentration trip, also for putative pure compounds!
Add. References:
General Beer-Lambert Law
'SPECIES'
Linearity |
Back to FAQ's Index
|
- What's the lower Limit of Concentration of the Beer-Lambert Law (Beer's Law)?
| |
Radio Yerevan: "In principle Zero plus five times a IMWU, but you have first to define a IMWU!"
What, you never heard about 'IMWUs'? — How is such possible?
'IMWU': "Irreducible Minimal WeightUnit". — And that should be true?
— YES!
If you cannot believe: The rules of the game tells: "Back to the startfield, labeled:
How to become a Good Modern Spectroscopist (GMS)?
Do you remember, when I told you: "It's wise to never forget (it)!"?
Now it's time to test yourself!: Remember, for what is the term: cn* d in EVERY Beer Lambert Law standing?
(Sounds that familiar to you, now?)
cn* d is representing the number of the absorbing "particle"
of the species(n) in the measuring beam!
And what have we to learn from this term? We have to learn, that we have to compensate the abscond of
the Absorbance value into the noise, by increasing the used pathlength to arrive back into the linear range of your spectrometer.
That means nothing else as to keep our term more or less constant and stay all times in the linear rang of the spectrometer, of course
with the respect of the noise limits.
It sounds very easy, and it is quite easy, but not sooo easy as you now may think!
For example: For measuring gas it is not uncommon to use cells with a optical pathlength of several times ten meter!
Now you must be able to tell me how big an IMWU approximately is!
Of course there are other instrumental parameters, and ε, which set you a significant higher limit of detection.
Add. References:
Google: Long gas cells
Linearity |
Back to FAQ's Index
|
- Why has direct proportionality from Concentration to Absorbance such Lacks?
- Why is ONLY the Absorbance directly proportional to Concentration for Beer's Law?
| |
Because: The 'Beer-Lambert-Bouguer Law' can NEVER BE one-to-one/reversible, even if
almost EVERYBODY thinks so !!
With simple words: You NEVER measure, what YOU THINK you have prepared !!! — But:
Of course: You ALWAYS measure, what YOU ———
HAVE prepared !!!
The mystery's Solution: It's sooo trivial: The 'General Beer-Lambert Law'.
IF you like (or dislike):
Study the 1st Discussion of The General Beer-Lambert Law
[3], and come back again!
For the one, who's coming back from [3]:
Why molecules do that?
- It seems, that molecules are savvier than humans, because they minimise their STRESS
(Gibb's energy[5])!
Add. References:
General Beer-Lambert Law
Spectroscopy
Linearity |
Back to FAQ's Index
|
- What is ε — It's called: 'Epsilon' or 'molar extinction coefficient'?
- What is molar absorptivity, molar absorbance, molar extinction coefficient?
| |
It is an Absorbance Value — but of course a little special!
It is also the letter ε ('epsilon') in The Beer-Lambert-Bouguer Law
but of such a kind, that we have to rewrite even the Special Beer-Lambert-Bouguer Law as:
A(λ, solv., [pH], Temp., μΘ, B, etc.) =
ε(λ, solv., [pH], Temp., μΘ, B, etc.)
* b * c
Or abbreviated:
A(λ, env.) =
ε(λ, env.) * b * c
env. stands for the Environment.
Now we can define:
| Definitiontheoretically: ε ('epsilon')
is the Absorbance Value you would have to read (measure) at your observation Wavelength, on an adequate Spectrometer,
if you insert 1.0000 Mol of your compound ('Species') into the measuring Beam, in exactly the identically Environment
as your Sample.! Peter Forster |
You ask: Where is the path-length (b) gone inside my definition? Have you not seen, it's
well defined!
From 1.0000 Mol and exactly the identically Environment (env.), you can easily and exactly calculate, how many
meters or kilo-meters the path-length has to be, and also your Spectrometer!
As I believe (how easy!), that you don't have such an adequate Spectrometer (extended linear range; Sample compartment),
what is the solution?:
Measure inside the linear range of your spectrometer, and do some calculations.
But never forget: For what is the product (c * d), or in our case (b * c) standing ?
Exactly!!
The product represents the number of molecules ('species') of your compound staying in your actual Measuring-Beam.
It's very wise, to never forget it anymore!
