So the question is: what is the optical density of the original sample?

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Discussion Overview

The discussion revolves around determining the optical density (OD) of a diluted sample of algae, particularly when the original sample exceeds the measurement range of the spectrometer. Participants explore the implications of dilution on OD measurements and the application of the Beer-Lambert law.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes the process of diluting a sample with an OD greater than 4.5 to obtain a measurable OD of 1.58 for the diluted sample.
  • Another participant agrees with the initial calculation that the original OD can be determined by multiplying the diluted OD by the dilution factor.
  • A different participant challenges this approach, arguing that OD is logarithmic and suggesting that the original OD should be calculated using a logarithmic adjustment, resulting in an OD of 2.43 instead.
  • One participant references the Beer-Lambert law, stating that absorbance varies linearly with concentration for sufficiently dilute samples.
  • A later reply indicates that the term "sufficiently" is a critical factor in evaluating the correctness of the dilution procedure discussed.

Areas of Agreement / Disagreement

Participants express differing views on the correct method for calculating the original optical density, with no consensus reached on the appropriate approach or the validity of the calculations presented.

Contextual Notes

There are unresolved assumptions regarding the applicability of the Beer-Lambert law at high concentrations and the definition of "sufficiently dilute." The discussion also highlights potential errors in understanding logarithmic relationships in OD calculations.

Arjan.
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The problem: how to determine the optical density of a diluted sample
Hi, i work on algae and bioenergy and i have a question about the OD.

I have to determine the optical density of about 400 samples. Some samples however are too "dense" for the photospectrometer, that is they have an optical density greater than the range of the spectrometer (>4,5 OD)

In order to determine the optical density of these samples I diluted them.

So for example:
The original sample has an OD > 4,5, which is too high for the machine
So it was diluted.
0,5 ml of the sample were taken and 3,0 ml distilled H2O were added.
The OD of the diluted sample was measured
The OD of this sample is 1,58.

Question
What is the optical density of the original sample?

Homework Equations



http://upload.wikimedia.org/wikipedia/commons/0/04/Beer_lambert.png

The Lamber-Beer equation says:

Absorbance = extinctioncoefficient x length of path x concentration

Optical density = log ( I0/I1)
Absorbance = log ( I1/I0)

Links: http://en.wikipedia.org/wiki/Optical_density
http://en.wikipedia.org/wiki/Beer-Lambert_law

The Attempt at a Solution



In the example above i diluted 7 times, so the optical density is 7 x 1,58 = 11,06
 
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Your answer is correct. The OD of the original sample is the OD of the diluted sample * the dilution factor.
 
This doesn't make sense to me. OD is a base-10 logarithm scale. So for example, if you dilute by 10x then the diluted OD will be 1 less than (not 1/10th) of the undiluted OD.

The original OD should be
1.58 + log(7)
= 1.58 + 0.85
=2.43

However, you should have been able to measure OD 2.43 in the original sample.
 
According to the Beer Lambert Law, the absorbance of a sample (aka optical density) varies linearly with the concentration for sufficiently dilute samples.
 
Deleted post ... just realized an error in how I was thinking about all this.
 
Last edited:
Ygggdrasil said:
varies linearly with the concentration for sufficiently dilute samples.

And this word "sufficiently" is the only reason why I have not posted earlier that Arjan procedure was correct...
 

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