ORIGINAL PAPER

Assessment of Different Measurement Methods Using 1H-NMRData for the Analysis of the Transesterification of Vegetable Oils

D. F. Andrade • J. L. Mazzei • C. R. Kaiser •

L. A. d’Avila

Received: 2 July 2011 / Revised: 22 August 2011 / Accepted: 6 October 2011

� AOCS 2011

Abstract In the present work we make assessments of the

correlation of equations based on 1H-NMR data for the

analysis of FAME in 45 transesterification products with

methanol from several vegetable oils (soybean, corn, sun-

flower, canola, linseed, cottonseed and jatropha). The

products employed in this study were of high and low

yield. A comprehensive approach to the applicability,

advantages and limitations of employing NMR expressions

is described. A new expression to determine the degree of

unsaturation of combined and free fatty acids was found to

be satisfactory when compared with the classic expression.

Estimates of uncertainties for classic equations, which have

been used to determine yield and degree of unsaturation,

were proposed in the present work. The results show that

either one or both of the expressions for estimating yields

could not be satisfactorily used for products from linseed

oil, and also indicate the possibility that products from

cottonseed oil may also be exceptions. Both the equations

were found to be satisfactory for the products obtained

from the other oils (soybean, corn, sunflower, canola and

jatropha), considering the uncertainties proposed in the

present work.

Keywords Biodiesel � 1H-NMR � Vegetable oil methyl

esters � Quality control

Introduction

Fatty acid alkyl esters (FAAE) are commercially produced

by the alcoholysis of fats and oils, especially vegetable oils,

and have been used as source materials in the manufacture

of other products, particularly biodiesel. In biodiesel pro-

duction, refined FAAE containing over 96.5% esters have

been used directly (B100) [1, 2] or in blends with fossil

diesel fuel [3].

It is necessary to control the quality of the composition

of FAAE both to assure that the product is suitable for its

intended use and to avoid the undesirable residues of non-

converted triacylglycerols (TAG) and their derivatives, free

glycerol (G), monoacylglycerols (MAG) and diacylglyce-

rols (DAG), which result from incomplete conversion or

insufficient purification [4]. The presence of these minor

components in biodiesel can lead to serious engine prob-

lems and increased hazardous emissions [4, 5]. In Europe,

the quality standard for biodiesel, EN 14214, establishes

maximum quantities of 0.02% G, 0.80% MAG, 0.20%

DAG and TAG, and 0.25% total glycerol (free and bound)

[2] in the rapeseed oil methyl ester. In the USA, the

American Society for Testing and Materials (ASTM) bio-

fuel standard, D6751, sets the upper limit of 0.02% G and

0.24% total glycerol for the soybean oil methyl ester [6].

The Brazilian National Agency of Petroleum, Natural Gas

and Biofuels published specifications for B100 that are in

D. F. Andrade (&) � L. A. d’Avila

Departamento de Processos Organicos, Escola de Quımica,

Centro de Tecnologia, Universidade Federal do Rio de Janeiro,

Bl. E, S/201, Ilha do Fundao, Rio de Janeiro 21949-900, Brazil

e-mail: debora.franca.andrade@gmail.com

J. L. Mazzei

Departamento de Biofısica e Biometria, Instituto de Biologia

Roberto Alcantara Gomes, Universidade do Estado do Rio de

Janeiro, Blv. Vinte e Oito de Setembro 87, Vila Isabel,

Rio de Janeiro 20551-030, Brazil

C. R. Kaiser

Departamento de Quımica Organica, Instituto de Quımica,

Centro de Tecnologia, Universidade Federal do Rio de Janeiro,

Bl. A, S/605, Ilha do Fundao, Rio de Janeiro 21949-900, Brazil

123

J Am Oil Chem Soc

DOI 10.1007/s11746-011-1951-4

accordance with both the ASTM standards and the Bra-

zilian Association of Technical Standards [1].1H Nuclear magnetic resonance (1H-NMR) spectros-

copy has been used with success in studies of fossil fuels

[7] and is frequently used in biofuels for monitoring the

synthesis, yield and quality of alcoholysis reactions and

processes [8–16]. The first reports on 1H-NMR analyses of

FAAE synthesis using the transesterification of vegetable

oils with alcohols focused primarily on determining the

yield of progressive transesterification with methanol [8,

12] or ethanol [9, 16]. Yields have been determined using1H-NMR analysis by means of simple equations [8, 12,

16], building a calibration curve [9] or using an internal

standard [11]. The relevant assignments of the chemical

shifts in the 1H-NMR spectra of soybean and rapeseed oil

and the respective fatty acid methyl esters (FAME),

obtained products by reaction with methanol [8, 11, 12], as

shown in Table 1, Fig. 1.

Gelbard et al. [8] described the utilization of 1H-NMR

for monitoring yields from the transesterification of rape-

seed oil, which they estimated directly (CG) by integrating

selected signals, according to Eq. 1 [8].

