Hygroscopicity and thermodynamic properties of grains of <i>Moringa oleifera</i> L.

Padilla, Jose Renato Robles; Andrade, Ednilton Tavares de; Araújo, Bárbara Lemes Outeiro; Rios, Paula de Almeida; Oliveira, Filipe da Silva de

doi:10.4025/actasciagron.v48i1.73552

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AGRICULTURAL ENGINEERING • Acta Sci., Agron. 48 • 2026 • https://doi.org/10.4025/actasciagron.v48i1.73552 linkcopy

Hygroscopicity and thermodynamic properties of grains of Moringa oleifera L.

Authorship SCIMAGO INSTITUTIONS RANKINGS

The Moringa plant, widely recognized for its uses in both animal and human nutrition as well as in medicine, has seeds rich in oil and protein. For their maintenance and processing, safe storage conditions are needed, in addition to an understanding of the energy required for this process. The objective of this work was to study the hygroscopic and thermodynamic properties of moringa grains. The static gravimetric method was used at temperatures of 20-70°C and relative humidities of 10.75-85.11%. Nine mathematical models were fitted to the experimental water sorption data. The modified Halsey model provided the best fit, with an R² of 97.72%, P of 6.71%, and SE of 0.01, and was therefore used to calculate the thermodynamic properties. An increase in the equilibrium water content from 0.039 to 0.162 (db) resulted in a decrease in the energy released during adsorption (Q_st) from -3613.589 to -2453.029 kJ kg^-1, the differential entropy (∆S) from -2.519 to -0.115, and Gibbs free energy (∆G) from -351.897 to -21.773. This process was considered spontaneous.

Keywords:
mathematical modelling; isosteric heat; Gibbs free energy, entropy

Authorship

person Jose Renato Robles Padilla *

schoolDepartamento de Engenharia Agronômica, Universidade Federal de Lavras, Caixa Postal 3037, 37200-000, Lavras, Minas Gerais, Brazil. Universidade Federal de LavrasBrazilLavras, Minas Gerais, BrazilDepartamento de Engenharia Agronômica, Universidade Federal de Lavras, Caixa Postal 3037, 37200-000, Lavras, Minas Gerais, Brazil.

0009-0008-9093-0231

person Ednilton Tavares de Andrade

person Bárbara Lemes Outeiro Araújo

person Paula de Almeida Rios

person Filipe da Silva de Oliveira

person* Author for correspondence. E-mail:
jose.padilla3@estudante.ufla.br

Associate Editor in charge:

Alessandro Lucca Braccini

https://orcid.org/0000-0002-6915-4804

Carlos Alberto Scapim

https://orcid.org/0000-0002-7047-9606

SCIMAGO INSTITUTIONS RANKINGS

Departamento de Engenharia Agronômica, Universidade Federal de Lavras, Caixa Postal 3037, 37200-000, Lavras, Minas Gerais, Brazil. Universidade Federal de LavrasBrazilLavras, Minas Gerais, BrazilDepartamento de Engenharia Agronômica, Universidade Federal de Lavras, Caixa Postal 3037, 37200-000, Lavras, Minas Gerais, Brazil.

Figures | Tables | Formulas

Figures (4)
Tables (6)
Formulas (9)

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Figure 1 Values of slope angle coefficients for each equilibrium water content (db) for Moringa oleifera L. grains.

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Figure 2 Calculated and estimated integral isosteric heats of adsorption as a function of equilibrium water content (db) for Moringa oleifera L. grains.

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Figure 3 Calculated differential Entropy of adsorption as a function of equilibrium water content (db) for Moringa oleifera L. grains.

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Figure 4 Calculated Gibss Free Energy of adsorption as a function of equilibrium water content (db) for Moringa oleifera L. grains.

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Table1 Saturated saline solutions with their respective relative humidities when exposed to different temperatures.

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Table 2 Mathematical models for obtaining adsorption isotherms of Moringa oleifera L. grains.

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Table 3 Mathematical models adjusted to water adsorption experimental data of Moringa oleifera L. grains with parameters and adjustment evaluators.

