Use of the Standard Addition Method in Quantitative Chromatographic Analysis

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Use of the standard addition method in quantitative chromatographic analysis

Article in Journal of Analytical Chemistry · October 2006

DOI: 10.1134/S1061934806100042

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ISSN 1061-9348, Journal of Analytical Chemistry, 2006, Vol. 61, No. 10, pp. 967–972. © Pleiades Publishing, Inc., 2006.

Original Russian Text © I.G. Zenkevich, I.O. Klimova, 2006, published in Zhurnal Analiticheskoi Khimii, 2006, Vol. 61, No. 10, pp. 1048–1054.

Methods of quantitative analysis that are used in chromatography are conventionally subdivided into several types, depending on the character of sample preparation operations and algorithms of data processing. These are the absolute calibration method (I), the external standard method (II), the internal standard method (III), the standard addition method (IV), and the internal normalization method (V) [1–4]. Several techniques for quantitative determination that are not used in chromatography are also known, e.g., the isoto- pic dilution method (version of the standard addition method, which can be implemented only in chromatography–mass spectrometry [5]) or detailed recommendations for performing these analyses in spectropho- tometry [6].

However, there are many examples when this strict classification of methods (I–V) cannot adequately rep- resent the variety of their versions, which are used in real analytical practice. For example, the controlled internal normalization method was considered in monograph [1] as an independent method, and “reference standard” method was considered in manual [3]

along with the external (II) and internal (III) standard methods and recommended for routine industrial control. There are versions of the standard addition method (IV) involving the additional comparison of the results with auxiliary compounds either existing in the sample or introduced into it artificially [1]. Nearly all methods (except for internal normalization, V) are adapted to head-space analysis [4, 7], the technique for the gas- chromatographic determination of the composition of condensed phases from the data for vapor–gas media that occur in contact with condensed phases, which requires different experimental operations and special techniques for processing the results.

The current characterization of the possibilities and limitations of different methods for quantitative chro-

matographic analysis is substantially behind the requirements of analytical practice. In some of the existing manuals, the differences between the methods are either discussed at the level of brief enumeration [2]

or not mentioned at all [8]. Up to now, one can run across instructions that calibration coefficients (f_i) must be measured for all mixture components using the internal normalization method (V) [4]. However, in the case of multicomponent samples, this is practically impossible. For a long time, this technique of data processing was used only in the approximation f_i≡ 1, e.g., in the analysis of petroleum products or in the represen- tation of the results of analyses by chromatography–

mass spectrometry. Even more out-of-date is such a known limitation on the use of this method as the necessity of the detection of the signals of all components in chromatograms. Actually, it can be used for any of the groups of components irrespective of the presence of other compounds in the samples (an arbitrary name is

“local” internal normalization). For example, to esti- mate the ratio of isomeric octanes in petroleum frac- tions by this technique, there is no need to take other hydrocarbons into account.

All methods of quantitative chromatographic analysis were historically recommended for the analysis of homogeneous samples. Only in 1998 was it demonstrated that one of these methods, the standard addition method (IV), is applicable to the determination of the total concentration of components of heterophase systems [9]. For the additional accuracy control of the results, the double (successive) standard addition of a reference sample into the same sample was proposed in [9]. An alternative technique of the implementation of an analogous recommendation is known: the introduction of nonidentical additions into a series of identical samples with the subsequent actual extrapolation of results to the “zero” standard addition [10], which was ARTICLES

Use of the Standard Addition Method in Quantitative Chromatographic Analysis

I. G. Zenkevich and I. O. Klimova

Research Institute of Chemistry, St. Petersburg State University, Universitetskii pr. 26, St. Petersburg, 198504 Russia Received March 16, 2005; in final form, August 18, 2005

Abstract—Using the standard addition method as an example, several versions of it recommended for the determination of volatile components in complex hydrophobic matrices additionally containing compounds with sorption properties were considered. It was demonstrated that, along with the extrapolation of results to the zero standard addition, the most efficient techniques are the artificial transformation of similar samples into heterophase systems, when the analytes are distributed between both phases and the interfering components are predominantly localized in only one of the phases.