CG ¼ 100 � 2 � IME

3� ICH2

� �ð1Þ

Signals from the methylene group adjacent to the

carbonyl group present in all fatty ester derivatives at d2.31 (Table 1) are one of the relevant signals chosen for

integration. However, as this signal appears as a triplet,

accurate measurements must be made to separate this

triplet from the multiplet at d 2.03, which is related to

allylic protons (Table 1).

Knothe [12] monitored the progress of the transesterifi-

cation of soybean oil by 1H-NMR using Eq. 2 and corre-

lating the results with fiber-optic near infrared spectroscopy.

CK ¼ 100 � 5� IME

5� IME þ 9� IAG

� �ð2Þ

In both Eqs. 1 and 2, the yield is assumed to depend on

the integration of the methoxyl group signal, which is

typical for FAME, meaning that these equations cannot be

used in the alcoholysis of oils and fats except with

methanol. In addition, in order to quantify the yield from

the transesterification of vegetable oils with ethanol, some

works [9, 10, 16] have correlated equations based on1H-NMR methods with other techniques (viscosity and

Fourier-transform-Raman measurements), but these

equations cannot be used for transesterification with

methanol.

The importance of these equations in monitoring the

yield of transesterification with methanol is evident from

their appearance in several works [17–20]. Correlations

with NMR approaches have been studied in the monitoring

of progressive transesterification of soybean and rapeseed

oils only. Gelbard et al. [8] correlated Eq. 1 using 1H-NMR

and molar weight, obtaining good agreement in the deter-

mination of the progressive transesterification of rapeseed

oil. Knothe [12] compared the yields of progressive

transesterification using Near-Infrared spectroscopy and

the NMR approaches presented in this paper (Eqs. 1, 2).

The author concluded that the approaches mutually con-

firmed each other based only on plotting the yield of soy-

bean oil methyl ester against the reaction time. The

minimum yield was approximately 55%.1H-NMR spectroscopy has also been employed to

estimate some physico-chemical analysis parameters in

vegetable oils and their transesterification products. The

iodine value [21, 22] and average molecular mass [22,

23] can be determined in vegetable oils. Furthermore, the

amounts of mono-, di- and tri-unsaturated fatty acid

Table 1 Reported assignments of chemical shifts (d) and peak area integrations in 1H-NMR spectra of soybean and rapeseed oils and their

transesterification products [8, 11, 12]

Protons Compoundsa db Integrationc

Terminal methyl group TAG, DAG, MAG, FAME 0.90 (t) ITM

Linolenic acid methyl group TAG, DAG, MAG, FAME 0.98 (t) ILAM

Methylenes, except the followings TAG, DAG, MAG, FAME 1.30 (m) IM

Methylenes b- to the carbonyl or to the olefin TAG, DAG, MAG, FAME 1.60 (m) IMB

Allylic protons TAG, DAG, MAG, FAME 2.03 (m) IMA

Methylene group adjacent to the carbonyl group TAG, DAG, MAG, FAME 2.31 (t) ICH2

Diallyl methylenes TAG, DAG, MAG, FAME 2.72 (t) IDAM

Methoxyl groups FAME 3.70 (s) IME

Glyceryl methylene TAG, DAG, MAG, G 4.10–4.40 (d) IAG

Olefin and glycerol methine TAG, DAG, MAG, FAME, G 5.30 (m) ICA

a TAG, DAG, MAG tri, di and monoacylglycerols, respectively; FAME fatty acid methyl esters, G glycerol. b s Singlet, t triplet, m multiplet. c

Notation adopted in the present work

J Am Oil Chem Soc

123

chains [14, 24] and the degree of unsaturation (DU) in

these chains [11, 25] can also be estimated in FAME

products that have been produced from vegetable oils.

The determination of average DU has only been reported

for FAME produced from soybean and olive oil [11, 18,

25, 26] from a comparison of the integration value for the

methylene group adjacent to the carbonyl group (d 2.31)

with that of the olefin protons (adjusted for the under-

lying methine proton) [11]. Morgenstern et al. [11] esti-

mated the DU (DUM) from soybean oil to be 1.52, which

corresponds closely to the DU values of 1.54 and 1.49

reported in previous works. An equation representing DU

according the definition given by Morgenstern et al. [11]

(DUM) can be expressed as:

DUM ¼ICA � IAG=4ð Þ

ICH2

� �ð3Þ

As can be seen, the use of 1H-NMR integration data in

estimating transesterification yields and parameters

associated with the quality of these products have only

been evaluated for soybean, olive and rapeseed oil.

However, a wide range of naturally available vegetables

can be used as source materials for FAME production. For

instance, there have been reports on the use of corn,

sunflower, linseed, cottonseed, castor, crambe, peanut,

palm, olive, coconut, tung, piqui (Caryocar sp.), jatropha

(Jatropha curcas), and karanj (Pungamia pinnata) oils [3,

27–35]. As such, the present work establishes assessments of

the correlation of equations based on 1H-NMR data for the

analysis of the FAME in products from transesterification

with methanol. Products from seven vegetable oils, namely

soybean, corn, sunflower, canola, linseed, cottonseed, and

jatropha oil, were studied in view of the importance of this

technique which has the potential to be applied successfully

as a tool in the validation of methods less expensive and

much easier to keep in operation.

