Notas de Aplicaciones
21jun/11

DETERMINACION DE PROTEINAS POR EL METODO DE KJELDAHL / KJELDAHL METHOD FOR PROTEIN DETERMINATION

Francisco Santiago. Engineering Department.

INTRODUCTION

The total protein content in food is made up of a complex mixture of proteins. These exist in a combination with carbohydrates or lipids, which may be physical or chemical. Currently, all methods for determining the total protein content of foods are of empirical nature. An absolute method is isolation and direct weighing of the protein but this method is only used occasionally in biochemical research, as it is difficult and not very practical.

In 1883, the Danish researcher Johann Kjeldahl developed the method currently most used for protein analysis (Kjeldahl method) by organic nitrogen determination. In this technique, proteins and other organic components of food are digested in a mixture with sulfuric acid in the presence of catalysts. The total organic nitrogen is converted by the digestion in ammonium sulfate. The digested mixture is neutralized with a base and distilled later. The distillate is collected in a boric acid solution. Borate anions thus formed are titrated with standarized HCl (or H2SO4) to determine the nitrogen content in the sample.

The analysis result is a good approximation of crude protein content of the food as nitrogen also comes from non-protein components.

Kjeldahl method has undergone several modifications. Originally, potassium permanganate was used to carry out the oxidation process (digestion); however, the results were not satisfactory, so that reagent was discarded. In 1885, Wilforth found that digestion could be speed up by using sulfuric acid and adding a catalyst.  Gunning in 1889 proposed the addition of potassium sulfate, which raises the boiling point of sulfuric acid used in the digestion, in order to reduce the reaction time.

Nowadays, copper sulfate pent hydrated CuSO4.5H2O is mainly used as a catalyst.

REACTIONS CARRIED OUT IN THE KJELDAHL METHOD

DIGESTION

catalysts→
(1) n - C -NH2 + mH2SO4 CO2 + (NH4)2 SO4 + SO2
Protein                                  heat→

NEUTRALIZATION AND DISTILLATION

(2)  (NH2)SO4 + 2 NaOH                        →                     2NH3 + Na2SO4+ 2H2O
(3)  NH3 + H3BO3 (boric acid)                  →                 NH4 + H2BO3- (borate ion)

TITRATION

Borate anion (proportional to the amount of nitrogen) is titrated with standarized HCl (or H2SO4):

(4)    H2BO3- + H+               → H3BO3

MATERIAL
J.P. SELECTA provides the necessary equipment for carrying out the process by the Kjeldahl method.

- 1 electronic burette “Digitrate-Pro 50” of resolution 0.01ml.
Part No 0182026.

-1 precision analytical balance “FA-2204B” of resolution 0,1mg. 
Part No.
5830039.

- 1 Digestion unit (Bloc Digest) for 6, 12 and 20 positions. 
Part No.
4000629, 4000630 and 4000631.

- 1 Scrubber unit. 
Part No. 4001611

 - 1 Water circulation pump.
Part No.
4001612

- 1 Kjeldahl distiller (Pro Nitro M, S or A). 
Part No.
4002627, 4002851 and 4002430.

- Laboratory miscellaneous material.

REAGENTS

Reagents prepared:

It is recommended to use reagents already prepared, specially the titration HCl (or H2SO4). Any error in its preparation may directly affect the determination result.

Use the following reagents, or other equivalent trademarks:

•      Boric acid (powder) 99.5%   PANREAC 141015
•      Mixed indicator 4.8 (or 5) RV   PANREAC 283303

(Methyl Red + Bromocresol Green)

•      Mixed indicator 4.4 RV   PANREAC 282430

(Methyl Red + Methylene Blue)

•      HCl 0.1N SV   PANREAC 171023
•      HCl 0.25N SV   PANREAC 182318
•      H2SO4 0.1N SV    PANREAC 181061
•      H2SO4 0.2N SV    PANREAC 182011
•      Sodium hydroxide 40% RE   PANREAC 171220

(For N determination)

•      Acetanilide 99% (Standard for validation)   PANREAC 151005
•      Ammonium sulfate (Standard for validation)   PANREAC 131140
•      Kjeldahl catalyst 6.25% Cu tabl. 8g   PANREAC 174428

Preparation of ammonia fixative solution.