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Table 4 Equilibrium water content estimated by the modified Halsey model for Moringa oleifera L. grains.

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Table 5 Water activity estimated by the modified Halsey model for Moringa oleifera L. grains according to equilibrium water content (db) and temperature (°C).

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Table 6 Line slope coefficient, net isosteric heat, and integral isosteric heat of adsorption calculated and estimated by the model for Moringa oleifera L. grains.

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imageFigure 1 Values of slope angle coefficients for each equilibrium water content (db) for Moringa oleifera L. grains. open_in_new

imageFigure 2 Calculated and estimated integral isosteric heats of adsorption as a function of equilibrium water content (db) for Moringa oleifera L. grains. open_in_new

imageFigure 3 Calculated differential Entropy of adsorption as a function of equilibrium water content (db) for Moringa oleifera L. grains. open_in_new

imageFigure 4 Calculated Gibss Free Energy of adsorption as a function of equilibrium water content (db) for Moringa oleifera L. grains. open_in_new

table_chartTable1 Saturated saline solutions with their respective relative humidities when exposed to different temperatures.

Temperature (°C)	Salts	RH (%)
20	Magnesium chloride (MgCl₂)	33.07 ± 0.18
	Lithium chloride (LiCl)	11.31 ± 0.31
	Potassium chloride (KCl)	85.11 ± 0.29
	Magnesium nitrate (Mg(NO₃))	54.38 ± 0.23
	Potassium acetate (CH₃COOK)	23.11 ± 0.25
30	Magnesium chloride (MgCl₂)	32.44 ± 0.14
	Lithium chloride (LiCl)	11.28 ± 0.24
	Potassium chloride (KCl)	83.62 ± 0.25
	Magnesium nitrate (Mg(NO₃)	51.40 ± 0.24
	Potassium acetate (CH₃COOK)	21.61 ± 0.53
55	Lithium chloride (LiCl)	11.03 ± 0.23
	Potassium chloride (KCl)	80.70 ± 0.35
	Sodium bromide (NaBr)	50.15 ± 0.65
	Magnesium chloride (MgCl₂)	29.93 ± 0.16
70	Lithium chloride (LiCl)	10.75 ± 0.33
70	Potassium chloride (KCl)	79.49 ± 0.57

Source: Greenspan (1977).

table_chartTable 2 Mathematical models for obtaining adsorption isotherms of Moringa oleifera L. grains.

Model Name	Model	Equation
BET¹	$X e = {\frac{1}{[(1 - a_{w}) (1 / a . b + ((a - 1) / a . b))]}}$	(1)
Chung-Pfost²	$X e = a - b l n [- (T + c) l n (a_{w})]$	(2)
Copace³	$X e = e x p [a - (b T) + (c a_{w})]$	(3)
Modified GAB⁴	$X e = (a . b . a_{w}) . \frac{(c / T)}{[1 - b . a_{w} + (c / T) . b . a_{w}] . (1 - b {. a}_{w})}$	(4)
Modified Henderson⁵	$X e = {\ln (1 - a_{w}) / [- a (T + b)]}^{1 / c}$	(5)
Sabbab⁶	$X e = a (a_{w}^{b} / T^{c})$	(6)
Sigma-Copace⁷	$X e = e x p {a - (b T) + [c \exp (a_{w})]}$	(7)
Modified Halsey⁸	$X e = {(\frac{\exp (a - (b . T))}{- \log (a_{w})})}^{1 / c}$	(8)
Andrade⁹	$X e = e x p {(a . a_{w}) + (T^{b}) + [{[\frac{(T - a_{w}}{a_{w}}]}^{b}]}^{c}$	(9)

Brunauer et al. (1938)¹; Chung and Pfost (1967)²; Corrêa et al. (1995)³; Van Den Berg (1984)⁴; Thompson et al. (1968)⁵; Mesquita et al. (2001)⁶; Corrêa et al. (1995)⁷; Iglesias and Chirife (1976)⁸; Andrade et al. (2017)⁹.

table_chartTable 3 Mathematical models adjusted to water adsorption experimental data of Moringa oleifera L. grains with parameters and adjustment evaluators.

