Estimating Error in Titration Results Using Second Derivative Analysis

[bb1]

I have an error analysis question...I carried out a titration, and I have error for each measurement, but I then took the second derivative of the data and graphed it. The actual value I am reporting was estimated from the x-intercept of this graph. The curve was not fit to anything. How do I find the error to report with this value? Or do I not report error because it was estimated from a graph?

 

[GCT]

I have an error analysis question...I carried out a titration, and I have error for each measurement, but I then took the second derivative of the data and graphed it. The actual value I am reporting was estimated from the x-intercept of this graph. The curve was not fit to anything. How do I find the error to report with this value? Or do I not report error because it was estimated from a graph?

You may need to consider error propagation , are you in college?

You may manipulate the axes to find the zero point more accurately , however , the sole error from this estimation is that of simply estimating between the left and right peaks and is similar to the procedure for measurement with a ruler. Are you using Excel?

 

[bb1]

Thanks for responding...
Yes, I'm in college and I'm using excel...I have considered error propagation. The problem I'm having is that each volume measurement I have also has a random error from the measurement (0.02 ml in this case). When I calculated the "second derivative" (really I calculated the change in the change of pH against the average volume for the change) I also propagated error. However, when I graphed the second deriv, I estimated the x-intercept by inspection of the graph. What happens to the error I propagated? I feel like I can't really use it because I just calculated error for each point, and the x-intercept on the graph is not an actual measured point, so it seems wrong to me to use that error. It also seems wrong to just use the error of estimation from the graph. Do I somehow combine the error of my estimation with the propagation error? Does anything I'm saying make sense?

 

[GCT]

Thanks for responding...
Yes, I'm in college and I'm using excel...I have considered error propagation. The problem I'm having is that each volume measurement I have also has a random error from the measurement (0.02 ml in this case). When I calculated the "second derivative" (really I calculated the change in the change of pH against the average volume for the change) I also propagated error. However, when I graphed the second deriv, I estimated the x-intercept by inspection of the graph. What happens to the error I propagated? I feel like I can't really use it because I just calculated error for each point, and the x-intercept on the graph is not an actual measured point, so it seems wrong to me to use that error. It also seems wrong to just use the error of estimation from the graph. Do I somehow combine the error of my estimation with the propagation error? Does anything I'm saying make sense?

Your concerns are legitimate , the error for each data is going to have certain effects on the domain of the x intercept since it is propagated until the second derivative data - this means that each of the two peak points are going to have error bars which you are going to need to take into account of when determining the error off of simply estimating the x intercept between the peaks.

You should consider whether it is possible to find the error for just these two peaks , to do this you are probably going to need to take into account the maximum error in reading until that point e.g. if the error for each is 0.2 mL then after 5 mL it is 1 mL and after 10 it is 2 mL. After this consider the fact that derivatives take into account the rate for a particular point.

Should I find something useful I'm going to post it.

 

[bb1]

What you're saying makes sense...thanks!