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Error Propagation Help!

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Help T^T I'm suffering so much

I'm doing a DCP and CE report on the UV-Vis spectroscopic determination of extinction coefficient

of potassium dichromate and the concentration of an unknown sample.

I used 500um standard stock solution of potassium dichromate and diluted to make 50,100,150.....to 300 through serial dilution (so that I can draw the calibration curve). I used a pipette with +/-0.05cm3 and a volumetric flask with +/-0.03cm3 for the dilution, and I'm having trouble with my error analysis. Because I did serial dilution, I have to add +/- 0.08cm3 to every further dilution right? So I'm cool with this I think, I converted the uncertainties into percentage uncertainty.

Ok, but when I use the concentration values and the absorption values to find out the extinction coefficient, what happens to my percentage uncertainty for the concentration? I thought i'll just carry it over to the extinction coefficient values.

Assuming that this is right, then I have to average the extinction coefficient values to arrive to one single value. THIS IS WHERE I'M STUCK. What happens to my uncertainties with the extinction coefficient values? Do I just ditch them and do the highest extinction coefficient value minus lowest and divide by half? How do I do this?

So say this is my extinction coefficient values with the percentage uncertainty carried from the uncertainty in the concentration







and say that the average is 0.00150

what happens to the uncertainty? T^T

and also, when I give the percentage uncertainty, how many decimal places would I give to?

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My bet would be you average the % errors as well. In your working it doesn't really matter how many decimal places or significant figuers you give your answers, just make it reasonable and consistent. It is your final answer that matters. A rule of thumb is that if the % error is 2% or higher it should be rounded to 1 significant figure, if it is less than 2% it should be rounded to 2 sig fig. Remember that your answer should also be rounded according to the error eg. (125 +/- 5.12% will become 130 +/- 5%)

Some additional information on erros can be found here:

Edit: Actually, having looked into this further, I found this:


Go down to "Finally, the statistical way of looking at uncertainty", it's probably the 'right' way of calculating the average error but I would seek your teacher's advice first.

Edited by Keel

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