Activities

Process for obtaining Sources of uncertainty

02/02/2022
Uncertainty calculation in chemical analysis
Sampling
Sample preparation
Instrumental analysis
Calibration
Data treatment
result

• Non-represented (not applicable for only the sample)

• Homogenization.
• Extraction.
• Purification.
• Concentration.

• Volatilities.
• Incomplete extraction.
• Losses during purifications.
• Adsorption.

• Instrumental sources ( noise , drift …etc.)
• Incomplete selectivity.

• Instrument sources.
• Purity, concentration of calibration (standards).

• Data treatment ( integration of peaks)

• Weighing uncertainty.
• Volumetric uncertainty.

± Uncertainty (unite)
Most common Sources of uncertainty
Type

• Sample preparation

(mass)

Source
B
1
B
2
B
3
B
4
A
5

• CRM stock solution

• IS stock solution

• Calibration curve

• Repeatability

Uncertainty
U

• The combined standard uncertainty, uc

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Uncertainty calculation in chemical analysis
Type
B
6

• Recovery

Source
B
7
B
8
B
9

• Sample preparation

(volume)

• Bias

• Drift

Uncertainty map

Measurand?
Sources?
Quantify
calculate
Identifying

• Specify the measurand.
• Identify Uncertainty sources.

components

• Quantify Uncertainty components.

Combined

• Calculate combined uncertainty

02/02/2022
Uncertainty calculation in chemical analysis

Example EToH in aqoues

02/02/2022
Uncertainty calculation in chemical analysis
Our sources of uncertainty

• Sample preparation (mass)

• CRM stock solution

• IS stock solution

• Calibration curve

• Repeatability

Uncertainty Calculations

02/02/2022
Uncertainty calculation in chemical analysis
1- Sample preparation
- Example EToH in aqoues
Step 2-
Step 4-
Step 1- =
this uncertainty is taken from the calibration certificate of balance with K=2
Step 3-
02/02/2022
Uncertainty calculation in chemical analysis
- Calculation of sample preparation

	1
sample(mg)	944.96
IS(mg)	26.86
Total(mg)	971.82
IS (µg/g)	1375.42

	m (g)
Sample	0.94496	0.002120851
IS	0.02686	2.38E-08

	m (g)
Sample	0.94496	0.002120851
IS	0.02686	2.38E-08

Step 2-
we got the U(exp) = 2.38E10-6 from the calibration certificate of balance
Step 4-
Step 5-
Step 3-
02/02/2022
Uncertainty calculation in chemical analysis
2- Preparation Stock solution
Step 3-
Step 2-
this uncertainty is taken from calibration certificate of balance with K=2
Step 6-
Step 4-
Step 5-
* To make it without units
Step 7-
* To convert the unit to [mg/Kg]
Step 1- =
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Uncertainty calculation in chemical analysis

Purity:	95.6
Ethanol (mg)	507.78
Water (mg)	99609.52
Total(mg)	100117.3
Const. (µg/g)	4848.69

	m (g)
EToH CRM	0.50778	0.001554681
Water	99.60952	0.000118535

	m (g)
EToH CRM	0.50778	0.001554681
Water	99.60952	0.000118535

we got the U(exp) = 2.38E10-6 from the calibration certificate of balance
we got the U(P) = 0.00994 from the certificate of CRM
Step 3-
Step 2-
Step 4-
Step 5-
Step 6-
Step 7-
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Uncertainty calculation in chemical analysis
2- Preparation Internal standard (IS)
Step 3-
Step 2-
Step 1- =
this uncertainty is taken from the calibration certificate of balance with K=2
Step 6-
Step 4-
Step 5-
* To make it without units
Step 7-
* To convert the unit to [mg/Kg]
02/02/2022
Uncertainty calculation in chemical analysis

	m (g)
IS	0.99528	0.002176587
Water	19.20359	2.28523E-05

	m (g)
IS	0.99528	0.002176587
Water	19.20359	2.28523E-05

we got the U(exp) = 2.38E10-6 from the calibration certificate of balance
we got the U(P) = 0.00301 from the certificate of IS
Step 3-
Step 2-
Step 4-
Step 5-
Step 6-
Step 7-

Purity:	99.7
IS(mg)	995.28
Water (mg)	19203.59
Total(mg)	20199
Const. (µg/g)	49126.22

