[pcm81]

Doing some titrations in the last couple of weeks got the thinking about error margins in chemical analysis.
Often on the bottles we see statements like "99.95% pure". I have to wonder about the production environment vs state of the art accuracy that can be attained.

My $20 burette is 50ml with 0.1ml markings. Even if we assume it to be perfectly accurate and i read it very consistently the best i can hope for is 1/1000 error (lets say my burette-fu is strong and i can read to half of a gradation) that would give me 1/1000 error if i titrated all 50ml. Error would grow if i titrated less.

The least possible error from my cheapie burette is 2x of the purity of "lab grade" chemicals available to general public (my KHP is 99.95% advertised purity). So for general public we can guesstimate a 0.1% being the best attainable accuracy.
Where does "real lab" equipment stack up against this? Do they make electronic burettes that can measure 0.01ml for 100ml volume? Bigger volume, smaller error? What is out there accuracy wise? Looks like for $4K you can buy a burette with 20,000 steps. So, that would in theory give 1/20,000=0.005% is this the limit of chemical analysis accuracy? They make multi-meters with 8.5 digits of precision. My personal multi-meter has 6.5 digits of precision. Chemical analysis seems to be less accurate due to need to measure "mechanical" things like mass or volume.

[Borek]

Most likely they determine impurities and subtract from 100%.

[pcm81]

Most likely they determine impurities and subtract from 100%.

I thought about that, but there is no free lunch there as well, because if you are measuring impurities you have to measure them in some quantity of the total substance, which means you still have to measure out total substance with some accuracy, which in turn will result in overall accuracy.

The best I can think of would be to have a very tall burette that uses ultra sound or laser to measure the distance to the top of the titration column. That could give very high accuracy. Lets say in a lab you have 200cm tall burette and the laser or ultra sound can measure down to 0.1 of a mm, that gives you 1 in 200,000 accuracy.

Now, granted that this is probably just a theoretical exercise... I do not know of any chemical process that would require accuracy better than 1%. If you are doing research then you probably care to find out molar ratios, so that means the measurements need to have accuracy good enough to determine measured ratio to be closest to one of possible rations, say 1:2 or 3:7 what ever. Probably 0.1% is good enough. In production environment you often run things to excess, with excess being a waste. So 1% waste is usually acceptable. Like in my particular case i am titrating to measure total acid, free acid and iron content in my phosphating bath. But those numbers will easily change by 10% or more as i use the bath, hence for me a 1% accuracy is more than enough.

Just wondering if i am missing something and there really is the need and tools available to do chemical analysis beyond the 1/20,000 error offered by $4000 digital burettes or is this basically the limit determined by most stringent needs for this field of science?

When you are sending a rocket to Mars 1/20,000 error in angle of trajectory is tens of thousands of miles, but for chemistry, is this the practical limit of needed accuracy?