REPORT: Spectrometric Determination of Mn in Steel
(Solution Photometry and Atomic Absorption)
Report Objectives
In addition to determining the Mn content of a steel sample, this analytical study also had the objective of comparing two different spectrometric techniques (solution photometry and AA spectrometry), and two different calibration procedures (linear calibration curve and standard addition). Thus, the report should provide the analytical results, and should also provide an objective comparison of the various methods.
Report Items
Solution Photometry
Percent Mn in steel:
X(av)SP = average of two separate samplings (% Mn)
RSP = range of values (% Mn)
SSP = standard deviation (n = 2)
AA Spectrometry
Calibration Curve Procedure:
X(av)AC = average of two separate samplings (% Mn)
RAC = range of values (% Mn)
SAC = standard deviation (n = 2)
Standard Addition Procedure:
X(av)AS = average of two separate samplings (% Mn)
RAS = range of values (% Mn)
SAS = standard deviation (n = 2)
Overall:
X(av)AA = average of two methods (X(av)AS and X(av)AC)
SAA = combined standard deviation from X(av)AS and X(av)AC (see below)
NOTE: Data as ppm Mn or MnO4- must be converted to %Mn in the steel sample.
Statistical Analysis
It is assumed that the major source of variance in the results is from sample to sample. Thus, standard deviations are calculated from the variance between the two different samples used for each method above; therefore, n = 2 for calculations of method standard deviations.
To compare methods, the t-test must be applied. However, the F-test must first be applied to the two sets of data compared to determine that the variances are not significantly different.
(F-test tables are in the Lecture Notes volume; t-test tables are in the textbook.)
F-test. The statistical quantity, F, is calculated by:
F = S12/S22 , where F ³ 1 (i.e., S1 ³ S2)
Because n is small (2) for these data sets, the F-test is not very reliable. That is, the value of F must be greater than about 200 in order to detect a significant difference in precision at the 95% confidence level. If such a value is obtained, it would not be proper to conduct a t-test.
The Report should include the following t-test results:
[1] X1 = X(av)AC; X2 = X(av)AS (comparing calibration and std addition)
[2] X1 = X(av)SP; X2 = X(av)AA (comparing solution and AA spectrometry)
t-test. For Case [1]: The statistical quantity, t, is calculated by:
±t = [(X(av)AC - X(av)AS)/SC][n1n2/(n1 + n2)]½
where SC is the combined std deviation for two sets (AC, AS), calculated as:
SC = [((n1-1)S12 + (n2-1)S22)/(n1+n2-2)]½
and the number of degrees of freedom is: (n1+n2-2)
t-test. For Case [2]: The statistical quantity, t, is calculated by:
±t = (X(av)SP - X(av)AA)/[SC(1/n1 + 1/n2 + 1/n3)½]
where SC is the combined std deviation for three sets (AA, AS, AC), calculated as:
SC = [((n1-1)S12 +...(n3-1)S32)/(n1+n2+n3-3)]½
and the number of degrees of freedom is: (n1+n2+n3-3)
Statistical Evaluation of Data. The values of t calculated should be compared to a standard t Table, to determine if there are significant differences between the various methods. Include these evaluations in the Report.
Estimated Detection Limit. The report should include an estimate of the detection limit (DL) for Mn (ppm). Use the IUPAC definition:
DL(Mn, ppm) = [Y(av)B + 3*SB]/b
where Y(av)B is the average value of the blank absorbance, abs. units
SB is the standard deviation of the blank, abs. units
b is the slope of the calibration curve (abs./ppm Mn)
For the purpose of this report, assume that Y(av)B is zero; that is, any non-zero blank measurement is only due to detector off-set and can be corrected to zero by simple subtraction.
Because a calibration curve is obtained only for the AA measurements, and the AA procedure allows calculation of the blank standard deviation, you are only required to report the detection limit estimated for AA spectrometry. For extra credit can you estimate the detection limit for the solution photometry method?
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SAMPLE Calculations
F-test
F(SP/AC) = (0.011)2/(0.009)2 = 1.5
F(AS/SP) = (0.028)2/(0.011)2 = 6.5
F(AS/AC) = (0.028)2/(0.009)2 = 10
FTab » 200. Therefore, NO significant difference in precision among the three methods.
t-Test
(1) Comparing AA(Calib) with AA(Std Addn):
±t = [(X(av)AC - X(av)AS)/SC][n1n2/(n1 + n2)]½
SC = [((n1-1)S12 + (n2-1)S22)/(n1+n2-2)]½
SC = [((2-1)(.009)2 + (2-1)(.028)2/(2+2-2)]½
SC = ±0.021
±t = [(0.686-0.812)/0.021][2x2/(2+2)]½
±t = 6.0
(2) Comparing Photometry and AA:
±t = (X(av)SP - X(av)AA)/[SC(1/n1 + 1/n2 + 1/n3)½]
SC = [((n1-1)S12 +...(n3-1)S32)/(n1+n2+n3-3)]½
SC = [((2-1)(.011)2 + (2-1)(.009)2 + (2-1)(.028)2)/(2+2+2-3)]½ = ±0.018
±t = (0.698 - 0.749)/[(0.018)(1/2 + 1/2 + 1/2)½] = 2.3
