Problem Set 2: Curvilinear Regression, Internal Standard, 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. Internal Standard Problem
A mixture of Benzene and Toluene in solution gave
the following chromatography results:
|
Compound
|
Concentration (µg/mL in mixture)
|
Peak area (cm2)
|
|
Benzene
|
236
|
4.42
|
|
Toluene
|
337
|
5.52
|
A solution was prepared by mixing 1.23 mg of Toluene
in 5.00 mL, with 10.00 mL of a solution containing only an unknown concentration
of Benzene, and then diluting the mixture to 25.00 mL. Peak areas of 3.33
and 2.22 cm2 were observed for Benzene and Toluene respectively.
Find the concentration of (µg/mL) in the unknown Benzene solution.
3. 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, IS techniques are found to be quantitative within 1%.
Compare this 1% standard with the CV's you each obtained for your 10 injections.