1.- With mixed indicator 4.8 (or 5):

Prepare the solution of the following formula for 1 litre of fixative solution:

•      Weight 10g of boric acid (powder).   PANREAC 141015
•      Dissolve in 1 litre of distilled water.
•      Add 15ml of mixed indicator 5.    PANREAC 283303

2.- With mixed indicator 4.4:

Prepare the solution of the following formula for 1 litre of fixative solution:

•      Weight 10g of boric acid (powder).   PANREAC 141015
•      Dissolve in 1 litre of distilled water.
•      Add 10ml of mixed indicator 4.4.   PANREAC 282430

PROCEDURE

SAMPLE PREPARATION

•   Triturate, homogenize and mix the sample.
•   Weight between 1 and 2g of sample.
•   In samples with very small nitrogen content, take sample enough to contain at least 5mg of     nitrogen.

DIGESTION

•   Add between 10 and 15ml (macro tube) of H2SO4 96-98% and 1 tablet (8 gm) of catalyst
(For micro tube, the H2SO4 maximum is 5ml).
•   Build a system for fumes extraction or a scrubber with Na2CO3.
•   Perform the digestion in three steps:

1. Depending on the sample water content, begin digestion by evaporating water at 150ºC     during 15-30 minutes.
2. Make a second step between 270 and 300ºC during 15 or 30 minutes to reduce production     of white fumes.
3. Continue the digestion at 400ºC between 60 and 90 minutes.

Some examples:

Cheese or meat:
Step 1: 150ºC / 30’              Step 2: 270ºC / 30’              Step 3: 400ºC / 90’

Cereals:
Step 1: 150ºC / 15’              Step 2: 300ºC / 15’              Step 3: 400ºC / 60’

Visual control: The result is a clear transparent liquid with light blue, green or yellow colour, depending on the catalyst used. There should be no black residues attached to the tube wall.

Note: During digestion, the samples foam production must be controlled. If this is excessive, step 1 should be extended.

DILUTION

•   Take the sample tubes out of the digestor block and let them cool at ambient temperature     (this could be forced by carefully immersing the tubes in a little water).
•   Add about 25ml of distilled water on each tube.
•   Add the water slowly and shaking the tube in order not to solidify the sample. If necessary,     heat slightly the tube (for example, by inserting it in the digestor block still hot).
•   Cool again until it arrives at ambient temperature.
•   To prevent nitrogen losses and violent reactions, do not insert the tube still hot in the distiller.

DISTILLATION

•   Place a 250ml Erlenmeyer flask at the coolant outlet with 50ml of boric acid and some drops     of indicator.
•   Program a dosage of NaOH from 50 to 75ml.
•   Insert the sample tube in the distiller.
•   Distillate it to collect 250ml in the Erlenmeyer flask (50ml boric + 200ml distilled).

Visual control: Once added the NaOH, the sample must have a bluish colour. If not, please add more NaOH.

TITRATION AND CALCULATION

•   Titrate the distillate with HCl or H2SO4, until the colour changes (endpoint: pH 4.65)
HCl moles = NH3 moles = N moles in the sample
H2SO4 moles = 2 NH3 moles = 2 N moles in the sample
•   Do the calculation:

mg N = N x  V   x  14

Where:

N = Titration acid normality.
V = Consumed acid volume.
14 = Nitrogen atomic weight.

•   To change to protein content, correct it by the appropriate factor according to the sample     nature (6.25 by default).
•   Periodically perform a blank test and subtract it from the result.

% proteins =  P2/P0 x 100 x F

Where:

P2: Nitrogen (mg).
P0: Sample weight (mg).
F: Protein factor.
(6.25 by default)

Protein factor in some foods:

Almonds 5,18
Nuts 5,30
Nuts - peanuts 5,41
Jelly 5,55
Soya 5,71
Barley, trenches, rye 5.83
Wheat, whole flour 5,83
Flours (not whole ones) 5,70
Rice 5,95
Corn 6,25
The rest of foods 6,25
Saved 6,31
Milk and milky products 6,38

VERIFICATION OF RECOVERY WITH AMMONIUM SULFATE

This verification is widely used to certify the distiller operation.

You have to prepare a sample whose nitrogen content is known. Then distil, titrate with HCl 0.25N and calculate the detected nitrogen.

The nitrogen percentage detected on the sample is called nitrogen recovery.