3- Calibration Curve

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Uncertainty calculation in chemical analysis

	Concentration		Ratio	Area		Ratio
	CN	CIS	CN/CIS	AN	AIS	AN/AIS
C1	99.72	953.33	0.104602	0.113	2.3602	0.047877
C1	99.72	953.33	0.104602	0.1238	2.5281	0.04897
C1	99.72	953.33	0.104602	0.1081	2.2544	0.047951
C2	286.07	943.46	0.303214	0.3061	2.1295	0.143743
C2	286.07	943.46	0.303214	0.3169	2.2178	0.142889
C2	286.07	943.46	0.303214	0.3152	2.2167	0.142193
C3	439.5	678.14	0.648096	0.5043	1.6366	0.308139
C3	439.5	678.14	0.648096	0.5047	1.6159	0.312334
C3	439.5	678.14	0.648096	0.4667	1.5371	0.303624
C4	867.35	934.94	0.927707	0.9607	2.1666	0.443414
C4	867.35	934.94	0.927707	0.9621	2.1504	0.447405
C4	867.35	934.94	0.927707	0.9452	2.1225	0.445324
C5	1153.31	903.63	1.276308	1.6809	2.7338	0.614858
C5	1153.31	903.63	1.276308	1.2731	2.0536	0.619936
C5	1153.31	903.63	1.276308	1.2795	2.0761	0.6163
C6	1403.67	856.79	1.638289	2.0505	2.678	0.765683
C6	1403.67	856.79	1.638289	1.7394	2.1706	0.801345
C6	1403.67	856.79	1.638289	1.7654	2.2178	0.796014
S1	1054.132	1327.42	0.794121	1.1335	2.9765	0.380816
S2	1066.74	1186.514	0.899054	1.1053	2.5611	0.431572
S3	1053.685	1199.96	0.8781	1.1536	2.7373	0.421437

R²: Preferably closer to 1

• So we will use the linear equation to find concentration of Unknown sample

y = ax+b if Y = Aratio and x = Cratio
Aratio = aCratio +b
Aratio = a Cs/CIS +b
Cs = (Aratio – 0.0033)/0.4837
= ( 0.380816 – 0.0033) x 1375.42(mg/Kg) /0.4837
Cs = 1054.132 (mg/Kg)
C0 = Concentration average of unknown sample
C0 = 0.857091

Uncertainty Calculations of calibration curve

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Uncertainty calculation in chemical analysis
S : Residual standard error
B1: slope
P : number of sample
n : number of calibration points
C0: average Concentration ratio of unknown sample
Caverage: average Concentration ratio of calibration points
A j : Calculated Area
B0: intercept
B1: slope
C j: Concentration ratio of calibration points
C j: Concentration ratio of calibration points
Caverage: average Concentration ratio of calibration points

S	0.00308373
B1	0.4937
n	18
p	3
C0	0.829469806
Caver	0.81637
(C0-Caver)2	0.000171624
Sxx	4.898100528

4- Repeatability

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Uncertainty calculation in chemical analysis
n : number of samples
SD: standard division

S1	1054.132
S2	1066.74
S3	1053.685

SD is found = 6.0435
n is number of samples = 3
Average concentration of unknown samples c0 = 1058.186 mg/Kg

COMBINED STANDARD MEASUREMENT UNCERTAINTY

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Uncertainty calculation in chemical analysis

Uncertainty Budget of EToH
Parameters	Unit	Value (X)	u(x)	u(x)/X
Mass of sample intake	g	0.945	0.002121	0.002244
stock solution	mg/kg	4848.689	48.228035	0.009947
IS	mg/kg	49126.221	148.057081	0.003014
Calibration		0.829	0.003895	0.004696
Repeatability	mg/kg	1058.185	4.278957	0.004044
Relative Standard Measurement Uncertainty				0.012
Result (mg/kg)		1058.1851
Combined Standard Measurement Uncertainty			13.0230
Expanded Uncertainty (mg/kg) (k=2)			26.0460
Relative Mesurement Uncertainty (%)			2.4614

02/02/2022
Uncertainty calculation in chemical analysis
Uncertainty calculation in chemical analysis
02/02/2022
Prepared by
Sowailem A. AlSowailem
[e-mail]
Abdulrahman M. AlZahrani
[e-mail]
Thank you