Task for a Laboratory Measurement of Mass Fraction of TiO₂ and Fe-tot in Ilmenite and Titanium Slag

Abstract

This procedure describes titrimetric determination of mass fraction of titanium dioxide (TiO₂) and total iron content (Fe-tot) in Ilmenite and Titanium Slag.

Appendices

Excercise 1: Establishing Traceability in Analytical Chemistry

1.:

Specifying the analyte and measurand

Analyte	TiO2 Fe-tot
Measurand	Mass fraction of TiO2 in Ilmenite Mass fraction of TiO2 in Titanium Slag Mass fraction of Fe-tot in Ilmenite Mass fraction of Fe-tot in Titanium Slag
Units	%

2. :

Choosing a suitable measurement procedure with associated model equation

Measurement procedure	The method is comprised of two parts. In the first the solution of potassium dichromate is standardized by using the certified reference material (CRM Ilmenite or CRM Titanium Slag), and in the second part the mass fraction of TiO2 and Fe-tot is determined in a sample of Ilmenite or Ti-Slag by titration. Determination of the equivalence points is potentiometric using a gold indicator electrode and an Ag/AgCl reference electrode The sample of Ilmenite or Ti-Slag is dried at 110 °C to constant mass. Dried sample is fused with melted potassium pyrosulfate and the melt is dissolved in hydrochloric acid. By addition of the excess of the solution of chromium(II) chloride Ti4+ is reduced to Ti3+ and Fe3+ is reduced to Fe2+ in the inert atmosphere of carbon dioxide With potassium dichromate is titrated the firstly exceeded chromium(II) chloride (1st equivalence point), then Ti3+ (2nd equivalence point) and then Fe2+ (3rd equivalence point)
Type of calibration *	standard curve	standard addition	internal standard

1. *None of the above

Model equation

Mass fraction of TiO₂ and Fe-tot is calculated by:

Ilmenite

$$\begin{array}{*{20}l} {\boxed{W_{{TiO_{2} }} = \frac{{(V_{EX1} + V_{EQ2} ) \cdot H_{8} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{8} = \frac{{m_{CRM} \cdot W_{{TiO_{2} }}^{CRM} \cdot V_{100} }}{{(V_{EX1} + V_{EQ2} ) \cdot V_{500} \cdot 100}}}\;[{\text{g}} \,{\text{mL}^{-1}}]\left( {{\text{g}}\,{\text{TiO}}_{2}\,{\text{mL}}\,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} } \right)} \hfill \\ {\boxed{W_{{Fe{\text{-}}tot}} = \frac{{(V_{EX2} + V_{EQ3} ) \cdot H_{9} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{9} = \frac{{m_{CRM} \cdot W_{{Fe{\text{-}}tot}}^{CRM} \cdot V_{100} }}{{(V_{EX2} + V_{EQ3} ) \cdot V_{500} \cdot 100}}}\;[\text{g mL}^{ - 1}]\left( {{\text{g}}\,{\text{Fe}} \,{\text{mL}^{-1}}\,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} } \right)} \hfill \\ \end{array}$$

Ti-Slag

$$\begin{array}{*{20}l} {\boxed{W_{{TiO_{2} }} = \frac{{(V_{EX1} + V_{EQ2} ) \cdot H_{11} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{11} = \frac{{m_{CRM} \cdot W_{{TiO_{2} }}^{CRM} \cdot V_{100} }}{{(V_{EX1} + V_{EQ2} ) \cdot V_{500} \cdot 100}}}\;[\text{g mL}^{ - 1}]({\text{g}}\,{\text{TiO}}_{2} {\text{mL}^{-1}}\,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} )} \hfill \\ {\boxed{W_{{Fe{\text{-}}tot}} = \frac{{(V_{EX2} + V_{EQ3} ) \cdot H_{12} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{12} = \frac{{m_{CRM} \cdot W_{{Fe{\text{-}}tot}}^{CRM} \cdot V_{100} }}{{(V_{EX2} + V_{EQ3} ) \cdot V_{500} \cdot 100}}}\;[\text{g mL}^{ - 1}]\left( {{\text{g}}\,{\text{Fe}}\,{\text{mL}}\,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} } \right)} \hfill \\ \end{array}$$