DOI: 10.1134/S1061934806100042

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JOURNAL OF ANALYTICAL CHEMISTRY Vol. 61 No. 10 2006 ZENKEVICH, KLIMOVA

also mentioned in the manual [4, p. 361]. This technique was also used in [11] in the determination of residual amounts of pesticides in vegetable materials.

The frequent use of a brief list of different versions of the standard addiction method without their detailed characterization is unsatisfactory if for no other reason than it commonly remains unclear when it is necessary to use a particular version. In particular, this is true for the determination of volatile components in complex matrices that are nonvolatile, viscous, hydrophobic, and sometimes thermally unstable compounds in a mixture with ingredients possessing pronounced sorption properties. The most important methodological technique in the analysis of these samples is their artificial transformation into heterophase systems. In this case, the suitable selection of solvents partially misci- ble with each other can provide a situation when all interfering components are predominantly localized in one of the phases, whereas the analytes are distributed between both phases. The aim of this work was to consider this version of the standard addition method.

EXPERIMENTAL

Gas-chromatographic analysis was performed on a Tsvet-500M chromatograph with a flame-ionization detector and a glass packed column 3 m × 2 mm with 15% Carbowax 20M polyethylene glycol on Chroma- ton N AW DMCS (0.16–0.20 mm) under isothermal conditions at a temperature of 120°C. The temperature of the detector thermostat was 150°C; the temperature of the injection port was 200–250°C. Nitrogen was used as the carrier gas; the flow rate was 30 mL/min.

The volume of injected samples was 0.3–1.2 µL (MSh-1 and MSh-10 microsyringes). Chromatograms were processed using MutiChrom software (version 1.52).

As a model sample of a mixture of a volatile analyte, a hydrophobic matrix, and a sorbent, we selected a mixture of 4-tert-butyltoluene (T_b = 192.8°ë, = 0.861,

= 1.492; 4.75%), lubricating oil (TU 6-15-691-77;

91%), and graphitized carbon black (S_specific about 100 m²/g, a pilot sample from the All-Russia Research Institute of Luminophors, Stavropol’, Russia, 1978;

4.3%). One milliliter of hexane (or less volatile hep- tane) was added to two weighed portions of the sample (about 1 g each), a weighed portion of the analyte (24.5 mg) was added to one of the solutions, and both samples were transformed into heterophase systems by the addition of 1 mL of acetonitrile with the subsequent separation of the acetonitrile layer.

Experimental samples of an anticongestive gel, a medicine that is at the stage of development, were pro- vided by the Interregional center “Adaptogen”

(St. Petersburg, Russia). The medicine contains about 90% oil extract of several types of vegetable medicine raw materials, 5–10% finely dispersed silica gel (Aero- sil A-380) with a specific surface area of 380 ± 40 m²/g

d₄²⁰ n_D²⁰

(as the gel-forming agent), and about 1.7% (when prepared) peppermint essential oil. Some samples additionally contained phosphatidyl choline (lecithin) and α-tocopherol acetate. The analytical problem was the quantitative determination of the concentration of multicomponent peppermint oil in this system.

Sample preparation included the dissolution of weighed portions of gel samples (m_x about 2 g) in 4 mL of hexane with the subsequent determination of the total mass of the solution (m). The resulting viscous homogeneous solutions were divided into two approximately equal parts (weighed portions m₁ and m₂) and placed in tightly sealed bottles with a volume of 7–

10 mL (of the penicillin type). The amount of the sample in each of the replicate samples was m_x₁ = m_xm₁/m and m_x₂ = m_xm₂/m, respectively. A weighed portion (about 50 mg) of peppermint oil (reference sample) was introduced into the second of these samples; next, equal amounts (1–2 mL) of acetonitrile were added to both samples, the mixtures were vigorously shaken and left for segregation for 5–10 min, samples of the upper (hexane) layers of the heterophase systems were injected into the chromatograph, and the total areas of all peaks eluted after the solvent were measured. The main components of peppermint oil are menthol (reten- tion index on the Carbowax 20M stationary phase is 1652 ± 20), menthone (1481 ± 22), pulegone (1658 ± 22), and menthyl acetate (1641 ± 15). In these determinations, it is reasonable to introduce an additional layer of glass wool (3–5 cm) into the initial portion of the chromatographic column and replace it within 20–

25 sample injections (working day), because the accu- mulation of nonvolatile components of samples in the layer can substantially decrease the efficiency of chromatographic separation.