Model	a	b	c	R² (%)	P (%)	SE (decimal)
BET	0.101	38.917	-	79.853	23.826	0.044
Chung-Pfost	0.239	0.038	47.259	93.609	12.603	0.025
Copace	-3.160	0.005	1.665	96.468	9.450	0.018
Modified GAB	0.045	0.825	2969.050	94.838	9.322	0.022
Modified Henderson	1.330	59.783	2.145	91.815	14.885	0.028
Sabbab	0.279	0.630	0.181	84.566	19.719	0.038
Sigma-Copace	-3.979	0.005	0.961	98.100	6.151	0.013
Modified Halsey	-5.610	0.009	2.182	97.724	6.718	0.015
Andrade	-1.098	0.049	-1.342	94.947	11.098	0.022

table_chartTable 4 Equilibrium water content estimated by the modified Halsey model for Moringa oleifera L. grains.

RH (decimal)	Temp (ᵒC)	Equilibrium water content (db) (calculated)	Equilibrium water content (db) (estimated)
0.113	20	0.056	0.049
0.544	20	0.085	0.088
0.851	20	0.154	0.162
0.113	30	0.051	0.047
0.514	30	0.080	0.081
0.836	30	0.157	0.148
0.110	55	0.043	0.042
0.502	55	0.062	0.072
0.807	55	0.132	0.123
0.108	70	0.037	0.039
0.795	70	0.107	0.112

table_chartTable 5 Water activity estimated by the modified Halsey model for Moringa oleifera L. grains according to equilibrium water content (db) and temperature (°C).

Equilibrium water content (db)	Temperature (ᵒC)
Equilibrium water content (db)	20	30	55	70
0.039	0.029	0.040	0.077	0.108
0.042	0.048	0.062	0.110	0.147
0.047	0.091	0.113	0.177	0.221
0.049	0.113	0.137	0.206	0.253
0.072	0.385	0.419	0.501	0.548
0.081	0.482	0.514	0.590	0.631
0.088	0.544	0.574	0.643	0.681
0.111	0.695	0.717	0.768	0.795
0.123	0.744	0.763	0.807	0.830
0.148	0.822	0.836	0.868	0.884
0.162	0.851	0.863	0.890	0.903

table_chartTable 6 Line slope coefficient, net isosteric heat, and integral isosteric heat of adsorption calculated and estimated by the model for Moringa oleifera L. grains.

Slope of the line	Net isosteric heat (kJ kg^-1)	Integral isosteric heat (kJ kg^-1) Calculated Q_st	Integral isosteric heat (kJ kg^-1) Estimated Q_st
-2632.5	-1215.952	-3613.589	-3553.410
-2265.5	-1046.434	-3444.072	-3438.915
-1780.1	-822.228	-3219.866	-3264.491
-1621.1	-748.786	-3146.424	-3200.425
-709.23	-327.593	-2725.231	-2743.308
-542.93	-250.779	-2648.417	-2641.701
-453.12	-209.296	-2606.934	-2585.648
-270.94	-125.147	-2522.785	-2476.250
-220.36	-101.784	-2499.422	-2449.681
-145.93	-67.405	-2465.043	-2417.785
-119.92	-55.391	-2453.029	-2409.627

X e = {\frac{1}{[(1 - a_{w}) (1 / a . b + ((a - 1) / a . b))]}}

X e = a - b l n [- (T + c) l n (a_{w})]

X e = e x p [a - (b T) + (c a_{w})]

X e = (a . b . a_{w}) . \frac{(c / T)}{[1 - b . a_{w} + (c / T) . b . a_{w}] . (1 - b {. a}_{w})}

X e = {\ln (1 - a_{w}) / [- a (T + b)]}^{1 / c}

X e = a (a_{w}^{b} / T^{c})

X e = e x p {a - (b T) + [c \exp (a_{w})]}

X e = {(\frac{\exp (a - (b . T))}{- \log (a_{w})})}^{1 / c}

X e = e x p {(a . a_{w}) + (T^{b}) + [{[\frac{(T - a_{w}}{a_{w}}]}^{b}]}^{c}

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