Prepare the sample:

Nitrogen content of an ammonium sulfate sample:

Formula: (NH4)2 SO4
Molecular weight: 132.14
Factor: 14 * 2 / 132.14 = 0.212
mg of nitrogen = 0.212 * mg of ammonium sulfate.

•   Weight about 100mg of ammonium sulfate. The exact weight will be P0.
•   Nitrogen exact weight is:

P1 (mg) = P0 x 0,212

•   Distil by adding 25ml of NaOH.
•   Once distilled and titrated, we get the detected nitrogen (mg): P2

P2 = N x V x 14

Where:

N = Titration acid normality (HCl 0.25).
V = Consumed acid volume.
14 = Nitrogen atomic weight.

•   Calculate the recovery:

R (%) = P2 / P1 *100

•   An acceptable recovery is between 99.5 and 100.5 %.

If we use HCl of different normality, prepare samples:

Normality Ammonium sulfate samples

0,05                               20... 40mg

0,1                                  40... 90mg

0,25                               100… 200mg

0,5                                 200… 400mg

VERIFICATION OF RECOVERY WITH ACETANILIDE

This verification is widely used to certify the complete process operation of the Kjeldahl nitrogen analysis, which includes digestion, distillation and titration stages.

You have to prepare a sample whose nitrogen content is known. Then digest, distil, titrate and calculate the detected nitrogen.
The nitrogen percentage detected on the sample is called nitrogen recovery.
Acetanilide is used to do this verification.

Prepare the sample:

Nitrogen content of an acetanilide sample:

Formula: C8H9NO
Molecular weight: 135.17
Factor: 14 / 135.17 = 0.1035
mg of nitrogen = 0.1035 * mg of acetanilide.

•   Weight about 250mg of acetanilide. The exact weight will be P0.
•   Nitrogen exact weight is:

P1 (mg) = P0 x 0,1035

Sample digestion:

•   Place the acetanilide in the tube, add 10ml of 98% sulfuric acid and a Kjeldahl catalyst tablet.
•   Digest at 400ºC for 1h (The result must be a transparent liquid with blue colour).
•   Cool and add 25ml of distilled water on each tube. Take care to avoid spillage. Water reaction     over sulfuric acid is violent.

Distillate:

•   Distil by adding 75ml of NaOH. Use HCI 0.25N for titration.
•   Once distilled and titrated, we get the detected nitrogen (mg): P2

Where:

N = Titration acid normality (HCl 0.25).
V = Consumed acid volume.
14 = Nitrogen atomic weight.
P2 = N x V x 14

•   Calculate the recovery:

R (%) = P2 / P1 *100

•   An acceptable recovery is between 99.5 and 100.5 %.

ERROR FONTS

The main error fonts are:

During the digestion process:

1.- The inclusion of non-protein nitrogen (although the amount of this nitrogen is usually negligible compared with the protein nitrogen one).
2.- Nitrogen loss during digestion:
An excess of sodium or potassium sulfate added to the acid to raise the boiling point may produce decomposition by the heat and therefore a loss of nitrogen.
On the other hand, the catalyst excess (generally copper) may also produce nitrogen loss.
3.- Sample incomplete digestion:
It is usually due to a lack of reaction time or sulfuric acid.

During distillation:

1.- Incomplete neutralization of digested mixture. It is necessary to add enough NaOH to neutralize the sulfuric acid excess resulting from the digestion as well as to transform the entire ammonium formed in the ammonia digestion.
2.- Ammonia loss due to leaks in the distillation circuit.
3.- Ammonia loss due to insufficient cooling in the condenser.

BIBLIOGRAPHY

A.O.A.C. 1980. Association of Official Agricultural Chemists.  Official Methods of Analysis. Washington, D.C.
Nielsen, S.S. 1994. Introduction to the Chemical Analysis of Foods. Ed. Jones and Bartlett Publishers. U.S.A. pp 209-212.
Ranganna, S. 1977. Manual of Analysis of Fruit and Vegetable Products.  Ed. McGraw-Hill Publishing Co. Ltd. New Delhi.
Yeshajahu P. & Meloan C.E. 1987. Food Analysis. Theory and Practice. 2on Ed. AVI U.S.A. pp 753-758.