Experimental Procedures

Vegetable Oils and Reagents

Refined food grade soybean, corn, sunflower, canola, and

cottonseed oil and a commercial edible grade linseed oil

were purchased from retail establishments in Rio de

Janeiro state (Brazil). Jatropha oil was supplied by

Greentec Laboratory (Escola de Quımica/UFRJ, Rio de

Janeiro).

Analytical grade anhydrous potassium carbonate,

sodium chloride and sodium sulfate were purchased from

Merck (Darmstadt, Germany). Analytical grade methanol

and hexane (mixture of isomers) were supplied by Vetec

(Rio de Janeiro, Brazil). NMR grade deuterated chloroform

(CDCl3) and tetramethylsilane (TMS) were purchased from

Cambridge Isotope Laboratories (Andover, USA).

The oils and reagents were employed without further

purification.

Yield from the Transesterification of Vegetable Oils

The transesterification of each vegetable oil was accom-

plished by heating with anhydrous methanol under reflux,

using potassium carbonate as a catalyst, following the

procedure described by Guarieiro [17] with modifications.

Fifty milliliters of vegetable oil, previously weighed, was

added to a 125 mL round-bottomed flask, containing

potassium carbonate (3% mol), methanol (oil:methanol

molar ratio of 1:3 or 1:9), a magnetic stirrer and an allihn

a

O

O

2.31

1.60

1.31

1.31

1.31

1.60

2.03

5.30 5.30

2.03

1.60

1.31

1.31 1.31

1.31

0.90

O

O

2.31

1.60

1.31

1.31

1.31

1.60

2.03

5.30 5.30 5.30 5.30

2.72 2.03

1.60

1.31

1.31

0.90

O

O

2.31

1.60 1.60

1.31

1.31

1.31 2.03

5.30 5.30 5.30 5.30 5.30 5.30

2.72 2.72 2.03

0.98

H2C

HC

__

__

__H2C

4.10 - 4.40

4.10 - 4.40

5.30

1.31

b

O

O

3.70

R

Fig. 1 Generic representation

of the structures of

a triacylglycerols and b the

respective methyl esters

derivatives (R, aliphatic chain),

containing the most prominent

fatty acid chains (oleic, linoleic

and linolenic) found in

vegetable oils and the respective1H-NMR assignments [8, 12]

J Am Oil Chem Soc

123

reflux condenser. The average molecular mass of the vege-

table oil components was estimated from the likely com-

position of the combined fatty acids and the equation

proposed by Guarieiro [17]. The reaction medium was kept

under magnetic agitation and reflux for 5, 10, 15, 30, and

90 min and was then cooled to room temperature. The

methanol residue was removed in a rotary evaporator using a

water pump. The glycerine phase (lower) containing alcohol

and excess catalyst was separated by decantation in a sepa-

ration funnel. The upper layer was extracted with 100 mL

hexane. The hexane phase was washed with distilled water

(3 9 50 mL) to remove any residual catalyst and any other

persistent impurities. The hexane extraction step is required

to prevent an emulsion from forming [17]. The hexane was

removed in a rotary evaporator (vacuum, water pump)

yielding a clear liquid FAME product of a light yellow color.

The products were kept in anhydrous sodium sulfate for 2 h

to remove any residual water, filtered again and then stored

in a freezer (approximately -10 �C) until analysis.

1H-NMR Method

1H-NMR spectra were obtained using a Bruker DPX-200

spectrometer, in the conditions described before [7].

Samples of the vegetable oils and their FAME products

were dissolved at 12 mg/mL in CDCl3. TMS was used as

an internal standard. The assignment of hydrogen chemical

shifts was identified following Gelbard et al. [8] and is

summarized in Fig. 1, Table 1. The integration of the NMR

peaks was calculated and normalized relative to the

methylene group adjacent to the carbonyl group (ICH2)

once that was found in the TAG, DAG, MAG and FAME.

Degree of Unsaturation of the Fatty Acid Chains

The degree of unsaturation (DU) of the free and combined

fatty acid chains in the vegetable oils and respective

products was determined using Eq. 3. We propose another

expression in order to estimate this parameter using Eq. 4,

which also represents the contribution of the number of

olefin groups in the fatty chains to 1H-NMR integration and

is based on the contribution by the protons in the vicinal

groups to the olefin groups.

DU ¼ IDAM þ IMA=2ð ÞICH2

ð4Þ

Determination of Transesterification Yield by Gelbard

and by Knothe

The yield of the transesterification of vegetable oils into

FAME was calculated using Eqs. 1 (CG, %) and 2 (CK, %)

for the products obtained in the present work.

