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Document Sample
Uncertainty Estimation: Lead in Soil by GF AAS
Result
Value unit Components of uncertainty Su
Mass of the Sample
drift(±) rep(su)
m soil 0.254 g 0.0002 0.00017 0.0002
Volume of the sample solution
cal(±) rep(±) temp(su)
V 50 50 ml 0.1 0.03 0.01818653 0.063
The Result: Lead content of the Soil
c 50 × V 50 2 2
æ u(C50 ) ö æ u(V50 ) ö æ u(msoil ) ö æ u(R) ö
2 2
Q Pb = ç
m soil × R u(QPb ) = QPb ç C ÷ +ç V ÷ +ç m
÷ ç ÷ ç ÷ +ç
÷ ÷
è 50 ø è 50 ø è soil ø è R ø
u rel(C 50) u rel(V 50) u rel(m soil) u rel(R )
Q Pb 22.2 mg/g 0.0172 0.0013 0.0008 0.0419 1.0
Index: 14.40% 0.08% 0.03% 85.49%
The Result: Lead content in soil: 22.2 mg/g
Expanded uncertainty (k = 2): 2.0 mg/g
Recovery
Value unit Components of uncertainty Su
Matrix CRM BCR 484
U(k = 2)
C CRM 47.9 mg/g 2.6 1.3
Results of Analysis of the Matrix CRM
Replicate analysis results: 46.2 45.2 47.4 47.7 44.2
Mean: 46.14
Std deviation: 1.472
std dev
C found 46.14 mg/g 1.47241299 1.472413
Recovery
2 2
C æ u (C CRM ) ö æ u (C found ) ö
R = found
u ( R) = R ç ÷ +ç ÷
C ç C ÷ ç C ÷
CRM è CRM ø è found ø
u rel(C CRM) u rel(C found)
R 0.963257 0.02713987 0.03191185 0.040353
Calibration
Concentration of lead in the 50 ml flask
quantity unit value Su Rsu A sample A0
A sample AU 0.466 0.005598 1.20% 0.466 0.471598 0.466
A0 AU 0.032 0.002708 8.46% 0.032 0.032 0.034708
C 1_calibartion_std mg/l 20.0 0.2 0.93% 20 20 20
C 2_calibartion_std mg/l 50.0 0.4 0.81% 50 50 50
C 3_calibartion_std mg/l 100.0 0.9 0.86% 100 100 100
C 4_calibartion_std mg/l 150.0 1.3 0.86% 150 150 150
C 5_calibartion_std mg/l 200.0 1.7 0.85% 200 200 200
A1 AU 0.081 0.002708 3.34% 0.081 0.081 0.081
A2 AU 0.197 0.002708 1.37% 0.197 0.197 0.197
A3 AU 0.4055 0.002708 0.67% 0.4055 0.4055 0.4055
A4 AU 0.5925 0.002708 0.46% 0.5925 0.5925 0.5925
A5 AU 0.8015 0.002708 0.34% 0.8015 0.8015 0.8015
C 50 mg/l 108.7 1.9 1.72% 108.6848 110.0866 108.0066
mg/ml 0.1087 1.401788 -0.67816
3.492413 1.96501 0.459896
index 56.27% 13.17%
C1 C2 C3 C4 C5 A1 A2 A3 A4
0.466 0.466 0.466 0.466 0.466 0.466 0.466 0.466 0.466
0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032
20.1863 20 20 20 20 20 20 20 20
50 50.40446 50 50 50 50 50 50 50
100 100 100.8647 100 100 100 100 100 100
150 150 150 151.297 150 150 150 150 150
200 200 200 200 201.6992 200 200 200 200
0.081 0.081 0.081 0.081 0.081 0.083708 0.081 0.081 0.081
0.197 0.197 0.197 0.197 0.197 0.197 0.199708 0.197 0.197
0.4055 0.4055 0.4055 0.4055 0.4055 0.4055 0.4055 0.408208 0.4055
0.5925 0.5925 0.5925 0.5925 0.5925 0.5925 0.5925 0.5925 0.595208
0.8015 0.8015 0.8015 0.8015 0.8015 0.8015 0.8015 0.8015 0.8015
108.6049 108.5755 108.6636 109.006 109.516 108.976 108.8718 108.6986 108.526
-0.07991 -0.10931 -0.02118 0.321221 0.831208 0.291174 0.187004 0.01383 -0.15879
0.006386 0.011948 0.000449 0.103183 0.690907 0.084782 0.034971 0.000191 0.025216