Add. References:
Special Beer-Lambert Law
ε ('epsilon')
'SPECIES'
General Beer-Lambert Law |
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- Is it wise to use molar absorptivity values from the literature?
| |
NEVER - with one 'little' exception !!!
The only practical use of such values is to calculate the approximate start concentration of your reference
solution !!!
Do you need some arguments:
Count the number of significant digits (tailing zeros are NOT significant digits!) and calculate their given precision
under the rule of rounding !!!
What for parameters except Wavelength and maybe solvent are documented for your preferred value, and compare your list
with the required parameters[4] for molar absorptivity ??
Do you know anything about the purity of the compound for their molar absorptivity ???
Do you know anything about the purity of the compound from your preferred Literature ???
Do you need more arguments, OR have I already meet your usual precision ?
Let's hope, that the situation in future will dramatically improve !!!
Add. References:
"Corrected Beer-Lambert Law" |
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- How to calculate molar absorptivity coefficients using Beer-Lambert Law?
- How to determine/find molar absorptivity/absorbance/extinction coefficients?
- How do I calculate the molar absorption coefficient of a substance?
- How to find molar absorbtion/absorption coefficient from Beer-Lambert graph?
| |
ONLY using Beer-Lambert-Bouger Law
— IF I EVER WOULD !!*)
Here the short recipe: — If I ever would have to do it !!*)
- ) Go for the best (most adequate) analytical purity degree value of your compound ("species") !!
- ) Think about, if purity value is high enough to legitimate any continuing !!
If you still there:
- ) Now it's time to determine the molecular weight of your compound ("species").
- ) It's time to weak up, because you have to do a dilution row over the concentration range of your
interest !! This 6 till 10 determinations of the absorbance value(s) you have to do in such a
kind, that your linearity graph looks more or less equal spaced on the linear concentration axis !!
- ) Probably the hardest step of all: You have to validate your linearity !!
What's that meaning? You have to check, if the linearity is high enough to .... (continue as in step
2.))!!
And worst of all you are nearly lost, because there is not any statistical parameter with enough significance
(R/R2/Sy.x/Fit Error/etc. are only 'Strongmen' !!!)
But where can you get help? You remember?: "If
you would like to be well served, - serve yourself!"
You own the best (most significant) "detector", who even works, when all statistics together 'have'
already to give up !! It's YOUR EYE !! Apropos:
The evidence can be given very easy !!!
- ) OOh. You still here? But be aware, if you failed the step before, you will have to
pay your bill for, at least within the last step of this recipe !!! (Don't discrete yourself
to a Strongman !)
- ) The end is near: Do you think you are able to calculate the slope of your Linearity?
Ok.: Slope = Δy/Δx =
ΔAbsorbance/ΔConcentration For one unit
on the x-Axis !!
Apropos: Why did you the concentrations not in Moles per Litre (= molar !)
The only thing left to do is to move the lower end of your Δ to the origin of
your graph and -
the result on the top will be, — your asked ε
!! Why?
- ) But what's about precision and 'some' accuracy ??
If I remember correct, you did a "validated Linearity" with hopefully 6 till 10 different concentration,
because you are now able to do some statistics for all ε's (mean,
rel. standard deviation, etc.) to inform everybody about your precision/reliability !!!
AND:
Draw the graph ε against concentration !!
Are you able to find any tendency ?? WHY? Did I not tell you,
NOT to continue, if your Linearity would not legitimate you !!
Do you like this recipe? Maybe I think similar, but from a different cause !! Don't fear, there
are for sure enough "everybody's" and special(ists) ".... ..", who tell you, you may shorten this procedure precisely
as much as ever you prefer. Why?
There is a Way to do it: much more comfortable,
more reliable (FDA, GLP, USP, EP, ISO900x, etc.), and with a Lot of time for coffee, too:
All what is then left to You is a little documentation, AND —
a little calculation for any wavelength you prefer!!: Linearity !
Add. References:
General Beer-Lambert Law
Spectroscopy
Linearity
*) In the moment, the only sense for do so, could be for a publication, probably. But please read first:
Is it wise to use molar absorptivity values from the literature? |
Back to FAQ's Index
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- How does pH affect the molar absorbtion/absorption coefficient of Beer-Lambert Law?
| |
Radio Yerevan: "In principle:
"Absolutely NOT", - but: Take care for the Ratio !!: -
The Ratio is affecting ""ε"" dramatically!"
