Advantage/Purpose of Transmission vs Absorbance in calibration curve

[~christina~]

Homework Statement

The problem involves a calibration curve which was created and where % T vs concentration was favored for use over the usual Absorbance vs concentration and a question of why would this be used in favor over the latter relationship curve was presented.

other details:

1. % concentration is from 0.35-0.05 with a 0.1 interval between points. Total points on graph = 7
2. Max transmitance occurring at the 0.05 % concentration is ~80%T
3. Minimum transmittance at the 0.35% concentration is ~ 15%T

Best fit line through the points is linear in relationship [exception for this is the highest concentration %T point which is somewhat above the line]

Homework Equations

[itex]A= abc[/itex]

[itex]A=-log (T) [/itex]

[itex]T= [/itex]Exiting light intensity / Incident light intensity = I / I_o

The Attempt at a Solution

What I know:

1. % Transmittance vs concentration plot usually has a negative sloping exponential relationship. (not talking about the one here which is linear in the range observed)
   
2. Due to #1 above, it is preferential to plot calibrations curves using absorbance vs concentration. This is a result of the relationship A = abc which demonstrates that concentration is directly proportional to the absorbance of a solution. Generally it is linear within the working range of absorbance being ~ 0.10-0.82 from what I looked up.

I was thinking that the reason that the % T vs concentration was used was that since the concentration range observed on the graph (0.05-0.3%) is small and as a result, in that area the relationship between %T and concentration is linear, it would not matter if one chose to use this calibration plot vs a abs vs concentration since the latter would be linear as well.

But as to why % T was chosen over using Abs for the graph, I am unsure about since from what my thoughts on the subject tell me, they would be equivalent in this case (except for the positive slope in the abs vs concentration graph). In addition, all I could generally find around the web and in my text enlighten me on the benefits of using abs vs concentration as opposed to the cases in which %T would more favorable for use.

I would appreciate any comments on whether my thoughts are correct or not.

Thanks!

 

[Borek]

Have you tried to plot A vs c?

 

[~christina~]

Have you tried to plot A vs c?

I have converted the values based on approximation of the values given on the graph (just have the graph).

Values based on my eyeball view:
% T values (concentration) => 80% (0.05%), 60% (0.10%); 45% (0.15%), 32% (0.20%), 22% (0.25%), 17% (0.30%), 15% (0.35%)

conversion:

Abs value (concentration) => 0.0969 (0.05%), 0.2218 (0.10%); 0.346 (0.15%), 0.495 (0.20%), 0.657 (0.25%), 0.769 (0.30%), 0.824 (0.35%)

Revelation: nothing much

It looks the exact same as the transmittance except with a positive sloping graph when abs is plotted. Of course, the last value deviates from beers law but that is because it is at a higher concentration I guess.

 

[Borek]

Strange. Neither plot looks completely linear, but T plot shows an obvious curvature, so I would prefer A plot. Unless some more advanced statistical analysis would point to T. Not that I have any idea what "more advanced" analysis could mean.

 

[~christina~]

Strange. Neither plot looks completely linear, but T plot shows an obvious curvature, so I would prefer A plot. Unless some more advanced statistical analysis would point to T. Not that I have any idea what "more advanced" analysis could mean.

Hm, It looks exactly the same to me as it is plotted except they just used linear regression to find the best fit line which left the last point out. It was a bit straighter though.

I just noticed something odd I didn't take notice of before for some reason. This may be why it was strange when you plotted it. The scale on the y-axis is not spaced evenly. I measured the spacing btw the %T values and it is as follows:

10-20%T (2cm), 20-30%T (1.2cm), 30-40%T (0.8cm), 40-50%T (0.65cm), 50-60%T(0.5cm), 60-70% (0.4cm), 70-80% (0.4cm), 80-90%T (0.35cm), 90-100%T (0.4cm)

Now I'm even more perplexed about the problem.

I'm not sure about the relationship between the numbers and isn't an axis usually spaced evenly? Is there any case where this would not happen like for my graph?

Thanks Borek

 

[Borek]

Sounds like a special graph paper - they come in many flavors, so that you don't have to convert your data. Google for logarithmic paper and you will see what I mean.

 

[~christina~]

Sounds like a special graph paper - they come in many flavors, so that you don't have to convert your data. Google for logarithmic paper and you will see what I mean.

Ah, that makes sense since that is what it was. I haven't seen something like this before. This explains what I'm seeing and probably the question I guess.

Thanks Borek!