Uncertainty Estimates of the Integration Measurements

Our main goal was to establish assessments of the corre-

lation of Eqs. 1 and 2, for which purpose an estimate of

their uncertainty was needed. Assuming that both equations

are dependent upon the integration of selected signals,

uncertainty in these equations may be calculated as the

result of the propagation of uncertainty of the experimental

variables. An estimate of experimental uncertainty was

determined from the following expression and through

derivations. Thus, a simple, hypothetical relationship (f)

can be defined as the difference between the two equations

that represent DU (Eqs. 3, 4):

f ¼ ICA � IAG=4ð Þ � IDAM � IMA=2ð Þ ¼ 0 ð5Þ

The theoretical value of function f is zero, independent

of the yield of the transesterification. Thus, the f values

calculated (Eq. 6) from the 1H-NMR integration data,

using Eq. 5, are related to its uncertainty (df), or the

deviation from its theoretical value (zero).

fcalculated ¼ 0 � df ð6Þ

Function f is an arithmetical expression based on the

independent experimental data of integrations, each of

which is subject to a random uncertainty (dICA, dIAG,

dIDAM and dIMA). Thus, its deviation (df) can be expressed

in terms of the propagation [41] of the uncertainties from

the integration values in Eq. 5, as expressed by:

dfð Þ2¼ ðof=oICAÞ2 � dICAð Þ2þðof=oIAGÞ2

� dIAGð Þ2þðof=oIDAMÞ2 � dIDAMð Þ2þðof=oIMAÞ2

� dIMAð Þ2

ð7Þ

The substitution of the derivatives from Eq. 5 gives:

dfð Þ2¼ dICAð Þ2þ 1=16ð Þ � dIAGð Þ2þ dIDAMð Þ2þ 1=4ð Þ� dIMAð Þ2

ð8Þ

Assuming a general uncertainty for the integration

values (dICA & dIAG & dIDAM & dIMA) and substituting

them for a generic parameter (dI), Eq. 8 can be reduced to:

dfð Þ2¼ 2þ 5=16ð Þ � dIð Þ2 ð9Þ

Thus, approximating the coefficient to 2/3 and

calculating the square root, the generic relationship can

be assumed by approximation for an average uncertainty:

dI ¼ 2=3� jdf j ð10Þ

If we substitute df from Eq. 6 and f from Eq. 5, we get

Eq. 11, which is proposed in the present work as the means

for expressing the uncertainty of the integrations:

J Am Oil Chem Soc

123

dI ¼ 2=3� ICA � IAG=4ð Þ � IDAM � IMA=2ð Þj j ð11Þ

Estimate of Yield Uncertainties

The Gelbard et al. [8] and Knothe [12] equations (1, 2,

respectively) were employed to derive a relationship that

enabled their uncertainties to be calculated: dCG (Eq. 12)

and dCK (Eq. 13) respectively. For this, the general

uncertainty of the integration determinations Eq. 11 was

assumed.

dCG ¼ ð1= IMEÞ2 þ ð1= ICH2Þ2h i1=2

� CG � dI ð12Þ

dCK ¼ 100 � 5� 9�I2ME þ I2

AG

� �1=2

5� IEM þ 9� IAGð Þ2� dI ð13Þ

Uncertainty of the Degree of Unsaturation

In order to compare the equations relative to the degree of

unsaturation, the uncertainties of Eqs. 3 and 4 were

deduced in the same way and are given by dDUM and dDU,

respectively.

dDUM ¼1þ DU2

M

� �1=2

ICH2

� dI ð14Þ

dDU ¼ 5=4þ DU2ð Þ1=2

ICH2

!� dI ð15Þ

Results and Discussion

1H-NMR Spectra of the Starting Oils

In order to analyze the significant differences among the

vegetable oils and their respective FAME products, 1H-

NMR spectroscopy was used on the different oils employed

as starting materials. A good resolution was obtained for all

the 1H-NMR spectra, as can been seen in Fig. 2. The

spectra for soybean oil presented the characteristic signals

and intensities widely illustrated in other works [10, 11,

36].

Very few differences in the spectrum profiles can be

observed in Fig. 2. The most important difference is the

relative area of the diallyl methylene signal at d 2.72,

which is increased by the linoleic and linolenic acid chains,

since they contain two and four diallyl methylene protons,

respectively. Low signals at d 0.98, relative to the terminal

methyl groups in the linolenic acid chains, can be observed

in the rapeseed and linseed oil spectra (Fig. 2c, d,

respectively).

Palm oil was also analyzed by 1H-NMR but its spectrum

is not discussed in this work because the oil was not

properly converted (B2%) under the test conditions. Castor

oil was also analyzed, and its spectrum (Fig. 3) was

markedly different than the spectra of the other oils, mainly

because of the composition of the combined fatty acids.