The Answer is easily given in the following two pictures:
 |
 |
This are Titration-Plots of corresponding Acid / Base Pairs!,
and tell you the Ratio, the absolutely most important Ratio!
How it works? Quite easy:
| 1.) |
The cambered Lines divide always a corresponding Acid-Base-Pair, with the corresp. Acid below,
and the corresp. Base above the borderline |
| 2.) |
If we draw a horizontal Line at our pH (at proxy. 6.3 in the small graph) and have to cross
the cambered Line, you have to accept, that the Beer-Lambert-Bourguer Law, - at least as you know -, will
not work any longer!!!
Because you have to realise, that you have now at least two species in your cuvette!!!!
Yes, a borderline, is generally located:
between - at least two "...."! |
|
| 3.) |
The intersection point between your pH line and the cambered borderline is able to tell you, what Acid-Base-Ratio
you will be able to find in your cuvette!
From the Acetic acid example above you can easily readout, that at a pH of 6.3 a ratio of ~95% corresp. Base and
~5% corresp. Acid has to be present.
|
| 4.) |
As even TWO S'BLBL with two wavelengths give you precisely the same reliability as sand on a strand in case
of a Tsunami (Zunami), there is only one practicable, reliable solution:
The G'BLBL. |
| 5.) |
Think about: The spectra of the two species never change, but the ε
(Epsilon) you tray to estimate will change all the time and will never be really stabile, too!! |
| 6.) |
What you can readout from the graph for sure, that the other way around is very easy and very reliable, too:
The estimation of the correct pH from the "Mixing colour" of the Sample, at least if you know how. |
| 7.) |
If you design the experiment as a "quasi closed" Reaction-System, then you will be able to determine at least an
Isosbestic (Isobestic) Point. |
|
(Pictures: Dr. sc. nat. H. R. Christen; Grundlagen d. allgemeinen u. anorganischen
Chemie.[6]; Switzerland)
Add. References:
General Beer-Lambert Law
Spectroscopy
Bad Example |
Back to FAQ's Index
|
- What is a Buffer, and why is it important for the Beer-Lambert Law?
- What is Buffer-Capacity, and why is it important for the Beer-Lambert Law?
| |
It is for sure the most disesteemed — Parameter by nearly all Spectroscopists!
It is for sure the cause of the most made mistake — by nearly all Spectroscopists!
But what is a buffer, - and what is 'its' capacity?:
Per definitionem: For a Buffer, there is at least one Corresponding Acid / Base Pair required!
More complicated Buffers may require several Corresponding Acid / Base Pair!
Even a STRONG Corresponding Acid / Base Pair as HCl
is a Buffer in ITS adequate pH-Range!
The most simple, but also most useful Buffer for Spectroscopy is the Acetic-Acid ("Vinegar"!).
As a Pair is required, the Vinegar-Buffer "exists" in the small Picture above —
Only in the pH-Range, where
the cambered Line "exists" !!! (Why?)
But this 'determined' pH-Range is not identical with the ('useful') Buffering-Range of the Buffer.
Also dropping ONLY the most curvilinear Part of the 'Line' is not enough ('not very useful'),
because a 'single-edge' Buffer at both Ends of the 'Line' doesn't make much sense, either!
You will easily find out, that for a 'ideal' Buffer the remaining 'Line' should be:
A absolutely horizontal Straight-Line!
Now we are able to define:
Definition: A Buffer (for pH)
is a 'Corresponding Acid / Base Pair' with an as less as possible resulting pH-Change, for the Addition of a recognisable, certain Amount of strong Acid, or strong Base !
The selected 'Corresponding Acid / Base Pair' defines the Location on the pH-Axis, where the buffer will work! Peter Forster |
And the second Definition follows directly from the first:
Definition: Buffer-Capacity (for pH)
is the IN-Sensibility of the pH for the given Buffer, for an Addition of a strong Base inside the whole Buffering-Range in the following Form:
β(CBuffer) = dCBase / dpH ; therein dC is the Change in Concentration.