9dic/10

VALIDACION DEL PROCEDIMIENTO DE ANALISIS DE N-KJELDAHL EN AGUAS RESIDUALES / N-KJELDAHL ANALYSIS PROCEDURE VALIDATION IN WASTEWATER

M. Monras, Degree in Chemistry (Institut Quimic de Sarrià);
Lourdes Margarit, Chemical Engineer (IQS), Analytical Chemistry Department;
Mª José Blanco, Quality Management (IQS);
David Pecanins, Quality Department Engineer (J.P. SELECTA, s.a.)

0. SUMARIO

In this research, the N-Kjeldahl analysis procedure has been validated in wastewater, in a concentration range between 20 and 1000 mg N/L, including the uncertainty calculation associated with the analysis.

All the analyses have been carried out with a JP Selecta “Bloc-digest” digestion unit and with a JP Selecta PRONITRO “A” automatic distillation unit.

1. INTRODUCTION

In the food and environmental field, there’s a great interest in the determination of nitrogen content of a sample. In 1883, the Danish chemist Johan Kjeldahl (1849-1900) first introduced to the “Danish Chemical Society” a method for determination known as “Kjeldahl nitrogen”, which provides the organic nitrogen content plus ammoniacal nitrogen of a sample. (1)

From this date, the Kjeldahl method has been the subject of an ongoing study in the analytical chemistry field and has been optimized in the three stages in which it is based: (2)

1. Sample digestion in acid medium: most of the organic and ammoniacal nitrogen to ammonium ion conversion takes place in this stage. The digestion process efficiency has been improved over the years with the addition of inorganic salts, to increase the sulphuric acid boiling point, the use of digestion blocks (introduced in 1970 by the Swedish chemist Roger Moosberg), the digestion time and temperature optimization and the use of different substances as catalysts.

2. Basification and distillation of the sample: ammonia is released in this stage, which is held in a solution with a known acid amount or with a boric acid solution. Initially, a simple distillation with a stem bath was performed, but now it has been replaced by a steam water distillation, which allows a significant reduction of the analysis time.

3. Acid-base evaluation: this could be a backward evaluation, if the ammonia released has been collected on an acid solution, or a direct evaluation, if the ammonia released has been collected on a boric acid solution. Initially, the evaluation end point was detected by means of an indicator colour change; later on, the automatic values were introduced with the detection of the evaluation end point by potentiometry.

Today, instrumentation in chemical analysis laboratories tends to automation. Thus, there are some equipments in the market that cover several stages of the Kjeldahl method, making it faster and easier of use, such as JP Selecta PRONITRO “A” automatic distiller.

Kjeldahl method is a reference method for ammoniacal and organic nitrogen determination and it is accepted by major international organizations such as International AOAC, EPA, AACC, AOCS, ISO or USDA. Nowadays, any laboratory working in a quality environment must demonstrate reliability of the data generated. Thus, it is necessary that each laboratory validates the analytical methods used.

2. MATERIALS

Reagents and Standards:

  • Ammonium sulphate standard.
  • Acetanilide standard.
  • Catalyst mineralization (it is prepared by intimately mixing 0.1g copper sulphate per gram of potassium sulphate).
  • Concentrated sulphuric acid.
  • Sodium hydroxide solution 40 % (p/v).
  • Hydrochloric acid (standard solutions 0.100 N and 0.500 N).
  • “Ammonium fixing solution” commercially prepared (composition: 1g of boric acid, 0.75mg of methyl red, 1mg of bromocresol green, 1.5mL of methanol, up to 100 mL with water).
  • Deionised water milli-Q quality.

Samples:

- Industrial wastewaters.
- Sewage from a comparison between laboratories.

3. EQUIPMENT

JP Selecta “Bloc Digest” digestion unit.

Unidad de digestión "Bloc-Digest"

- JP Selecta PRONITRO “A” automatic distiller.

JP Selecta PRONITRO “A” automatic distiller is an equipment which performs nitrogen analysis by Kjeldahl method. This equipment measures out the amount of reagent required for the analysis, makes a steam distillation of the sample from the digestion stage and an on-line evaluation of distillate, automatically detecting the end point by colour change.