The absence of a signal at d 2.72 is due to the absence of

linoleic and linolenic acid, while the presence of a signal at

d 3.70 is assigned to the chemical shift in the carbinol

hydrogen, which is located at the b-position of the olefin

group [37], found in ricinoleic acid, the main constituent of

castor oil (Fig. 3). However, this chemical shift is also

characteristic of the methoxyl groups in methyl esters, so

this finding could be seen as a limitation of the use of1H-NMR in the characterization of FAME products from

this starting oil. In fact, our data were inconclusive for the

analysis of the FAME from castor oil (data not shown).

1H-NMR Spectra of the Transesterification Products

In the literature, the determination of the yield of transe-

sterification by 1H-NMR has only been reported for soy-

bean and rapeseed oil [8, 12]. It would be expected that all

vegetable oils would contain the same functional groups in

the majority of the components and would hence yield the

same collection of peaks in their NMR spectra. In the

present work, a good resolution was obtained for all the 1H-

NMR spectra of the transesterification products, and the

profile spectra of the products from soybean and rapeseed

oils were clearly similar to the spectra from the other oils

under study, excepting palm and castor oils, as described

above. The major differences observed among the 1H-

NMR spectra of the resulting products and the respective

starting vegetable oils were the expected increase and

decrease in the signal intensities of methoxyl (d 3.70) and

glyceryl methylene (d 4.10–4.40) protons, respectively, as

seen in Fig. 4, which shows the spectra of the products

from corn oil.

Apart from castor oil, the oils studied in the present

work did not present a signal at d 3.70, which contributed

towards the determination of their yield, since this signal is

used in the two NMR equations (Eqs. 1, 2). The glyceridic

protons in the structures of MAG and DAG exhibited 1H-

NMR signals in the same region as the glyceryl methylene

protons of the TAG (at d 4.10–4.40) in the feedstock.

Correlation Between the Absolute Values Calculated

Using the Two 1H-NMR Equations

By using the Gelbard and Knothe equations, the yield of

the transesterification was calculated for the 45 products,

which were derived from seven different vegetable oils,

under oil:methanol molar ratios of 1:3 and 1:9 and for 5,

10, 15, 30, and 90 min reaction times (Table 2). It is well

known that the molar ratio of methanol to vegetable oil is

one of the parameters that most affects the yield of FAME

J Am Oil Chem Soc

123

[38]. This assumption is reasonable because a large excess

of alcohol is what drives the equilibrium reaction of the

transesterification to yield the FAME [38]. Thus, an

oil:methanol molar ratio that is higher than the stoichi-

ometry 1:3 ratio is recommended for a good yield. A molar

ratio of 1:6 has been widely used in industrial processes,

giving ester yields of over 98% w/w. In this work,

oil:methanol molar ratios of 1:3 and 1:9 were employed

with the aim of obtaining low- and high-yield products,

respectively. Several sources were used to verify whether

the two equations could be used for products obtained from

vegetable oils other than those previously reported (soy-

bean and rapeseed oil). In fact, the results presented in

Table 2 show that yields were higher for an oil:methanol

molar ratio of 1:9 than for 1:3. Reaction times were set

between 5 and 90 min because this is another important

variable that affects ester yield. In our data the yield

increased with the reaction time, which tallies with the

literature [39, 40]. The one exception we cannot explain

was the yield of the products obtained from soybean oil at

an oil:methanol molar ratio of 1:3 at 15 min.

In order to identify whether there was any direct rela-

tionship between the values obtained from the two yield

equations, CG/CK was introduced in Table 2. It can be seen

that this ratio was closer to one, the expected value, pri-

marily when the yield values were closer to 100%. Con-

sidering that uncertainty in yield determinations is

independent of the respective value, it would be expected

that the highest percentage differences between CG and CK

would be obtained at very low yield values, as can be seen

for the six products obtained at yields lower than 20% with

1:3 oil:methanol molar ratio (Table 2). The fact that

CG \ CK was constantly identified, suggests that NMR

signals of triacylglycerols could reduce the accuracy of the

Fig. 2 1H-NMR spectra (200 MHz, CDCl3) of the vegetable oils used as starting materials in the present work: a corn, b sunflower, c rapeseed,

d linseed, e cottonseed, and f jatropha

J Am Oil Chem Soc

123

results from one or both equations. When the yield was

between 20 and 55%, lower differences between CG and

CK were observed and the ratio was close to one (\10%

difference), but an increased relationship between CG/CK

could also be observed (n = 11), which might suggest that

signals from the other derivative residues from the

transesterification could have interfered in the yield esti-

mate when Eqs. 1 and 2 were used. Exceptions of this kind

were not observed by Knothe [12], who compared the

yields of progressive transesterification using Eqs. 1 and 2,

because the minimum yield studied was approximately

55%.