As the remaining 'Line' is still of cambered nature, so β(CBuffer) can't be a constant over the Buffering-Range,
AND depends also very strong on the current Concentration of the Buffer itself! Peter Forster |
- But why is the Definition using strong Base and not strong Acid? — Because the Sign of β(CBuffer).
- Why define Other a Buffer as a Combination of a week Acid/Base with a strong Base/Acid, or 'vice versa'?
Because their missing knowledge. Using a week Acid or Base is only ""moving"" —
the cambered Line CLOSER to pH 7 (The neutral pH value!). See the larger Picture above.
- With Acid from the lower pH-Side; with Base from the upper pH-Side.
As easily can be seen, that for a given Buffer-Concentration, β
reaches its Maximum by the condition: cc.Acid = cc.Base.
At which pH will this Maximum always be located?
What is now the Importance of Buffers, - and 'its' Capacity for the Beer-Lambert Law?:
Buffers Are the ONLY Possibility to FIX/ADJUST
the pH for ALL your Samples,
AND keep
your Method as reproducible as possible!
| ( |
Because using Buffers, we are able to use Referenc-Spectra
recorded/digitised 15(!!!) Years ago and Today-Samples
with an even better Reproducibility AND Standard-Deviation THEN
0.25 Percent !!!) |
|
Keep also all the time in mind, that ε ('Epsilon'), the Molar absorptivity/absorbance/Extinction Coefficient
has a significant till strong Dependency on pH !!! |
| It is of exactly the same Importance, that you keep all the time in mind, NEVER to OVERLOAD the Capacity of your Buffer in use,
because ALREADY small Changes in the pH will result in a dramatically Lost of Buffer-Capacity and so also result in a even higher pH-Change, TOO, and on !!! |
Add. References:
General Beer-Lambert Law
Spectroscopy
ε ('epsilon')
Bad Example |
Back to FAQ's Index
|
- What is the Relationship between Light/Absorption and Energy?
- What is the Relationship between Wavelength and Energy?
- Why Einstein meets Beer-Lambert?
| |
"Einstein!": — is the Relationship!
As you may know: "The Energy required to produce an exited state is obtained by inspection of the Absorption-
or Emission- Spectrum of the molecule in question, together with the application of the following Equation"[10]:
ΔE = E2 - E1 = hν
where h is Planck's constant, ν is the frequency [sec-1] at wich absorption occurs, and
E2 and E1 are the energies of a single molecule in the final and initial states.
As the frequency ν is given by: c / λ , the Equation results in:
ΔE = E2 - E1 = h(ν)c = 2.86 * 10-3
(ν) cm-1 [kcal/mole] or:
ΔE = E2 - E1 = 2.86 * 104 / λ nm [kcal/mole]
The amount of enery produced through the apsorption of one mole of Photons by a compound
at a given wavelength is equivalent to the energy of 6.02214 * 1023 Photons.
This Energy is called an "Einstein"[10]. — For Example:
One Einstein(800 nm) = 2.86 * 104 / 800 nm = 35.75 kcal/mole.
One Einstein(200 nm) = 2.86 * 104 / 200 nm = 143.00 kcal/mole.
This and a few of other Relationships you can find in this Poster.
(Many Thanks to: Departement of Chemistry, University of Florida!) |
 |
| | |
Add. References:
"Corrected" Beer-Lambert Law
General Beer-Lambert Law/Linearity |
Back to FAQ's Index
|
- Why are different Slit-Widths needed for UV/Vis-Spectroscopy?
(6.October 2007 17.51 GMT)
| |
Radio Yerevan: "In principle:
"NOT", - but: Some times it may be convenient anyway!
Ideal would be a Slit-Width of zero to use highest possible "Resolution", but then
nothing would be left for the detctor to be measured !!
Therefore the real Slit-Width is a Compromise between enough Energy and highest "Resolution".
Usually Slit-Width is keept fixed during the whole recording of a particular Spectrum.
Convenient it may be for Single Wavelength Measurements, to broaden Slit-Width, to lift the Signal out of the Threshold of Noise!
(The increase of the Signal is nearly linear, while the Increase of Noise is only of Square Route)
But take care!: Changing Slit-Width may affect
the 'molar extinction coefficient' ε!
Add. References:
General Beer-Lambert Law
ε ('epsilon') |
Back to FAQ's Index
|
Back to FAQ's Index
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- How does UV/Vis Diode Array Spectrometer (PADs/DADs) work?
