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### Topic: Interpretting first / second derivative for acid-base titrations  (Read 23959 times)

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#### noiseordinance

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##### Interpretting first / second derivative for acid-base titrations
« on: August 08, 2009, 04:24:35 PM »
Hi there,

I'm curious if someone could help me interpret the data generated by our lab software we used to do an acid-base titration. From what I understand, the first derivative is half of the equivalence point. Is this correct? Also, if the first derivative is half of the equivalence point, what is the significance of the second derivative?

Thanks for any help.

#### Borek

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##### Re: Interpretting first / second derivative for acid-base titrations
« Reply #1 on: August 11, 2009, 02:10:56 PM »
the first derivative is half of the equivalence point

First derivative is a function, equivalence point is a point, you are comparing apples and oranges.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info

#### kd.gns

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##### Re: Interpretting first / second derivative for acid-base titrations
« Reply #2 on: August 11, 2009, 03:37:11 PM »
Taking the first derivative of your data set will give a clearer view of where the equivalence point is, often this is done because just looking at your data, your equivalence point is hard to tell, but looking at the first derivative, the equivalence point should be where the first derivative of the data is at a maximum, that is when the data is changing the most.

The second derivative is an alternative way to find the equivalence points. When looking at the second derivative, you are looking for a X-intercept which indicates a change in concavity of the original data, corresponding to the equivalence point, doing both the first and second derivative is just double checking your interpretation.

#### marquis

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##### Re: Interpretting first / second derivative for acid-base titrations
« Reply #3 on: August 13, 2009, 02:36:47 PM »
Try Chemical Separations and Measurements, by Peters, Hayes, and Hieftje, Page 379.  Its an older manual.

Usually, you have titration points (a volume of titrant and mv, if working potentiometrically).  My analytical professor said (many, many years ago) that the first derivative plot will identify the titration point nearest the end point.

The second derivative allows mathmatical interpolation between titration points.  Supposedly, the second derivative is more accurate, giving a more precise volume of titrant.