For the highest yield, 1:9 oil:methanol molar ratio, most

of the products showed a 5% difference between CG and

CK, or in other words, a CG/CK ratio of between 0.95 and

1.05. One important exception was the products from

Fig. 3 1H-NMR spectrum

(200 MHz, CDCl3) for castor

oil. The chemical shifts of

ricinoleic acid and the chain

characteristic of the castor oil

composition are indicated. The

proposed chemical shift at d2.21 is based on the assignment

for the contribution of two

functional groups attached to

the methylene group [37] and

others are typical of fatty acid

chains

Fig. 4 1H-NMR spectra (200 MHz, CDCl3) of products from corn oil at different yields: a 38%, b 46%, c 91%, and d 94%. Spectrum for corn

oil is shown in Fig. 2a

J Am Oil Chem Soc

123

Ta

ble

2Y

ield

(%)

calc

ula

ted

by

Gel

bar

d(C

G)

and

Kn

oth

e(C

K)

equ

atio

ns

and

deg

ree

of

un

satu

rati

on

asd

efin

edb

yM

org

enst

ern

(DU

M)

and

asd

efin

edin

the

pre

sen

tw

ork

(DU

),w

ith

the

resp

ecti

ve

un

cert

ain

ties

pro

po

sed

her

ein

,o

fth

ep

rod

uct

so

bta

ined

un

der

dif

fere

nt

reac

tio

nti

mes

and

oil

/met

han

ol

mo

lar

rati

os

fro

md

iffe

ren

tv

eget

able

oil

s(n

=4

5)

So

urc

e

mat

eria

ls

Rea

ctio

n

tim

e(m

in)a

Mo

lar

rati

o1

:3M

ola

rra

tio

1:9

CG

CK

CG

/CK

DU

MaD

Ua

dIa

CG

CK

CG

/CK

DU

MD

Ud

I

So

yb

ean

––

––

(1.4

7±

0.0

8)

(1.5

4±

0.0

9)

(0.0

5)

––

––

––

52

9±

63

2±

50

.91

±0

.24

1.3

5±

0.1

41

.48

±0

.15

0.0

88

1±

68

2±

60

.99

±0

.10

1.3

8±

0.0

91

.47

±0

.10

0.0

6

10

––

––

––

81

±4

81

±4

1.0

0±

0.0

71

.41

±0

.07

1.4

7±

0.0

70

.04

15

13

±3

15

±3

0.8

7±

0.2

61

.39

±0

.07

1.4

6±

0.0

80

.04

83

±4

84

±4

0.9

8±

0.0

71

.40

±0

.07

1.4

6±

0.0

70

.04

30

40

±6

40

±5

1.0

0±

0.1

81

.37

±0

.12

1.4

8±

0.1

40

.07

86

±8

83

±7

1.0

4±

0.1

31

.35

±0

.12

1.4

6±

0.1

30

.07

90

––

––

––

92

±5

91

±5

1.0

2±

0.0

81

.34

±0

.07

1.4

1±

0.0

80

.04

Co

rn–

––

–(1

.28

±0

.02

)(1

.30

±0

.02

)(0

.01

)–

––

––

–

53

8±

54

0±

40

.96

±0

.17

1.1

5±

0.1

01

.25

±0

.11

0.0

78

1±

58

0±

41

.01

±0

.08

1.2

0±

0.0

71

.27

±0

.08

0.0

4

10

––

––

––

85

±5

87

±4

0.9

9±

0.0

71

.23

±0

.07

1.3

0±

0.0

70

.04

15

40

±6

39

±5

1.0

2±

0.2

11

.17

±0

.13

1.3

0±

0.1

40

.08

85

±5

87

±5

0.9

8±

0.0

81

.20

±0

.07

1.2

7±

0.0

80

.05

30

46

±6

44

±5

1.0

4±

0.1

81

.20

±0

.12

1.3

2±

0.1

30

.08

91

±7

88

±7

1.0

3±

0.1

11

.20

±0

.10

1.2

9±

0.1

10

.06

90

––

––

––

94

±5

94

±5

1.0

0±

0.0

71

.20

±0

.07

1.2

6±

0.0

70

.04

Su

nfl

ow

er–

––

–(1

.36

±0

.05

)(1

.41

±0

.06

)(0

.03

)–

––

––

–

51

0±

31

2±

30

.81

±0

.30

1.2

7±

0.0

71

.34

±0

.07

0.0

49

2±

12

75

±8

1.2

3±

0.2

11

.22

±0

.17

1.3

8±

0.2

00

.11

10

––

––

––

79

±4

73

±4

1.0

8±

0.0

80

.96

±0

.06

1.0

3±

0.0

70

.04

15

29

±7

30

±6

0.9

8±

0.3

01

.29

±0

.15

1.4

3±

0.1

70

.10

89

±5

94

±5

0.9

5±

0.0

81

.32

±0

.07

1.3

9±

0.0

80

.04

30

39

±7

37

±5

1.0

3±

0.2

41

.30

±0

.15

1.4

3±

0.1

60

.09

91

±7

88

±6

1.0

2±

0.1

11

.29

±0

.10

1.3

8±

0.1

10

.06

90

––

––

––

10

3±

99

7±

81

.06

±0

.13

1.3

6±

0.1

21

.47

±0

.13

0.0

7

Can

ola

––

––

(1.2

1±

0.0

4)