RESULTS AND DISCUSSION

General features of the standard addition method. Speaking about the standard addition method, it is necessary first to comment on some historically prevalent stereotypes in its use, which deal with the main computational relationships. Indeed, both in monograph [1] and in the most recent tutorials [4], the following formula is presented for the calculation of the concentrations of analytes in samples (c_x) by this method:

(1) where M_samp is the mass of the sample, m_add is the mass of the addition, P_x₍₁₎ and P_x₍₂₎ are the parameters of the chromatographic peaks (areas or heights) of the analyte before and after addition, respectively, and P_i₍₁₎ and P_i₍₂₎ are the parameters of the chromatographic peaks (areas or heights) of any other component of the mixture (occurring in it or introduced artificially) before and after addition, respectively.

c_x m_add/M_samp P_{i 1}_{( )}/P_{i 2}_{( )}

( )(P_{x 2}_{( )}/P_{x 1}_{( )})–1 ---,

=

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USE OF THE STANDARD ADDITION METHOD 969 The derivation of this rather simple relationship was

presented in Novak’s monograph [1]. In subsequent manuals (see, e.g., [4]), it is commonly given without justification and, as a result, is perceived inadequately (the standard addition method is used much less frequently than the absolute calibration or external standard method). Indeed, the P_i₍₁₎ and P_i₍₂₎ parameters must be taken into account only in the particular (rare) cases when the volumes of addition solutions are com- parable with the volumes of initial sample solutions and their mixing leads to a substantial dilution of the analyzed samples. In practice, it is much more convenient to use the standard addition method for the determination of the total amount of the analyte in the sample when the reference compound (m_add) practically does not change the volume of the sample, which can even remain unknown. The main computational relationship follows from the simplest proportion

P_x/P_x + add = m_x/(m_x + madd).

Then

(2) where P_x and P_{x + add} are the parameters of the chromatographic peaks (areas or heights) of the analyte before and after addition, respectively.

Basic differences in formulas (1) and (2) manifest themselves not only in a significant simplification of calculations and the elimination of the necessity for measuring the chromatographic peak parameters of other compounds, but also in a decrease in the random component of the error in determination. For the function of several variables y = f(x1, x2, …, x_n), these errors (δy) are estimated on the basis of known differential relationships

Then, for Eq. (2) on the condition that δm δP_i, we obtain

(3) where δP_x and δP_{x + add} are the errors in the determination of peak areas (heights) of the analytes in the initial sample and in the sample with the addition, respectively.

The presence of the factor [P_{x + add}/(P_{x + add} – P_x)] in this formula means that the highest accuracy is attained on the condition that P_{x + add} P_x, whereas at small additions P_{x + add} – P_x P_x the degree of uncertainty of the results can be too high. For example, if the addition is about one-third of the analyte contained in the analyzed sample, the random component in this technique

m_x m_addPx

P_x₊_add–P_x ---,

=

δy≈ Σ(df /dx)².

δm P_x₊_add P_x₊_add–P_x

--- δP_x² δPx+add

+ 2 ,

≈

is approximately two times larger than in the external standard method.

As for Eq. (1), its differentiation leads to a cumber- some expression inconvenient for practical use and containing four rather than two contributions from different components δP_i. Hence, the random component of the error in determinations c_x (or m_x) can be at least two times larger than with the use of the simplest version based on relationship (2) and substantially exceeds random errors in quantitative determinations by other methods (I–III, V). Naturally, this version has not received practical acceptance. Moreover, uncritical rep- resentation of formula (1) produces a distorted notion of the possibilities of the standard addition method as a whole.

Of particular interest is the comparison of the possibilities of different methods for quantitative analysis in the case when some part of the analyte contained in initial samples (m_x) is lost at the step of sample preparation, i.e., their recovery from the matrix (the ratio of the actually available (extracted) amount of the analyte (mextr) to its true amount) is generally unknown (α = m_extr/m_x < 1). Under these conditions, the majority of methods for quantitative analysis fail to provide accurate results. For example, in the case of the external standard method, from the proportion

αP_x/Pst = m_x/mst, it follows that

Thus, the result is underestimated by a factor of (1/α). However, in the standard addition method on the introduction of additional amounts of the analyte into the sample and approximately equal losses at the step of sample preparation, the errors in determinations are largely cancelled:

αP_x/αP_{x + add} = m_x/(m_x + madd).