0.18% 0.34% 0.01% 2.95% 19.78% 2.43% 1.00% 0.01% 0.72%
A5
0.466
0.032
20
50
100
150
200
0.081
0.197
0.4055
0.5925
0.804208
108.3539
-0.33087
0.109475
3.13%
Absorbance Measurements
Value unit Components of uncertainty Su
Absorbances of the standard solutions
stab(±) rep(±) base(±)
A1 0.081 AU 0.003 0.002 0.003 0.0027
A2 0.197 AU 0.003 0.002 0.003 0.0027
A3 0.406 AU 0.003 0.002 0.003 0.0027
A4 0.593 AU 0.003 0.002 0.003 0.0027
A5 0.802 AU 0.003 0.002 0.003 0.0027
Absorbance of the procedural blank
3 replicates: 0.030 0.034 0.032
Mean: 0.032
Std deviation: 0.002
Std dev of mean: 0.001155
stab(±) rep(su) base(±)
A0 0.032 AU 0.003 0.001155 0.003 0.0027
Absorbance of the sample solution
3 replicates: 0.456 0.470 0.472
Mean: 0.466
Std deviation: 0.008718
Std dev of mean: 0.005033
stab(±) rep(su) base(±)
A0 0.466 AU 0.003 0.005033 0.003 0.0056
Preparation of the Working Solution
Value unit Components of uncertainty Su
Temperature and thermal expansion of water
t 20 °C 1.732051
g 0.00021 1/°C
Lead Stock Solution
tol(±)
C stock 1000 mg/ml 3 1.732051
Pipetted volume of the Stock Solution for preparation of the working solution
cal(±) rep(su) temp(su)
V i_stock 1 ml 0.007 0.004 0.000363731 0.005698
Volume of the working solution
cal(±) rep(±) temp(su)
V i_1000 1000 ml 0.6 0.03 0.36373067 0.502593
Concentration of the Working Solution
2 2
Vi_stock æ u(Vi_stock) ö æ u(Vi_1000) ö æ u(Cstock) ö
2
C work_sol = C stock × u(Cwork_sol) = Cwork_sol ç ÷ +ç ÷ +ç ÷
Vi_1000 ç V ÷ ç V ÷ ç C ÷
è i_stock ø è i_1000 ø è stock ø
u rel(C stock) u rel(V i_stock) u rel(V i_1000)
C work_sol 1 mg/ml 0.001732051 0.005697862 0.000502593 0.005976
Calibration Standard Solutions
Value unit Components of uncertainty Su
Volumes of the Working Solution taken for preparation of calibration standards
cal(±) rep(su) temp(su)
V 1_work_sol 1 ml 0.01 0.004 0.000364 0.007033
V 2_work_sol 2.5 ml 0.015 0.01 0.000909 0.01326
V 3_work_sol 5 ml 0.04 0.02 0.001819 0.030605
V 4_work_sol 7.5 ml 0.06 0.03 0.002728 0.045907
V 5_work_sol 10 ml 0.075 0.04 0.003637 0.059061
Volumes of the flasks used for preparation of the calibration standards
cal(±) rep(±) temp(su)
V 1_25 50 ml 0.1 0.03 0.018187 0.062961
V 2_25 50 ml 0.1 0.03 0.018187 0.062961
V 3_25 50 ml 0.1 0.03 0.018187 0.062961
V 4_25 50 ml 0.1 0.03 0.018187 0.062961
V 5_25 50 ml 0.1 0.03 0.018187 0.062961
Concentrations of the calibration standards
Vi_work_sol
Ci_cal_std = C work_sol ×
Vi_25
2 2 2
æ u(Vi_work_sol) ö æ u(Vi_25) ö æ u(Cwork_sol) ö
u(Ci _ cal_std ) = Ci _ cal_std ç ÷ +ç ÷ +ç ÷
ç V ÷ ç V ÷ ç C ÷
è i_work_sol ø è i_25 ø è work_sol ø
u rel(V i_work_sol)u rel(V i_25) u rel(C work_sol)
C 1_cal_std 20 mg/l 0.007033 0.001259 0.005976 0.1863
C 2_cal_std 50 mg/l 0.005304 0.001259 0.005976 0.404463
C 3_cal_std 100 mg/l 0.006121 0.001259 0.005976 0.864694
C 4_cal_std 150 mg/l 0.006121 0.001259 0.005976 1.29704
C 5_cal_std 200 mg/l 0.005906 0.001259 0.005976 1.699249