(1.2

5±

0.0

4)

(0.0

2)

––

––

––

52

9±

63

2±

60

.91

±0

.25

1.1

1±

0.1

31

.24

±0

.14

0.0

99

3±

58

8±

41

.06

±0

.07

1.1

4±

0.0

61

.21

±0

.07

0.0

4

10

––

––

––

74

±5

75

±5

0.9

9±

0.1

01

.13

±0

.08

1.2

1±

0.0

90

.06

15

49

±7

47

±6

1.0

4±

0.2

01

.12

±0

.13

1.2

5±

0.1

50

.09

90

±1

93

±1

0.9

7±

0.0

11

.19

±0

.01

1.2

0±

0.0

10

.01

30

55

±8

50

±6

1.1

0±

0.2

01

.15

±0

.14

1.2

8±

0.1

50

.09

94

±7

87

±6

1.0

8±

0.1

11

.12

±0

.09

1.2

1±

0.1

00

.06

90

––

––

––

97

±8

95

±8

1.0

2±

0.1

21

.17

±0

.11

1.2

8±

0.1

20

.07

Lin

seed

––

––

(1.2

6±

0.0

2)

(1.2

4±

0.0

3)

(0.0

2)

––

––

––

53

±1

4±

20

.74

±0

.45

1.2

6±

0.0

31

.23

±0

.04

0.0

27

8±

38

0±

30

.98

±0

.05

1.1

8±

0.0

51

.23

±0

.05

0.0

3

10

––

––

––

86

±1

90

±1

0.9

6±

0.0

21

.21

±0

.02

1.2

0±

0.0

20

.01

15

4±

15

±1

0.8

0±

0.2

31

.24

±0

.02

1.2

2±

0.0

20

.01

81

±2

88

±2

0.9

2±

0.0

31

.19

±0

.03

1.2

2±

0.0

30

.02

30

4±

15

±2

0.8

0±

0.3

41

.27

±0

.03

1.2

4±

0.0

30

.02

79

±1

92

±1

0.8

7±

0.0

21

.12

±0

.01

1.1

0±

0.0

20

.01

90

––

––

––

89

±2

95

±2

0.9

3±

0.0

31

.18

±0

.03

1.2

1±

0.0

30

.02

J Am Oil Chem Soc

123

linseed oil at the lowest yields (until 15 min reaction time),

since these products were the ones that gave the lowest

ratio values (CG/CK \ 0.95). CG/CK ratio values of over

1.05 were also observed for products obtained with a 1:9

oil:methanol molar ratio, but under different conditions for

different sources.

The conversion results obtained by 1H-NMR, according

to the expressions by Gelbard [8] and Knothe [12]

(Table 2), were statistically compared using t-test: two

paired samples for means. As the critical value of the one-

tailed something |t| was 1.68 and the calculated value |t|

was 0.75, we found that the conversion values obtained for

the Gelbard [8] and Knothe [12] expressions yielded no

significant differences (P [ 0.05). This is well illustrated

by the diagram of CG against CK (Fig. 5), which shows the

linear relationship between the CG and CK values.

Importance of the Uncertainty Estimate

As shown in Table 2, the absolute DUM values were very

similar to the proposed DU, independent of the sources or

the FAME yield, as would be expected for accurate

parameters. This similarity validates the hypothetical

relationship f (Eq. 5) between their expressions, which was

originally used to determine the uncertainty of the inte-

gration values and consequently of the yield and degree of

unsaturation. Equations 1–4 studied in the present work,

which were used to calculate CG, CK, DUM and DU, are

arithmetical expressions based on independent experi-

mental data for integrations and also are subject to random

uncertainties. Thus, the respective uncertainties dCG, dCK,

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120CG (%)

CK (

%)

Fig. 5 Diagram of CG (%) versus CK (%); values calculated from the

transesterification products (n = 45) obtained under different reaction

times and oil/methanol molar ratios from seven different vegetable

oils, using 1:3 (filled circle) and 1:9 (filled diamond) oil:methanol

molar ratioTa

ble

2co

nti

nu

ed

So

urc

e

mat

eria

ls

Rea

ctio

n

tim

e(m

in)a

Mo

lar

rati

o1

:3M

ola

rra

tio

1:9

CG

CK

CG

/CK

DU

MaD

Ua

dIa

CG

CK

CG

/CK

DU

MD

Ud

I

Co

tto

nse

ed–

––

–(1

.17

±0

.05

)(1

.22

±0

.06

)(0

.03

)–

––

––

–

59

±2

11

±2

0.8

1±

0.1

81

.15

±0

.04

1.1

9±

0.0

40

.02

––

––

––

10

––

––

––

10

2±

58

9±

41

.14

±0

.07

1.1

3±

0.0

61

.19

±0

.07

0.0

4

15

––

––

––

10

5±

69

5±

31

.14

±0

.08

1.1

5±

0.0

71

.22

±0

.08

0.0

5

Jatr

op

ha

––

––

(1.1

8±

0.0

3)