$V_{EX1}$ :

excess volume of K₂Cr₂O₇ 1st titration [mL]

$V_{EX2}$ :

excess volume of K₂Cr₂O₇ 2nd titration [mL]

$V_{EQ2}$ :

volume of K₂Cr₂O₇ used for Ti³⁺ titration (2nd titration) [mL]

$V_{EQ3}$ :

volume of K₂Cr₂O₇ used for Fe²⁺ titration (3rd titration) [mL]

$V_{500}$ :

volume of dissolved sample or CRM (500 mL flask) [mL]

$V_{100}$ :

volume of sample aliquot or CRM aliquot (100 mL pipette) [mL]

$m$ :

mass of sample or CRM [g]

$W$ :

mass fraction [%]

$H$ :

standardization parameter [g mL⁻¹].

3. :

List the input quantities according to their influence on the uncertainty of the result of the measurement (first the most important ones). At this point, your judgement should be based on your previous experience only

1	Standardization of K2Cr2O7 with CRM Ilmenite or CRM Titanium Slag – $H$
2	Volume of K2Cr2O7 used for titration – $V_{EQ}$
3	Repeatability – $P$
4	Volume of dissolved sample – $V_{500}$
5	Volume of sample aliquot – $V_{100}$

4.:

List the reference standards needed and state the information regarding traceability of the reference value

For the analyte

1	Name/Chemical Formula/Producer:	Ilmenite SARM 59/Mintek
2	Name/Chemical Formula/Producer:	Titanium Slag SARM 58/Mintek

For the other input quantities

1	Quantity/Equipment/Calibration: e.g. mass/balance/calibrated by NMI, U = xx (k = 2), see also data yellow sheet	Analytical and precise balance – calibrated by NMI
2	Quantity/Equipment/calibration:	Automatic titrator Mettler DL70ES with gold indicator electrode and Ag/AgCl reference electrode – calibrated by producer
3	Quantity/Equipment/calibration:	Burettes Mettler – calibrated by producer
4	Quantity/Equipment/calibration:	Volumetric flask – class A quality
5	Quantity/Equipment/calibration:	Volumetric pipette – class A quality

5. :

Estimating uncertainty associated with the measurement

Are all important parameters included in the model equation?	Yes	No
Other important parameters are:	Within-lab repeatability or reproducibility

6. :

How would you prove traceability of your result?

1	Analysis of matrix CRM
2	Participation in a proficiency testing scheme

7. :

Any other comments, questions…

.

.

Exercise 2: Single Laboratory Validation of Measurement Procedures

2.1 Part I: General Issues

1. :

Specify the measurement procedure, analyte, measurand and units

The measurement procedure	Titrimetric determination of mass fraction of titanium dioxide (TiO2) and total iron content (Fe-tot) in Ilmenite and Titanium Slag
Analyte	TiO2 Fe-tot
The measurand	Mass fraction of TiO2 in Ilmenite Mass fraction of TiO2 in Titanium Slag Mass fraction of Fe-tot in Ilmenite Mass fraction of Fe-tot in Titanium Slag
Unit	%

2. :

Specify the Scope

Matrix	Ilmenite and Titanium Slag
Measuring range	Analyte	Ilmenite	Titanium Slag
	TiO2	from 30 to 60%	from 60 to 90%
	Fe-tot	from 20 to 40%	from 5 to 20%

3. :

Requirement on the measurement procedure

Intended use of the results	Quality control of Ilmenite and Titanium Slag (raw materials)
Mark the customer’s requirements and give their values	Parameters to be validated		Value requested by the customer
		LOD
		LOQ
		Repeatability
		Within-lab reproducibility
		Trueness
		Measurement uncertainty	TiO2: Urel < 1% Fe-tot: Urel < 5%
		Other-state

4. :

