[eb51111]

Hi,

I have a query about propagating errors in a serial dilution process:
Using the following glassware:
500 mL volumetric flask (±0.25 mL) (0.05% error)
100 mL volumetric flask (±0.1 mL) (0.1% error)
5 mL pipette (±0.015 mL) (0.3% error).

If I have a stock solution made in the 500 mL flask (with the error associated with that), then take 5 mL --> 100 mL and then 5 mL of that solution to another 100 mL volumetric flask - how do I work out the overall % error associated with the process. I've had a play around with square rooting the sum of the squares of the % errors but it's turned out to be a much less trivial calculation than I first assumed.


Any help with this would be massively appreciated!

Thanks

[mjc123]

That ought to be right. Can you show us your calculation so we can see if you've gone wrong at some point?

[pcm81]

Keep in mind that when you "Take 5ml" there is also error associated with that 5ml measurement, in addition to the error of filling the target flask to 100ml level.

You need to multiply the errors from all steps including the weighing of what ever you are using to make original solution.
Let's say the error in each step is "e1", e2 etc.
Then you have: (1+e1)×(1+e2)...×(1+en)

Your error sources are:
1. Weigh chemicals
2. Fill 500ml flask
3. Take 5ml sample
4. Fill 100ml flask
Etc for any additional steps.