Then

(4) which, after the cancellation of α, yields relationship (2).

If we assume that the recovery of the analyte depends on its concentration in the sample (i.e., α = f(m_x)) and, consequently, the addition of a reference sample changes its value (α2 > α1), relationship (4) must be rewritten in the following form:

α1P_x/(α2P_{x + add}) = m_x/(m_x + m_add).

Then

m_x αm_stPx

P_st ---.

=

m_x αm_addPx

α(Px+add–Px) ---,

=

mx

α₁m_addP_x α2Px+add–α1Px

---

=

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970

or

(5) where α* = α₂/α₁.

These are the cases when it is reasonable to use such a modification of the method as the extrapolation of the results (m_x) to the zero value of the standard addition, when α2 α1 and α* 1. In this case, the form of the extrapolating function m_x = f(m_add) in the general case is unknown; however, at a first approximation, this dependence can be assumed to be linear. This technique was used in [11] in the determination of residual amounts of pesticides in vegetable materials, when the distribution of analytes in vegetable tissues is unknown.

Artificially introduced standard additions predominantly arrive at the surface of matrix particles; consequently, the conditions of their subsequent extraction are substantially different (α2 > α1). The technique with the introduction of several standard additions into several replicate aliquot portions of analyzed samples [4, p. 361; 10] and the previously recommended verifica- tion of the results of determinations using the second (successive) standard addition to heterophase systems [9], which are combinations of two organic solvents partially soluble in each other, have the same purpose.

Use of the standard addition method in the deter- mination of components of complex matrices (con- taining sorbents) and heterophase systems. The quantitative determination of components of heterophase systems is of particular importance for the analytical practice. The number of real samples of this type is rather small; however, there are many complex samples for which the artificial transformation into heterophase systems is the optimum operation of sample preparation.

Among these samples are, e.g., mixtures of compounds with viscous, hydrophobic, and, frequently, thermally unstable matrices; the direct injection of these samples (or their solutions) into chromatographic columns is undesirable. Such a seemingly natural technique as exhaustive extraction of analytes in each particular case requires such long-term preliminary opti- mization of conditions that, in practice, it is used very rarely. If these samples are transformed into heterophase systems at the step of sample preparation, so that interfering matrix components are predominantly concentrated in one of the layers and the analytes are distributed between both layers according to their par- tition coefficients (K_p = c₂/c₁), the phase containing a smaller amount of interfering compounds can be selected for analysis. The total amount of the analyte (m_x) is distributed between the two phases with the volumes V1 and V2, and then

m_x = c1V1 + c2V2 = c1V1 + K_pc1V2 = c1V1(1 + K_pr), m_x m_addPx

α*P_x₊_add–P_x ---,

=

where r = V₂/V₁ is the ratio between the volumes of the phases.

The amount of the compound in phase 1 is related to the total amount of the analyte in the system as c1V1 = βm_x, where β = (1 + K_pr)^–1. Consequently, to use the standard addition method in this case, we can proceed from the following proportion:

βP_x/(βP_{x + add}) = m_x/(m_x + m_add),

which, after the cancellation of the coefficient β, leads to computational relationship (2). If, to increase the amount of the analyte in the system, the values of K_p or r are significantly changed (β ≠ const), the extrapolation of results to the zero value of the standard addition can be recommended similarly to the previous case.

An alternative technique for the quantitative analysis of the samples of this type is a much more time-con- suming and laborious procedure of the successive liquid extraction, which was mentioned in manual [1] and considered in detail in [12].

The transformation of samples into heterophase systems at the step of sample preparation allowed, e.g., the determination of menthol in the antimigraine medicine

“Menthol pencil” (solid solution of racemic menthol in paraffin) and m-toluic acid diethylamide in an aqueous emulsion stabilized with detergents (domestic deter- gent DETA) by a common scheme (varying only solvent combinations) [9]. However, in spite of the obvi- ous advantages of quantitative analysis by the standard addition method, the selection of particular versions of this method is governed by the character of analyzed samples rather than by some theoretical principles.

