Suppose I am making a solution of a particular concentration and I am doing it with step wise dilution from a stock solution. If I use a same volumetric flask for 2 time for the consecutive dilution, then do I have to add uncertainty of that volumetric flask two(2) time or only one(1) time in the calculation of total measurement uncertainty.
Your answer in this guide:
https://www.eurachem.org/index.php/publications/guides/quam
"Add" following the rules of error propagation.
Dear Gaurav Vyas,
You are right, it is implicitly assumed in the common guides on the uncertainty evaluation in analytical measurement that different items of volumetric glass are used in different operations, so that application of the volumetric tolerance to derive the standard uncertainty for each operation would be justified. If, however, you repeatedly use the same glass (same pipette and same flask) e.g. for making a consecutive dilution, only random error contribution should be taken into account on each subsequent step, but systematic error contribution should not. It is straightforward to do so if you use an individually calibrated glass, by following the “actual performance-based approach” as described in my paper attached. In the case of the “tolerance-based approach” and repeated use of the volumetric tolerance in the calculation, the resulting uncertainty will, of course, be overestimated. However, given that the volumetric uncertainty is generally small as compared to other sources of uncertainty, it is possible in practice to disregard this redundancy in volumetric uncertainty evaluation.
Best regards,
Rouvim Kadis
Dear Gaurav Vyas ! The glass measure dilution method creates an extremely high level of error. I dilute solutions to the desired concentration using the gravimetric method. This method is orders of magnitude more accurate.
Dear Oleg Novikov,
I am curious to know in which area of applied or fundamental research the relative volumetric uncertainty at the level of (0.1 ‒ 0.2) % provided by common volumetric glassware is insufficiently small compared to other sources of uncertainty, so that the gravimetric method for solution preparation is required. If that is really the case, one can simply use the volumetric glass that has been in-hose calibrated (in the user’s hand), thus reducing the resulting uncertainty considerably. An adequate effort is generally required.
Regards,
Rouvim Kadis
Dear Rouvim Kadis ! I have become convinced of the greater reliability of gravimetry in practice. You trust your measuring glass suppliers too much. Check it at least once and you will be convinced that the volumetric method is an ancient technology.
Dear Rouvim Kadis
As per your paper you shared in the previous comment, I observed that in case of glassware that are used for delivery, we can avoid adding up the measurement uncertainty upon repeat usage (Please correct me if I have interpreted wrongly. Although please go through the attachment I am sharing here, and checkout pages 36 to 38, where they have taken an example of dilution of a particular stock solution. In that case, they are using a 100 mL flask for each step dilution and they are considering its uncertainty of that flask on each step. It will be great help if you can put your thoughts on the same example for my better understanding.
Dear Gaurav Vyas,
It is not at all implied from my article (and from my answer to your question either) that you can avoid adding the uncertainty arising from repeat use of the volumetric ware (regardless of using it for delivery or not). I wrote in my comment that because of repeated counting the uncertainty derived from the volumetric tolerance, that is, the tolerance divided by √6 (see the first line in Table 2(a) in the paper), the resulting uncertainty will be overestimated. (Overestimated as compared to that uncertainty value that would be obtained if the identity of volumetric ware used at several steps would be taken into account.) Also, I wrote that in practice it is reasonable to disregard this redundancy in volumetric uncertainty evaluation. Thus, answering specifically to your question, you should add (by root-sum-squaring) the uncertainty derived from the tolerance for your volumetric flask and your pipette, respectively, two (2) times.
I am very familiar with the uncertainty evaluation procedure described in the QUAM95 Guide and its subsequent editions – this procedure was criticized in my referred article and in an earlier article added here. The weak points in QUAM procedure are: 1) the joint use of the specified tolerances and the experimentally estimated variability, while only the first one converted into the standard uncertainty is required; 2) the use of the coefficient √3 in the denominator to convert the specified tolerance into the standard uncertainty, assuming a rectangular probability distribution instead of a triangular probability distribution that is much more realistic in this case. Otherwise, what is described in the Guide is not objectionable. Note that the case of the same glassware used in the dilution chain is not considered there, since “in practice, different pipettes and flasks (of the same nominal capacity) will be used” (QUAM95, p. 37, left column above). Also note that the uncertainty arising from temperature effects should additionally be taken into account.
Best,
Rouvim Kadis
Thank you so much Rouvim Kadis
It majorly solves the issue and clears the things
Thank you for taking out the time for explaining in detail.
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