Problem Set 3: Curvilinear Regression and Injection Variability

1. Curvilinear Regression: Table 1 lists the data obtained from the calibration of an atomic emission spectrometer's response for a range of alkali ion concentrations. The data are nonlinear above 5.0 ppm.

*Concentration (ppm)*	*Counts/msec*
0.2	0.8
0.5	1.3
1.0	2.2
2.0	3.7
3.0	5.1
4.0	6.5
5.0	7.8
6.0	8.9
7.0	9.9
8.0	10.5
9.0	10.8
10.0	11.0

Using all points, conduct a 2nd order fit of these data; plot the predicted curve, the data points, and write the equation for the predicted curve that includes appropriate units.
For an unknown analysis that gave a reading of 10.6 counts/msec, determine the unknown's concentation. Show all calculations on a separate sheet of paper; graphically illustrate this on your calibration plot.
Using all points, conduct a 1st order fit of the data, show the equation, and compare the Coefficients of Determination for the 1st and 2nd order fits. State what percent of the overall variability is accounted for in each of these fits

2. Injection Variability:

The purpose of this exercise is to characterize the variability associated with GC injection techniques. In Room Sims 310 is a GC syringe (in a box), two small beakers and two analytical balances. Working with a lab partner, each person should make 10 separate 5 mL syringe injections into the tared beaker. Prepare a spreadsheet that determines the following:

The volume of each injection (remember to measure the temperature)
the average volume injected for each lab partner
The average volume for the overall group
The standard deviation for each person
The standard deviation for the overall group
The Coefficient of Variation (CV) for each person and the overall CV. CV is the standard deviation divided by the average, represented in %.
Internal standard quantification is designed to minimize injection errors. Generally, internal standard techniques are found to be quantitative within 1%. Compare this 1% standard with the CV's you each obtained for your 10 injections.