There are more complex samples for which the use of the above techniques is insufficient. In particular, these are viscous matrices additionally containing compounds with the pronounced sorption properties mentioned above; i.e., the samples contain two phases, and their artificial segregation leads to three-phase systems.

It is expected that, unlike heterophase systems, samples containing components with sorption properties are rather common in the analytical practice. For example, these properties are characteristic of vegetable materials [11], many inorganic materials, and, evi- dently, complex systems such as soils. Therefore, it is interesting to note that, according to manual [13], which presents about 500 official EPA procedures (Environment Protection Agency, United States), none of them takes into account potential sorption properties of the matrices, which is obviously invalid.

To reveale the main features of the analysis of samples of this type, we prepared (see the Experimental section) a model mixture of hydrocarbon lubricating oil (hydrophobic matrix) with graphitized carbon black (hydrophobic sorbent). As the analyte component, we selected 4-tert-butyltoluene (4.7%). The direct gas- chromatographic analysis of this sample is impossible not only because of the ingress of matrix components into the chromatographic column, but mostly because

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USE OF THE STANDARD ADDITION METHOD 971

of an ambiguous degree of sorption of the target analyte on the sorbent. The use of the previously proposed technique of the transformation of the sample into a heterophase system [9], e.g., using a combination of hexane and acetonitrile, which are partially soluble in each other, does not give satisfactory results either, because the conditions of the sorption of the target compound and the reference sample in this case are not identical.

Therefore, to solve this analytical problem, it is necessary to provide identical conditions of analyte distribution between the sorbent and the matrix before and after the addition of the reference sample. Unsatisfac- tory results cause the necessity of the further optimiza- tion of analytical procedures and the method as a whole, preferably, without its complication. For example, the above technique of data extrapolation to the zero standard addition could be used; however, in this case we found a more efficient technique, which involved an insignificant modification of the procedure of sample preparation. When sorbents occur in the composition of complex samples, it is more reasonable to introduce the standard addition before rather than after their transformation into heterophase systems when the sorbent is localized in one of the phases. The implementation of this simple condition means that the initial sample (m_x) must be divided into two approximately equal parts, one of which (m_x1) is analyzed directly and to the other (m_x2) the reference sample (m_add) is added, and only after that are both samples segregated by additions of the second solvent. Then, taking into account that in the general case m_x2 ≠ m_x1, a somewhat modified general relationship (2) should be used for the correction of the results:

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This division of analyzed samples into several replicate samples does not substantially complicate the analytical procedure and was known previously [4, p. 361].

This simple modification of the procedure provides reliable results of the analysis of a model sample com- plying with the added–found criterion (see Table 1).

m_x m_addPx

P_x₊_add m_x2 m_x1 ---P_x –

---.

=

As an additional example, we can consider experimental preparations of a gel containing an oil extract of different medicinal herbs, several artificial additives (including peppermint essential oil, which should be determined), and additionally 5–10% finely dispersed polar (hydrophilic) inorganic sorbent (Aerosil A-380).

The version of the standard addition method recommended previously [9] for heterophase systems (addition is introduced into the previously obtained heterophase system) was found unsuitable in the presence of compounds possessing sorption properties, because it gave nonreproducible results (spread of values was 6–7 times):

In this case, unlike the previous example, the acetonitrile layer is unsuitable for the chromatographic analysis, because nearly all finely dispersed hydrophilic sorbent is concentrated in this layer. Only the hexane phase is suitable for injection in spite of the fact that nonpolar matrix components are transferred into this phase and, consequently, the initial portion of the chromatographic column must be regenerated after every 20–25 determinations. If the order of the introduction of the reference sample addition and the formation of the heterophase system is reversed, it is possible to attain the repeatability of replicate determinations at a

Sample Portion, g Addition, mg

Determined concentration of peppermint oil, %

1 1.36 22 1.77

2.96 56 0.64

2 1.64 26 1.71

2.55 49 2.75

49 + 57 = 106 1.58

0.83 40 1.99

2.34 63 2.56

3 1.04 27 2.22

3.69 78 4.25

Table 1. Results of the determination of the concentration of 4-tert-butyltoluene in a model sample (from the data of the analysis of the acetonitrile layer of the heterophase system)

Portion of the sample m_x1, g

Mass of the addition, mg

Total peak areas, mV ms

c = m_x/M, %

P_x P_{x + add}

1.106 1.065 24.5 1591.9 2254.5 4.52

1616.3 2361.9

1582.1 2342.5

1596.8 2319.6

Specified, % 4.75

δc, % –4.8

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972

level of 1.9–3.2 rel %, which is illustrated by the data presented in Table 2.