Origin of the Measurement Procedure

		VALIDATION
New In-House Method		Full
Modified Validated Method		Partial
Official Standard Method		Confirmation/Verification

2.2 Part II: Parameters to Be Validated

5. :

Selectivity/Interference/Recovery

Where yes, please give further information e.g. which CRM, reference method

	CRM/RM: analysis of available CRM or RM
	Further information: CRM SARM 59 – Ilmenite, CRM SARM 57 – Titanium Slag
	Spike of pure substance
	Compare with a reference method
	Selectivity, interferences
	Test with different matrices
	Other – please specify
	Participation in the inter laboratory comparison organized by the Quality Control Department of Cinkarna Celje, “Measurements of various parameters in some TiO2 based materials, March 2011”

6. :

Measuring range

	Linearity
	Upper limit
	LOD
	LOQ

7. :

Spread – Precision

	Repeatability
	Reproducibility (within Lab)
	Reproducibility (between Lab)

8. :

Robustness

Variation of parameters

9. :

Quality Control

	Control charts
	Participation in PT schemes

10. :

Other parameters to be tested

	Working range and testing of homogeneity of variances
	R square
	Residual standard deviation
	Standard deviation of the analytical procedure
	Coefficient of variation of the analytical procedure
	Measurement uncertainty

2.3 Part III: Some Calculations and Conclusions

11. :

Calculation of parameters requested by the customer

Parameters requested to be validated		Calculations
	LOD
	LOQ
	Repeatability
	Within-lab reproducibility
	Trueness
	Measurement uncertainty
	Other-please state

12. :

Does the analytical procedure fulfil the requirement(s) for the intended use?

Parameter	Value requested by the customer (the same as stated in question 3)	Value obtained during validation	The requirement is fulfilled Yes/No
LOD
LOQ
Repeatability
Within-lab reproducibility
Trueness
Measurement uncertainty	TiO2: Urel < 1% Fe-tot: Urel < 5%	Ilmenite: TiO2: Urel = 0.74% Fe-tot: Urel = 1.2% Ti-Slag: TiO2: Urel = 0.54% Fe-tot: Urel = 2.9%	Yes
Other

The analytical procedure is fit for the intended use:

Yes          No

For Measurement Uncertainty and Traceability refer to the corresponding sheets

Building An Uncertainty Budget

1. :

Specify the measurand and units

Measurand	Mass fraction of TiO2 in Ilmenite Mass fraction of TiO2 in Titanium Slag Mass fraction of Fe-tot in Ilmenite Mass fraction of Fe-tot in Titanium Slag
Unit	%

2. :

Describe the measurement procedure and provide the associated model equation

Measurement procedure:

The method is comprised of two parts. In the first the solution of potassium dichromate is standardized by using the certified reference material (CRM Ilmenite or CRM Titanium Slag), and in the second part the mass fraction of TiO₂ and Fe-tot is determined in a sample of Ilmenite or Ti-Slag by titration. Determination of the equivalence points is potentiometric using a gold indicator electrode and an Ag/AgCl reference electrode.

The sample of Ilmenite or Ti-Slag is dried at 110 °C to constant mass. Dried sample is fused with melted potassium pyrosulfate and the melt is dissolved in hydrochloric acid. By addition of the excess of the solution of chromium(II) chloride Ti⁴⁺ is reduced to Ti³⁺ and Fe³⁺ is reduced to Fe²⁺ in the inert atmosphere of carbon dioxide.

With potassium dichromate is titrated the firstly exceeded chromium(II) chloride (1st equivalence point), then Ti³⁺ (2nd equivalence point) and then Fe²⁺ (3rd equivalence point).