The equipment allows a tritant reagent dosage up to 30mL and a concentration selection between 0.01 and 0.50N in increments of 0.01N. Thus, by appropriately selecting the tritant acid concentration, one can determine nitrogen in sample range between 0.5 and 200mg. (3)

4. EXPERIMENTAL METHOD

All the analyses in this work have been carried out by using the following methods: (4)

  • Insert in a sample tube, the volume of wastewater for the analysis, 1g of mineralization catalyst and 6mL of concentrated sulphuric acid.
  • Place the sample tube in the digestor block at a temperature slightly above 100ºC during enough time for the water to evaporate.
  • Increase the digestor block temperature to approximately 420ºC and maintain it enough time to produce the sample total digestion. When the sample becomes a transparent clear green-blue colour, we consider the digestion has finished.
  • Samples are cooled down at room temperature and about 25mL of milli-Q water is added.
  • Analyze the sample tube content from the digestion with the JP Selecta PRONITRO “A” automatic distiller, selecting the tritant reagent concentration according to the estimated nitrogen amount in the sample.

5. VALIDATION PROTOCOL (5) (6)

The above described method validation covers the range from 20 to 1000mg N/L. In order to do this, we work in three concentration levels: low (around 20mg N/L), medium (around 500mg N/L) and high level (around 1000mg N/L).

The low concentration level (ad1 sample) is daily prepared from acetanilide standard and milli-Q water. Whereas in the medium (ad2 sample) and high levels (ad3 sample) the concentrations are prepared by adding acetanilide standard to the industrial wastewater sample.

5.1. LINEARITY

The Linearity study is performed with standard solutions of ammonium sulphate.

The obtained results are presented in tables 1 and 2.

Nominal value
Experimental values
N/ mg (1)
HCl/ mL(2)
N / mg(3)
Recov./%
CV/%
white 0.26 --------- --------- ---------
0.50 2.05 0.50 99.9 1.80
1.00 3.74 0.97 97.5 1.58
2.00 7.27 1.96 98.1 1.05
4.00 14.78 4.07 101.7 1.63
5.00 18.32 5.06 101.2 0.56
6.00 21.83 6.04 100.7 0.57
8.00 29.32 8.14 101.7 0.65

Table 1. Results obtained by using HCl 0.02 N as tritant reagent.

Nominal value
Experimental values
N/ mg (1)
HCl/ mL(2)
N / mg(3)
Recov./%
CV/%
White 0.04 --------- --------- ---------
20 2.81 19.4 97.0 1.65
40 5.67 39.4 98.5 1.61
50 7.21 50.2 100.5 0.08
70 9.78 68.2 97.5 1.75
100 14.50 101.3 101.3 0.21
125 18.19 127.1 101.7 0.19
150 21.88 152.9 102.0 0.19
175 25.43 177.8 101.6 0.19
200 29.10 203.5 101.8 0.14

Table 2. Results obtained by using HCl 0.50 N as tritant reagent.

The average values of three consecutive determinations made under the same conditions are shown in each table row.

(1) Amount of nitrogen inserted by means of ammonium sulphate standard solutions.
(2) Amount of tritant reagent used.
(3) Amount of nitrogen derived from experiments in the analysis. This is calculated using the following formula: mg N = (mL HCl used – mL HCl white)*14.007*NHCl

5.2. INTERMEDIATE PRECISION AND RECOVERY

The intermediate precision and recovery study is performed by analysing, on three different days, the following samples sequence: two whites (one analyzed with HCl 0.02N, while the other with HCl 0.10N), a wastewater sample (since knowing its concentration will allow a later on calculation of recovery in every concentration level), a low concentration level sample (ad1 sample), a medium concentration level sample (ad2 sample) and a high concentration level sample (ad3 sample), getting the following results:

(Press the image to ampliate)

Table 3. Results obtained in three different days.

Below you can find the recovery data analysis obtained according to the concentration level, the analysis day and globally.

Low level
(ad1 sample)
Medium level (ad2 sample)
High level
(ad3 sample)
Average
Value
Average/%
97.5 99.0 98.3 98.2
S/%
3.6 1.2 0.8 2.0
CV/%
3.7 1.3 0.8 2.1

Table 4. Statistical parameters according to the concentration level studied.

5.3. QUANTIFICATION LIMIT

To study the quantification limit, we work with ammonium sulphate standards, tritant reagent HCl 0.02 N and three replicates are made. Results obtained are shown in the following table:

Nominal value
Experimental values
N/ mg
HCl/ mL
N / mg
Recov./%
CV/%
white 0.26 --------- --------- ---------
0.1 0.59 0.09 90.6 11.71
0.2 0.91 0.18 90.6 4.09
0.5 2.05 0.50 99.9 1.80

Table 5. Results obtained for the equipment quantification limit determination.