The accuracy of the obtained results in this case cannot be verified, because the specified concentration of peppermint oil in the samples was 1.7% when prepared and the concentration of volatile compounds can somewhat decrease on storage. The determination of the degree of their loss was the final aim of the determinations. The obtained results and the proposed procedure are recommended for use in the development of the pharmacopoeia article of the enterprise for the corre- sponding medicine.

Thus, the standard addition method can be used in the quantitative determination of the concentration of volatile components in complex matrices additionally containing compounds with sorption properties. The main point of the proposed recommendations is that two replicate samples must be prepared from the analyzed sample, the reference sample addition is introduced into one of these two samples, and only then are both samples transformed into heterophase systems with the subsequent chromatographic analysis of the layer containing the smallest amount of interfering components.

REFERENCES

1. Novak, I., Quantitative Analysis by Gas Chromatogra- phy, New York: Marcel Dekker, 1975.

2. Quantitative Analysis Using Chromatographic Tech- niques, Katz, E., Ed., New York: Wiley, 1987.

3. Guiochon, G. and Guillemin, C., Quantitative Gas Chro- matography for Laboratory Analyses and On-Line Pro- cess Control, Amsterdam: Elsevier, 1988.

4. Stolyarov, B.V., Savinov, I.M., Vitenberg, A.G., et al., Prakticheskaya gazovaya i zhidkostnaya khromatografiya (Practical Gas and Liquid Chromatography), St. Peters- burg, 2002.

5. Khmel’nitskii, R.A. and Brodskii, E.S., Khromato-mass- spektrometriya (Chromatography–Mass Spectrometry), Moscow: Khimiya, 1984.

6. Bernshtein, I.Ya. and Kaminskii, Yu.L., Spektromet- richeskii analiz v organicheskoi khimii (Spectrometric Analysis in Organic Chemistry), Leningrad: Khimiya, 1986.

7. Vitenberg, A.G. and Ioffe, B.V., Gazovaya ekstraktsiya v khromatograficheskom analize (Gas Extraction in Chro- matographic Analysis), Leningrad: Khimiya, 1982.

8. Kogan, L.A., Kolichestvennaya gazovaya khromato- grafiya (Quantitative Gas Chromatography), Moscow:

Khimiya, 1975.

9. Zenkevich, I.G. and Ragozina, T.N., Zh. Prikl. Khim., 1998, vol. 71, no. 5, p. 763.

10. Vigdergauz, M.S. and Krauze, I.M., Zh. Anal. Khim., 1986, vol. 41, no. 11, p. 2064.

11. Ostroukhova, O.K. and Zenkevich, I.G., Zh. Anal.

Khim., 2006, vol. 61, no. 5 [J. Anal. Chem. (Engl.

Transl.), vol. 61, no. 5].

12. Zenkevich, I.G., Pimenov, A.I., and Makarov, V.G., Labor. Zh., 2002, no. 1, p. 10.

13. Drugov, Yu.S. and Rodin, A.A., Monitoring orga- nicheskikh zagryaznenii prirodnoi sredy: Prakticheskoe rukovodstvo (Monitoring of Organic Contamination in Natural Environments: A Practical Manual), St. Peters- burg: Nauka, 2004.

Table 2. Results of the determination of the concentration of peppermint oil in experimental samples gel with the use of the discussed version of the standard addition method

Sample Portion of the sample m_x1, g

Mass of the addition, mg

Total peak areas, mV ms Concentration of peppermint oil, %

P_x P_{x + add}

1 1.099 1.083 52 145.0 602.7 1.60

158.5 591.4

1.358 1.322 58 99.9 352.4 1.62

91.6 338.3

2 1.135 1.118 64 95.8 420.4 1.54

88.2 434.8

1.133 1.149 63 87.4 393.5 1.60

88.4 396.9

3 1.128 1.147 62 90.8 422.2 1.52

90.7 418.8

1.089 1.139 57 108.4 473.1 1.49

101.6 487.6

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