(1.2

1±

0.0

3)

(0.0

2)

––

––

––

52

0±

52

2±

40

.92

±0

.29

1.1

2±

0.1

11

.23

±0

.12

0.0

7–

––

––

–

30

––

––

––

90

±4

93

±4

0.9

7±

0.0

61

.14

±0

.05

1.1

9±

0.0

50

.03

aD

ata

inb

rack

ets

are

val

ues

for

the

resp

ecti

ve

veg

etab

leo

ils

J Am Oil Chem Soc

123

dDUM and dDU can be given in terms of the uncertainty

propagation equations [41] and using the expression dI,

resulting in Eqs. 12–15, respectively.

The uncertainties are presented in Table 2. When the

values for CG/CK are correlated to the yield of each product

(in relation to CG) and the uncertainties are taken into

account (Fig. 6), it can be seen that only nine of all 45

products failed to represent the expected value of one, even

after uncertainty was taken into account. A rigorous anal-

ysis of these exceptions showed that six of them were

products of linseed oil, which particularly indicates that the

values obtained from the two expressions applied to the

yield are very different from each other for these products.

It was also found that two of the cottonseed oil products

also had CG/CK values that were far from one, even con-

sidering the uncertainty values, which indicates that their

products may also be exceptions when it comes to using

one or both the equations for determining their yields.

In view of these results, it can be suggested that one or

both of the expressions for estimating yields may not be

satisfactory for the products from linseed oil and cotton-

seed oil. Minor compounds other than acylglycerols, in the

composition of the original oils could have contaminated

the products, interfering in the NMR signals. On the other

hand, the products studied from soybean, corn, sunflower,

canola and jatropha oils (total of 34 products) were close to

one when the uncertainties proposed in this work were

considered.

Conclusion

It could be expected that the relative intensities of the

NMR peaks would vary only with differences in the degree

of unsaturation among oils/esters due to the similar com-

position of the main components. However, in this study

we showed that expressions designed to determine the

yield of transesterification products cannot be used for

products obtained from vegetable oils other than the ones

usually reported in the literature. The results showed that

either one or both of the expressions usually employed for

yield estimates could not be satisfactorily applied to

products from linseed oil. It was also found that one or both

of the equations for determining yields may not be suitable

for products from cottonseed oil. However, both expres-

sions were found to be suitable for the products from

soybean, corn, sunflower, canola and jatropha oil when the

uncertainties proposed in this work were considered.

The results showed that castor oil, with its hydroxyl

group, present spectra markedly different than the spectra

of the other oils. The presence of a signal at d 3.70 is

assigned to the chemical shift in the carbinol hydrogen

(located at the b-position of the olefin group) found in

0.40

0.60

0.80

1.00

1.20

1.40

0 20 40 60 80 100CG

CG

/CK

0.40

0.60

0.80

1.00

1.20

1.40

0 20 40 60 80 100 120

CG

CG

/CK

0.40

0.60

0.80

1.00

1.20

1.40

0 20 40 60 80 100 120

CG

CG

/CK

a

b

c

Fig. 6 Plot of CG/CK versus CG, including the uncertainties proposed

in the present work, for the products from: a soybean (circles) and

corn (triangles) oils; b linseed (circles), cottonseed (triangles) and

jatropha (squares) oils; c sunflower (circles) and canola (triangles)

oils

J Am Oil Chem Soc

123

ricinoleic acid, the main constituent of castor oil. This

chemical shift is also characteristic of the methoxyl groups

in methyl esters, so this finding could be seen as a limi-

tation of the use of 1H-NMR in the characterization of

FAME products from this starting oil. Another character-

istic of the spectra of castor oil is the absence of a signal at

d 2.72 due to the absence of linoleic and linolenic acid.

Other techniques, such as chromatography, have been

used to ascertain the biodiesel yield compared with the NMR

method. However, so far just one or other of the equations

has been correlated, and even in these cases uncertainties

were not considered. With the presented results, better

approaches can be developed to assess these correlation

relationships. The expression proposed in the present work to

determine the degree of unsaturation of combined and free

fatty acid chains was more satisfactory than the established

expression, and the results were very similar, independent of

the sources and the yield of the transesterification.

Acknowledgments The authors are grateful to the Brazilian

National Agency of Petroleum, Natural Gas and Biofuels through its

Human Resources Program (PRH-13/UFRJ, Rio de Janeiro, Brazil),

the National Council for Scientific and Technological Development

(CNPq/Brasılia, Brazil) and the Carlos Chagas Filho Research Sup-

port Foundation of the State of Rio de Janeiro (Faperj/Rio de Janeiro,

Brazil), for the financial support and grants they provided for this

work. The authors also thank Greentec Laboratory (Escola de Quı-

mica/UFRJ, Rio de Janeiro) for supplying the jatropha oil.

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