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### Help with Propagating Errors

Posted: **Sun May 06, 2012 12:07 pm**

by **jane b**

Hi. I did the Which Orange Juice Has the Most Vitamin C? experiment using the kit I ordered. It was very helpful to have everything I needed; it is a great idea to offer those kits so thanks! Anyway, I had to change the experiment a little to check for the vitamin C in 5 different citrus fruits. Following the experiment instructions, I made 3 measurements of how much iodine solution it took to titrate the juice/starch mixture, writing down the volume of iodine solution at the start and end of the titration. I know that the instrument limit of error for a 50 mL buret is +/- 0.05 mL so the uncertainity of the starting and stopping reads would be +/-0.05 + +/- 0.05 = +/-0.10 mL. But that is where it stops, I am really not up on my chemistry yet (next year). So, I would really apppreciate some help in trying to figure out how to include this uncertainity when I have to take the average of the three measurements of the juices. Then as the final step to solving for the amount of vitamin C in the juices, I have to set up a proportion per experiment instructions of : (using the average amounts i just solved for) amount of iodine required to titrate vitamin C standard/ 20 mg of Vitamin C (the amt in the standard) = amount of iodine required to titrate the citrus juices/x - with x being the amt of vitamin C in the juices. I am just not grasping how to figure in that uncertainity in these last two steps. And I have searched the internet for further instructions, but I am not catching on. Thanks for any help you can offer.

### Re: Help with Propagating Errors

Posted: **Sun May 06, 2012 5:33 pm**

by **donnahardy2**

Hi,

Welcome to Science Buddies! I think you are doing this really great project, and I’m glad the kit was helpful for you.

https://www.sciencebuddies.org/science- ... p044.shtml
It seems that you primary question is regarding the error in your measurements. The first consideration is regarding the accuracy or precision of the buret. According to this website, which includes a good discussion on this topic, the accuracy of a 50 ml buret or pipette is .05 or .1 ml.

http://dwb.unl.edu/Teacher/NSF/C14/C14L ... p01017.htm
The standard error is an estimate of the standard deviation for a group of sample results. Using the triplicate results you obtain from each sample, you can calculate the standard error of your measurements using the following online calculator. The Wikipedia article includes a good discussion of standard error.

http://www.miniwebtool.com/standard-error-calculator/
http://en.wikipedia.org/wiki/Standard_error
So you should go ahead and do the experiment and measure the results for each sample in triplicate as accurately as possible. After you have all of your results, you can calculate the standard error. I hope this answers your question. Please let us know if you have a question about actually calculating the concentration of vitamin C from the titrated results or if you need additional explanation.

Donna Hardy

### Re: Help with Propagating Errors

Posted: **Sun May 06, 2012 11:53 pm**

by **jane b**

Thanks for responding so quickly. The information you provided is a little confusing to me, but yes, that is the experiment that i am working on. I understand the idea of using the proportion to solve for the amount of vitamin C in the fruit juices when you have the average of the 3 volume measures of how much of the iodine titration solution it took to titrate the vitamin C standard and the average measure of how much it took to titrate a citrus fruit juice - and then knowing that the vitamin C tablet has 20 mg of vitamin C. I just don't know how to work in the uncertainty.

Example: in any trial, i am making 3 measures of how much iodine solution it takes to titrate a juice/starch mixture by finding the difference between the starting level of the solution in the buret and the ending level in the buret. I read that the instrument limit of error for a 50 mL buret is +/-0.05; so finding the difference of the start and finish levels would have double that.. an uncertainty of +/- 0.10 mL. So, if my measurements of lime juice were 2.45; 2.32; and 2.40 would i just find the average...2.39 and add the{ +/-0.10} ? But if this is correct so far, how would i then plug it {2.39 +/- 0.10 mL} into that proportion I mentioned above to find the amount of vitamin C in the lime juice ?

Thanks so much.