(26.January 2007 06.56 GMT)
| |
With a "Inverted Optics"!: —
That's the "Terminus technicus" for.
Some Differences to "Scanning Spectrometers" ("?Normal? Optics"):
| A) |
The Sample and the GratingC) have changed/inverted their place on the optical bench.
So the Line is: Source - Sample - GratingC) - DetectorD)
(Lenses and Shutter suppressed!). |
| B) |
The consequence of A) is, that now polychromatic ("white") Light is passing the Sample,
instead of monochromatic ("Single Wavelength").
So the whole Spectrum can be taken at once, without any Disadvantage! |
| C) |
The Grating is now called "Polychromator" instead of "Monochromator", because we need
ONLY one Slit, on its entrance!
The full Spectrum, all Wavelengths, are "send" simultaneously
to the DetectorD). |
| D) |
The Detector is now an Array of PhotoDiodes (PDA) on a single Chip(DAD), instead of
a single PhotoDiode or a PhotomultiplierTube (most common).
As fast scanning as ever, can NEVER beat the Advantages
of simultaneously!!
Some times you find a CCDE) instead of a real PDA/DAD inside the Spectrometer! Take care for! |
| E) |
CCD's Charge Coupled Device Detectors have, by their construction/electronics,
only a few, and rarely required Advantages over PDA's/DAD's, but several Disadvantages! |
| F) |
Some other important "Adjectives":
| • Single Beam (mostly). |
• No closed Sample Compartment required! |
| • Real Spectrum instead of Single Wavelength. |
• Predestinated for reliable Spectroscopy. |
| • Really fix Wavelength scale. |
• Only quasi equidistant Wavelength scale. |
| • Quasi fix Wavelength resolution. |
• Time stable Wavelength resolution! |
| • Exorbitant stable! (>15 Years/>30 Instr.!) |
• Predestinated for reliable Chemometrics. |
| • Predestinated for stable/secure Production. |
• Predestinated for validated Quality Control. |
| • etc. |
|
|
| G) |
etc. |
It follows from all above:
It must be one of the easiest "to be validated" and lowest expensive
Analytical Instrument/Method ever! (FDA/ISO 900x/etc.!)
(Keywords: SST: "20 seconds a day is more then enough!, to achieve a lot more than ....")
See the picture of a famous PDA/DAD Spectrometer with its "optical bench" under:
www.p-forster.com/english/themes/Spectroscopy/BASICS/DiodeArrays.htm
See the picture of a conventional, scanning Spectrometer with its schematic under:
www.p-forster.com/english/themes/Spectroscopy/BASICS/UV-Vis Instrumentation.htm
Add. References:
Polychromator/Monochromator/Photomultiplier
PhotoDiode Array Spectrometer Quiz |
Back to FAQ's Index
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Back to FAQ's Index
|
- Where can I find/get a Spectrum (UV/Vis/NNIR/NIR/IR), published?
- Where can I find/get published Spectra (UV/Vis/NNIR/NIR/IR)?
| |
At NIST: — Nearly one of the Best, where you can find Spectra for Compounds!
NIST: National Institute of Standards and Technology.
| Big Lack!: |
The measuring Environment/Parameters are NOT documented!!
[7, 8, 9] |
| Big Advantage!: |
The Big Lack!: You will nearly NEVER USE ANY numeric value from this Spectra for your
Concentration Estimation, NOR USE ANY Lambda(max) for your Identification!!!! |
| Big HINT!: |
A.) Place always the cursor inside the Graph/Spectrum, and
B.) Toggle with the Key/Letter 'L' the Y-Scale to 'logarithmic' to get a
qualitative better representation of Absorbance!
(Not a real Disadvantage!:
The NUMERIC Y-Scale doesn't change to
'Absorbance', because nobody knows THE used Concentration!) |
In this Atlas you have the Options to search by 'chemical formula', by 'name', by 'CAS registry number', etc.
The Spectra Atlas: "
NIST Chemistry WebBook" you will find under:
http://webbook.nist.gov/chemistry/
(A quite good alternative may be:
ChemExper Chemical Directory http://www.chemexper.com)
Add. References:
Is it wise ... ?