Model equation:

Mass fraction of TiO₂ and Fe-tot is calculated by:

Ilmenite

$$\begin{array}{*{20}l} {\boxed{W_{{TiO_{2} }} = \frac{{(V_{EX1} + V_{EQ2} ) \cdot H_{8} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{8} = \frac{{m_{CRM} \cdot W_{{TiO_{2} }}^{CRM} \cdot V_{100} }}{{(V_{EX1} + V_{EQ2} ) \cdot V_{500} \cdot 100}}}\;[{\text{g}}\,{\text{mL}}^{ - 1} ]\left( {{\text{g}}\,{\text{TiO}}_{2} \,{\text{mL}}^{ - 1} \,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} } \right)} \hfill \\ {\boxed{W_{{Fe{\text{-}}tot}} = \frac{{(V_{EX2} + V_{EQ3} ) \cdot H_{9} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{9} = \frac{{m_{CRM} \cdot W_{Fe\text{-}tot}^{CRM} \cdot V_{100} }}{{(V_{EX2} + V_{EQ3} ) \cdot V_{500} \cdot 100}}}\;[{\text{g}}\,{\text{mL}}^{ - 1} ]\left( {{\text{g}}\,{\text{Fe}}\,{\text{mL}}^{ - 1} \,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} } \right)} \hfill \\ \end{array}$$

Ti-Slag

$$\begin{array}{*{20}l} {\boxed{W_{{TiO_{2} }} = \frac{{(V_{EX1} + V_{EQ2} ) \cdot H_{11} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{11} = \frac{{m_{CRM} \cdot W_{{TiO_{2} }}^{CRM} \cdot V_{100} }}{{(V_{EX1} + V_{EQ2} ) \cdot V_{500} \cdot 100}}}\;[{\text{g}}\,{\text{mL}}^{ - 1} ]({\text{g}}\,{\text{TiO}}_{2} \,{\text{mL}}^{ - 1} \,\,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} )} \hfill \\ {\boxed{W_{{Fe{\text{-}}tot}} = \frac{{(V_{EX2} + V_{EQ3} ) \cdot H_{12} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100}\quad [{\% }]} \hfill & {\boxed{H_{12} = \frac{{m_{CRM} \cdot W_{Fe\text{-}tot}^{CRM} \cdot V_{100} }}{{(V_{EX2} + V_{EQ3} ) \cdot V_{500} \cdot 100}}}\;[{\text{g}}\,{\text{mL}}^{ - 1} ]\left( {{\text{g}}\,{\text{Fe}}\,{\text{mL}}^{ - 1} \,\,{\text{K}}_{2} {\text{Cr}}_{2} {\text{O}}_{7} } \right)} \hfill \\ \end{array}$$

$V_{EX1}$ :

excess volume of K₂Cr₂O₇ 1st titration [mL]

$V_{EX2}$ :

excess volume of K₂Cr₂O₇ 2nd titration [mL]

$V_{EQ2}$ :

volume of K₂Cr₂O₇ used for Ti³⁺ titration (2nd titration) [mL]

$V_{EQ3}$ :

volume of K₂Cr₂O₇ used for Fe²⁺ titration (3rd titration) [mL]

$V_{500}$ :

volume of dissolved sample or CRM (500 mL flask) [mL]

$V_{100}$ :

volume of sample aliquot or CRM aliquot (100 mL pipette) [mL]

$m$ :

mass of sample or CRM [g]

$W$ :

mass fraction [%]

$H$ :

standardization parameter [g/mL]

3. :

Identify (all possible) sources of uncertainty

	Repeatability
	Volume of sample aliquot
	Volume of dissolved sample
	Mass of sample
	Standardization of K2Cr2O7 with CRM
	Volume of K2Cr2O7 used for titration

4. :

Evaluate values of each input quantity

Determination of mass fraction of TiO ₂ in Ilmenite [%]

Input quantity	Value	Unit	Remark
$V_{100}$	100	mL	Volume of sample aliquot
$V_{500}$	500	mL	Volume of dissolved sample
$m_{s}$	0.5101	g	Mass of sample
$H_{8}$	0.009585	g mL−1	Standardization of K2Cr2O7 with CRM Ilmenite
$V_{EX1} + V_{EQ2}$	5.7155	mL	Volume of K2Cr2O7 used for titration

Determination of mass fraction of Fe-tot in Ilmenite [%]