From these data we conclude that the equipment quantifies with a satisfactory accuracy and precision from 0.5mg of Nitrogen. Bearing in mind that the usual sample volume is 50mL, the equipment quantification limit is set to 10mg N/L.

When working with samples, the lowest concentration level studied (ad1 sample) has been of 20mg/L, so when using a sample volume of 50 mL, this means that the equipment quantifies around 1 mg N.

5.4. UNCERTAINTY

From the validation results obtained, uncertainty (u) is calculated associated to analysis, to each concentration level, by using the following formula: (4)

(Press the image to ampliate)

Expanded uncertainty (u) is calculated associated to analysis, as U=k*u, with a coverage factor of k=1.96 for a significance level of 95%.

So, the result of an analysis can be expressed as x ± U*x / 100.

The following table shows the uncertainty calculation values for each concentration level studied:

Concentration level
u standard /%
u accuracy/%
u precision /%
u/%
U (k=1.96)/%
Low level
0.29 2.48 3.67 4.44 8.7
Medium level
0.29 1.02 1.26 1.65 3.2
High level
0.29 1.74 0.80 1.93 3.8

Table 6.

6. ANALYSIS OF A WASTEWATER

A wastewater sample has been tested from a comparison between laboratories. A couple of blanks and four repetitions of the sample have been tested on the same day and under the same operating conditions, according to the procedure described in paragraph 3, using a sample volume of 50mL and as a tritant reagent HCl 0.05 N, with the results shown below:

Sample
Tritant reagent volume/ mL
Concentration/ mgN.L-1
Blank
0.10 --------
Blank
0.08 --------
Replication nº1
1.99 26.61
Replication nº2
1.83 24.37
Replication nº3
1.98 26.47
Replication nº4
1.85 24.65

Table 7. Water analysis results from a comparison between laboratories.

Then, the results obtained are compared to the results provided in the comparative between laboratories.

Results obtained
Result between laboratories (*)
Recov/%
Average/ mgL-1
25.5 27.0 94.4
S/ mgL-1
1.18 3.27
CV/ %
4.62 12.1

Table 8.

(*) Circuit Calitax. Agencia Catalana de l’aigua. October 2002

According to the uncertainty calculation made in the previous section (low concentration level), the result obtained in this analysis can be expressed as 25.5 ± 2.2 mg N.L-1.

7. CONCLUSIONS

1. The equipment provides satisfactory results working with standards in the range between 0.5 and 200 mg of Nitrogen, with recovery values between 97 and 103 %.
2. The accuracy of the analysis method applied to wastewaters is considered satisfactory, as recoveries between 95 and 102% are obtained.
3. The method intermediate precision is also considered satisfactory, since we obtain variation coefficient values of recoveries lower than 5% in all cases. It should also be noted that in medium and high concentration levels, these variation coefficient values are lower than 2%.
4. A result of 25.5 ± 2.2 mg N.L-1 has been obtained in the water analysis from the comparison between laboratories. This range includes the value 27.0 mg N.L-1 considered true.
5. The JP Selecta Automatic Distiller PRONITRO “A” is an easy to use and maintenance equipment, and saves time in Nitrogen determinations by Kjeldahl method.

8. BIBLIOGRAPHY

(1) Thiex, N.J., Manson, H., Anderson, S., Persson, Determinacion of crude protein in Animal Feed, Forage, Grain, and Oilseeds by Using Block Digestion with a Copper Catalyst and Steam Distillation into Boric Acid: Collaborative Study, Journal of AOAC International, 85, 2, 309-317 (2002)
(2)
Ogg, Clyde L., Treatise on analytical chemistry: edited by I.M.Kolthoff and Philip J.Elving with the assistance of B.Sandell, Vol x. Part 2. Kjeldahl Method, ………John Wiley and Sons, New York
(3)
JP Selecta, JP Selecta Automatic Distiller PRONITRO “A” Instructions Manual (2006)
(4)
IQS internal procedure.
(5)
Several authors, 2001, Validación de métodos analíticos, AEFI, Barcelona.
(6)
Miller, J.N., Miller, J.C., 2002, Estadística y quimiometría para química analítica, 4th edition, Ed. Prentice Hall, Madrid.