Linearity
G'BLBL: General Beer-Lambert-Bouguer Law |
Back to FAQ's Index
|
- What is an Isosbestic (Isobestic) Point and when it appears?
- What is a Hidden Isosbestic (Isobestic) Point and when it appears?
| |
That's exactly the correct question: And when it appears?
In real, it's never a 'Point'. But, it's named. because 'everybody' is recognising it from his wrong 'Point' of view!!
Let's give the 'shortest' possible Definition:
| Definition: An "Isosbestic (Isobestic) Point" is the Absorbance Value
at a constant wavelength of a closed Reaction System, measured along its Reaction Coordinate
(RC), and is constant! Peter Forster |
Or as Formula:.
AλIP(rc) = G'BLBLλIP(rc) = const.
rc: reaction coordinate (mostly time*)).
|
(A small hint: Set m = # of all Educts plus # of all Products.) |
(SORRY: - But Wiki's (Wikipedia's) Definition of the Isosbestic (Isobestic) Point is VERY INADEQUAT and
INCOMPLETE at the same time !! 1.Nov.2006 P.F.)
Now it should be absolutely clear and evident, that it is not possible to have any
'Hidden Isosbestic (Isobestic) Point', except you have hidden it by yourself, before!!!
(An Example may be, if the volume over the RC is not constant, as during a titration, or similar. To normalise the measured
set of Spectra in one or the other way, can be very dangerous, special for your own expertise!)
To name it as a 'Point' is the result of the wrong 'Point of view', because drawing the spectra along the Reaction
Coordinate (RC) into the same graph, is nothing else as collapsing the RC to ZERO (dropping/losing
a whole dimension of view), and so an imaginary intersection 'Point' is/was bourn:
 |
'Isosbestic (Isobestic) Points': Of course, a closed RS easily can contain
several IPs. But it is of the exactly same true, that not every closed RS must contain at least one IP.
It is not only a question of the observed wavelength range, of course!
Note: . Recognize, that each spectrum has an imaginary, additional
parameter, - its place on the Reaction Coordinate (RC)!!! |
*) In Literature, very often you find the value of [pH] as Reaction Coordinate (RC), what —
identify them doubtless as a Simulation.
Of course, for learning/visualise, Simulation is a technique absolutely to prefer!
Add. References:
G'BLBL: General Beer-Lambert-Bouguer Law
Spectroscopy
Linearity |
Back to FAQ's Index
|
- Has an Isosbestic (Isobestic) Point a special power of evidence?
| |
Of course: NOT AT ALL !!!!
What from the given Definition of the Isosbestic (Isobestic) Point:
AλIP(rc) = G'BLBLλIP(rc) = const.
rc: reaction coordinate (mostly time).
must follow absolutely clear, is:
Δ G'BLBLProducts; λIP(rc) =
_ Δ G'BLBLEducts;
λIP(rc).
At least now, it must be absolutely obvious for everybody, that without other additional limits and/or without additional
observations, an Isosbestic (Isobestic) Point by itself cannot be of any evidence, any significance, others then
its Definition is telling!
Remember: Only the Whole (system) is more/"more significant", then the/any
Sum(mation) of its "members"!
Add. References:
Definition: Isosbestic (Isobestic) Point
G'BLBL: General Beer-Lambert-Bouguer Law |
Back to FAQ's Index
|
Back to FAQ's Index
|
- Chemometrics that work (to use) with UV/Vis- NNIR- NIR- IR-Spectroscopy?
- Which Chemometric(s) Methods work (to use) within spectroscopy?
Back to FAQ's Index
|
- Chemometrics: Introduction
for Use in UV/Vis- NNIR- NIR- IR-Spectroscopy?
Back to FAQ's Index
|
- How to VALIDATE Chemometric(s) Methods! —
Not only for spectroscopy?
| |
A CORRECT Validation is the Alpha (α)
AND Omega (Ω) of absolute every Chemometric Method!!
Correct Validation MUST combine both; Calibration Validation AND SMV, Sample Method Validation!!
Both Validations are the biggest Lack of nearly every Chemometrist/Chemometrician
and Specialist, too!
That's exactly the cause, why both, Chemometrics AND their Specialists have lost a Lot of Reliability, and this would not have to been necessary!
RSS, SEP, MSEP, RMSEP, RMSEC, STD, B |
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