Input quantity	Value	Unit	Remark
$V_{100}$	100	mL	Volume of sample aliquot
$V_{500}$	500	mL	Volume of dissolved sample
$m_{s}$	0.5101	g	Mass of sample
$H_{9}$	0.006835	g mL−1	Standardization of K2Cr2O7 with CRM Ilmenite
$V_{EX2} + V_{EQ3}$	4.5732	mL	Volume of K2Cr2O7 used for titration

Determination of mass fraction of TiO ₂ in Titanium Slag [%]

Input quantity	Value	Unit	Remark
$V_{100}$	100	mL	Volume of sample aliquot
$V_{500}$	500	mL	Volume of dissolved sample
$m_{s}$	0.5050	g	Mass of sample
$H_{11}$	0.004862	g mL−1	Standardization of K2Cr2O7 with CRM Titanium Slag
$V_{EX1} + V_{EQ2}$	16.2883	mL	Volume of K2Cr2O7 used for titration

Determination of mass fraction of Fe-tot in Titanium Slag [%]

Input quantity	Value	Unit	Remark
$V_{100}$	100	mL	Volume of sample aliquot
$V_{500}$	500	mL	Volume of dissolved sample
$m_{s}$	0.5050	g	Mass of sample
$H_{12}$	0.003480	g mL−1	Standardization of K2Cr2O7 with CRM Titanium Slag
$V_{EX2} + V_{EQ3}$	1.8276	mL	Volume of K2Cr2O7 used for titration

5. :

Evaluate the standard uncertainty of each contribution

Determination of mass fraction of TiO ₂ in Ilmenite [%]

Input quantity	Standard uncertainty	Unit	Remark
P	0.068	%	Repeatability
$V_{100}$	0.0489	mL	Volume of sample aliquot
$V_{500}$	0.2086	mL	Volume of dissolved sample
$m_{s}$	0.00015	g	Mass of sample
$H_{8}$	0.0000298	g mL−1	Standardization of K2Cr2O7 with CRM Ilmenite
$V_{EX1} + V_{EQ2}$	0.00836	mL	Volume of K2Cr2O7 used for titration

Determination of mass fraction of Fe-tot in Ilmenite [%]

Input quantity	Standard uncertainty	Unit	Remark
P	0.064	%	Repeatability
$V_{100}$	0.0489	mL	Volume of sample aliquot
$V_{500}$	0.2086	mL	Volume of dissolved sample
$m_{s}$	0.00015	g	Mass of sample
$H_{9}$	0.0000360	g mL−1	Standardization of K2Cr2O7 with CRM Ilmenite
$V_{EX2} + V_{EQ3}$	0.00836	mL	Volume of K2Cr2O7 used for titration

Determination of mass fraction of TiO ₂ in Titanium Slag [%]

Input quantity	Standard uncertainty	Unit	Remark
$P$	0.066	%	Repeatability
$V_{100}$	0.0489	mL	Volume of sample aliquot
$V_{500}$	0.2086	mL	Volume of dissolved sample
$m_{s}$	0.00015	g	Mass of sample
$H_{11}$	0.0000105	g mL−1	Standardization of K2Cr2O7 with CRM Titanium Slag
$V_{EX1} + V_{EQ2}$	0.0174	mL	Volume of K2Cr2O7 used for titration

Determination of mass fraction of Fe-tot in Titanium Slag [%]

Input quantity	Standard uncertainty	Unit	Remark
P	0.030	%	Repeatability
$V_{100}$	0.0489	mL	Volume of sample aliquot
$V_{500}$	0.2086	mL	Volume of dissolved sample
$m_{s}$	0.00015	g	Mass of sample
$H_{12}$	0.0000344	g mL−1	Standardization of K2Cr2O7 with CRM Titanium Slag
$V_{EX2} + V_{EQ3}$	0.0163	mL	Volume of K2Cr2O7 used for titration

6.:

