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### C09-hints&helps

Course: CHEM 227, Fall 2010
School: BYU
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Word Count: 470

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227 Helps Chem and Hints for Homework Assignment #9 Making a baseline correction is easy to picture but harder to program. The baseline can be established by picking a couple of regions on either side of a peak (or group of peaks) and performing a least squares fit through them to get an equation describing the baseline. To do this, however, you must copy the data points for the two regions to a section of a...

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227 Helps Chem and Hints for Homework Assignment #9 Making a baseline correction is easy to picture but harder to program. The baseline can be established by picking a couple of regions on either side of a peak (or group of peaks) and performing a least squares fit through them to get an equation describing the baseline. To do this, however, you must copy the data points for the two regions to a section of a spreadsheet where they can be listed sequentially as a single array. If you use the slope and intercept functions instead of linest, you won=t need to worry about blank spaces, but you will still need to input both regions as a single array. Then it is a simple matter in a spread sheet to subtract a calculated baseline value from each data point across the peak (ycorr,i = yi ! [mbase xi + bbase]). What about picking the region to integrate over? Take as an example the two overlapping peaks in the figure below. Even though these two peaks strongly overlap, we can see that picking the mid point between the two peaks (the bottom of the trough) as one limit of integration would not lead to large errors in determination of peak area because the extra area from one of the peaks would compensate for the missing area from the other peak of interest. In fact, in this example of two symmetrical, equal intensity 0.050659 peaks, the areas exactly compensate each (If f( other. ) you are interested, you can g( ) play around with creating h( ) overlapping peaks of different intensity and see . 13 6.83462610 what the error would be in 3 3 1.1.10 1 .10 the peak area determination by this approach.) The other limit of integration (for example, the left point for the left peak in the figure) can be picked according to your best judgment of where the peak seems to come down close to the baseline. Even though, mathematically, the peak continues on to infinity, the area under the curve rapidly converges; that is, extending the integration to larger regions increases the area by negligible amounts (and, indeed, the additional area becomes dominated by noise). The trapezoidal rule for integration involves treating each pair of points as the corners of a trapezoid, the area of which is x (yi + yi+1), where x = xi+1 xi. Simpson=s method involves approximating every three consecutive points on a curve as defining a parabola. The area under a segment of a parabola can be shown to be x (yi + 4 yi+1 + yi+2), where yi and yi+2 are the end points, yi+1 is the midpoint, and again x = xi+1 xi. [Note that this formula assumes equally spaced points; an alternative formula is (1/6)(xi+2 xi)(yi + 4 yi+1 + yi+2).] A final caution: when you set up your Simpson routines, make sure that each segment doesnt get integrated twice.
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