Calculate the value of the measurand, using the model equation

Ilmenite – TiO ₂

$$W_{{TiO_{2} }} = \frac{{(V_{EX1} + V_{EQ2} ) \cdot H_{8} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100 = \frac{{(0.1483\;\text{mL} + 5.5672\;\text{mL}) \cdot 0.009585\,\text{g mL}^{ - 1} \cdot 500\;\text{mL} \cdot 100}}{{0.5101\,{\text{g}} \cdot 100\;\text{mL}}} = 53.70{\% }$$

Ilmenite – Fe-tot

$$W_{{Fe{\text{-}}tot}} = \frac{{(V_{EX2} + V_{EQ3} ) \cdot H_{9} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100 = \frac{{(0.1008\;\text{mL} + 4.4724\;\text{mL}) \cdot 0.006835\,\text{g mL}^{ - 1} \cdot 500\;\text{mL} \cdot 100}}{{0.5101\,\text{g} \cdot 100\;\text{mL}}} = 30.64{\% }$$

Titanium Slag – TiO ₂

$$W_{{TiO_{2} }} = \frac{{(V_{EX1} + V_{EQ2} ) \cdot H_{11} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100 = \frac{{(0.1407\,\text{mL} + 16.1476\,\text{mL}) \cdot 0.004862\,\text{g mL}^{ - 1} \cdot 500\,\text{mL} \cdot 100}}{{0.5050\,\text{g} \cdot 100\,\text{mL}}} = 78.41{\% }$$

Titanium Slag – Fe-tot

$$W_{{Fe{\text{-}}tot}} = \frac{{(V_{EX2} + V_{EQ3} ) \cdot H_{12} \cdot V_{500} }}{{m_{s} \cdot V_{100} }} \cdot 100 = \frac{{(0.1184\,\text{mL} + 1.7092\,\text{mL}) \cdot 0.003480\,\text{g mL}^{ - 1} \cdot 500\,\text{mL} \cdot 100}}{{0.5050\,\text{g} \cdot 100\,\text{mL}}} = 6.30{\% }$$

7.:

Calculate the combined standard uncertainty (u _c ) of the result & specify units

Using: Mathematical solution; Spreadsheet Approach; Commercial Software

Ilmenite
		TiO 2			Fe-tot
	Unit	Value	u	$u_{rel}$	Value	u	$u_{rel}$
P	%	–	0.068	0.00127	–	0.064	0.00209
$V_{100}$	mL	100	0.0489	0.00049	100	0.0489	0.00049
$V_{500}$	mL	500	0.2086	0.00042	500	0.2086	0.00042
$m_{s}$	g	0.5101	0.00015	0.00029	0.5101	0.00015	0.00029
H	g/mL	0.009585	0.0000298	0.00311	0.006835	0.0000360	0.00527
$V_{EX} + V_{EQ}$	mL	5.7155	0.00836	0.00146	4.5732	0.00836	0.00183
W	%	53.70	0.200	0.00373	30.64	0.184	0.00600

Titanium slag
		TiO 2			Fe-tot
	Unit	Value	u	$u_{rel}$	Value	u	$u_{rel}$
P	%	–	0.066	0.00084	–	0.030	0.00476
$V_{100}$	mL	100	0.0489	0.00049	100	0.0489	0.00049
$V_{500}$	mL	500	0.2086	0.00042	500	0.2086	0.00042
$m_{s}$	g	0.5050	0.00015	0.00030	0.5050	0.00015	0.00030
H	g/mL	0.004862	0.0000105	0.00216	0.003480	0.0000344	0.00989
$V_{EX} + V_{EQ}$	mL	16.2883	0.0174	0.00107	1.8276	0.0163	0.00892
W	%	78.41	0.208	0.00265	6.30	0.089	0.0142

8. :

Calculate expanded uncertainty (U _c ) & specify the coverage factor k and the units

k = 2		ILMENITE		TITANIUM SLAG
		TiO2	Fe-tot	TiO2	Fe-tot
U *	%	0.40	0.37	0.42	0.18

1. *U is expanded uncertainty calculated using a coverage factor of 2, which gives a level of confidence of approximately 95%

9. :

Analyse the uncertainty contribution & specify the main three input quantities contributing the most to U _c

1	Standardization of K2Cr2O7 with CRM Ilmenite or CRM Titanium Slag – H
2	Volume of K2Cr2O7 used for titration – $V_{EQ}$
3	Repeatability – P

10. :

Prepare your Uncertainty Budget Report

Ilmenite:

• (53.7 ± 0.40) % TiO₂ (k = 2)*

• (30.6 ± 0.37) % Fe-tot (k = 2)*

Titanium Slag:

• (78.4 ± 0.42) % TiO₂ (k = 2)*

• (6.3 ± 0.18) % Fe-tot (k = 2)*

*The reported uncertainty is expanded uncertainty calculated using a coverage factor of k = 2, which gives a level of confidence of approximately 95%.

Addendum I. Measurement Uncertainty Calculation

	ILMENITE						TITANIUM SLAG
	TiO 2			Fe-tot			TiO 2			Fe-tot
	Value	u	u rel	Value	u	u rel	Value	u	u rel	Value	u	u rel
P [%]	–	0.068	0.00127	–	0.064	0.00209	–	0.066	0.00084	–	0.030	0.00476
V 100 [mL]	100	0.0489	0.00049	100	0.0489	0.00049	100	0.0489	0.00049	100	0.0489	0.00049
V 500 [mL]	500	0.2086	0.00042	500	0.2086	0.00042	500	0.2086	0.00042	500	0.2086	0.00042
m s [g]	0.5101	0.00015	0.00029	0.5101	0.00015	0.00029	0.5050	0.00015	0.00030	0.5050	0.00015	0.00030
H [g/mL]	0.009585	0.0000298	0.00311	0.006835	0.0000360	0.00527	0.004862	0.0000105	0.00216	0.003480	0.0000344	0.00989
V EX  + V EQ [mL]	5.7155	0.00836	0.00146	4.5732	0.00836	0.00183	16.2883	0.0174	0.00107	1.8276	0.0163	0.00892
W [%]	53.70	0.20	0.00373	30.64	0.18	0.00600	78.41	0.21	0.00265	6.30	0.089	0.0142
U		0.40			0.37			0.42			0.18
			ri [%]			ri [%]			ri [%]			ri [%]
P			11.53			12.14			10.10			11.32
V (100)			1.72			0.67			3.41			0.12
V (500)			1.25			0.48			2.48			0.09
m (s)			0.62			0.24			1.26			0.04
H			69.50			77.18			66.48			48.75
V (EX) + V (EQ)			15.38			9.30			16.27			39.68
W			100.00			100.00			100.00			100.00

	H8			H9			H11			H12
	Value	u	u rel	Value	u	u rel	Value	u	u rel	Value	u	u rel
V 100 [mL]	100	0.0489	0.00049	100	0.0489	0.00049	100	0.0489	0.00049	100	0.0489	0.00049
V 500 [mL]	500	0.2086	0.00042	500	0.2086	0.00042	500	0.2086	0.00042	500	0.2086	0.00042
m CRM [g]	0.5088	0.00015	0.00029	0.5088	0.00015	0.00029	0.5054	0.00015	0.00030	0.5054	0.00015	0.00030
V EX  + V EQ [mL]	5.1810	0.00836	0.00161	5.2405	0.00836	0.00160	17.4827	0.0174	0.00100	1.9490	0.0163	0.00836
W CRM [%]	48.8	0.125	0.00256	35.2	0.175	0.00497	84.1	0.150	0.00178	6.71	0.035	0.00522
H [g/mL]	0.009585	0.0000298	0.00311	0.006835	0.0000360	0.00527	0.004862	0.0000105	0.00216	0.003480	0.0000344	0.00988
			ri [%]			ri [%]			ri [%]			ri [%]
V (100)			2.47			0.86			5.12			0.24
V (500)			1.80			0.63			3.72			0.18
m (CRM)			0.90			0.31			1.89			0.09
V (EX) + V (EQ)			26.94			9.17			21.20			71.63
W (CRM)			67.89			89.03			68.08			27.86
H			100.00			100.00			100.00			100.00