







































 

 

 
64 

© 2024 Conscientia Beam. All Rights Reserved. 

Nitrogen and sulphur release dynamics and kinetics in soils incubated with sulphur-
augmented nitrogen sources   

 

 

 Omogoye, 
Adewale Mubo1+ 

 Akinrinde, 
Ezekiel Akinkunmi2 

 Lawal, 
Babatunde  
Akeem3 

 Abdulraheem, 
Mukhtar 
Iderawumi4 

1,2Department of Crop and Horticultural Sciences, University of Ibadan, 
Ibadan, Nigeria. 
1Email: omogoye@yahoo.com  
2Email: akinainrindee@gmail.com  
3Department of Crop Production and Soil Science, Ladoke Akintola 
University of Technology, Ogbomoso, Nigeria. 
3Email: lawalba@gmail.com  
4Department of Electrical Engineering, International Joint Laboratory of 
Laser Technology in Agriculture, Henan Agriculture University, Zengzhou, 
China. 
4Email: abdulraheem@stu.henau.edu.cn  

 
(+ Corresponding author) 

 ABSTRACT 
 
Article History 
Received: 1 August 2024 
Revised: 30 September 2024 
Accepted: 10 October 2024 
Published: 21 October 2024 
 

Keywords 
Nitrogen sources 
Sulphur powder 
N and S dynamics 
N and S kinetics 
Order kinetics 
Potentially releasable quantity 
release rate constant. 

 
The study investigated N and S release dynamics and kinetics in soils incubated with 
sole and sulphur-augmented N fertilizer sources to evaluate their release patterns, 
potentially releasable quantities, and release rate constants. 50g of soil samples (from 
Ibadan and Ogbomoso, Nigeria) were measured into incubation cups and treated with 
Cattle Manure (CM) at 90 kg Nha-1, CM at 90 kg Nha-1+sulphur powder (SP) at 30 kg 
Sha-1, Cocoa Pod Powder (CPP) at 90 kg Nha-1, CPP at 90 kg Nha-1+SP at 30 kg Sha-1, 
NPK 20-10-10 at 90 kg Nha-1, NPK 20-10-10 at 90 kg Nha-1+SP at 30 kg Sha-1 and No 
Fertilizer Treatment (NFT). The incubated soils were moistened with distilled water at 
60% field capacity thrice per week throughout a 105-day incubation period under 
ambient laboratory conditions and were analysed for N and S contents at 21, 42, 63, 84, 
and 105 days. The experiment was a completely randomized design with three 
replicates. Data on N and S release were evaluated, and fitted into zero, first- and 
second order kinetics equations. Release dynamics of N followed the order; 
NPK+SP/NPK/CPP+SP/CPP>CM+SP/CM>NFT in soils of both locations, while 
orders of S release were CPP+SP/CPP>CM+SP>CM/NPK+SP>NPK>NFT and 
CPP+S/CPP/CM+SP>CM>NPK+SP>NPK>NFT in soils of Ibadan and Ogbomoso, 
respectively. The release of N and S conformed to zero, first, and second order kinetics 
with coefficients of determination (R2), ranging from 0.20 to 0.99. Therefore, soil 
incorporation of sole and sulphur-augmented CM and CPP could be substituted for sole 
and sulphur-augmented NPK 21 days before planting of N and S-demanding crops.  

 

Contribution/ Originality: Augmentation of fertilizer materials such as cattle manure and cocoa pod powder 

with sulphur powder and their comparison with sole and S-augmented NPK for nitrogen and sulphur release 

dynamics and kinetics studies have not been researched. 

         

1. INTRODUCTION 

Nitrogen (N) is an indispensable element and usually becomes the first to be limiting as crop cultivation 

intensifies. It is the most dynamic of all nutrients [1]. Its functions in plants are numerous. It is a constituent of 

chlorophyll, amino acids, nucleic acids, enzymes, and proteins [2]. It is responsible for leaf and root expansion, as 

Current Research in Agricultural Sciences 
2024 Vol. 11, No. 2, pp. 64-75 
ISSN(e): 2312-6418 
ISSN(p): 2313-3716 
DOI: 10.18488/cras.v11i2.3946 
© 2024 Conscientia Beam. All Rights Reserved. 

 
 
 

 
 
 
 

 

 
 
 
 

https://orcid.org/0000-0003-3294-4105
https://orcid.org/0000-0002-3498-4234
https://orcid.org/0000-0003-0357-992X
http://orcid.org/0000-0002-6745-378X
mailto:omogoye@yahoo.com
mailto:akinainrindee@gmail.com
mailto:lawalba@gmail.com
mailto:abdulraheem@stu.henau.edu.cn
https://www.doi.org/10.18488/cras.v11i2.3946


Current Research in Agricultural Sciences, 2024, 11(2): 64-75 

 

 
65 

© 2024 Conscientia Beam. All Rights Reserved. 

well as general growth and development of crops. Nitrogen deficiency causes many biochemical and physiological 

disturbances leading to the reduction in cell division rates and disruption in photosynthetic process. Roggatz, et al. 

[3]. Akanbi, et al. [4] reported that increased N levels led to an increase in photosynthetic rate and leaf area. In 

enhancing soil productivity, N application is crucial [5].  It plays an important role in synthesis of growth 

hormones such as auxin and takes part in regulation of metabolic activities [6]. Nitrogen, being a great 

determinant of crop’s yield, needs to be carefully managed amidst astronomically rising cost of inorganic sources of 

the element, which is prone to leaching and volatilization.  

Sulphur plays a key role in oil, protein, and chlorophyll syntheses. Higher oil content of seed crops due to 

sulphur application has been attributed to the influence of sulphur in rapid conversion of nitrogen to crude protein 

and finally to oil as brought about by acetic thiolinase, a sulphur-based enzyme in the presence of S, which converts 

acetyl Coenzyme-A to melonyl Coenzyme-A, rapidly resulting in higher oil content Krishnamurthy and Mathan 

[7]. Cecotti [8] reported that S plays an important role in plant metabolism as a component of proteins, 

glucosinolates, and other compounds that relate to several parameters determining the nutritive quality of plants. 

High yield and quality of oilseed crops are possible when crops have access to the optimum amount of sulphur [9]. 

Sulphur is a prominent component of various plant proteins and plays a critical role in root growth and seed 

production.  

It is the component of several amino acids (Cystine cysteine and methionine), which are the basic structural 

units of protein molecules and responsible for the development of taste and flavour in oilseed crops [10].  

Therefore, this study was carried out to evaluate (i) N and S release dynamics in soils incubated with sole and 

S-augmented N fertilizer sources and (ii) N and S kinetics of soils incubated with sole and S-augmented N fertilizer 

sources using kinetic equation models as bases for estimating their release potentials and rate constants. 

 

2. MATERIALS AND METHODS 

Soil samples were taken at 0-15 cm depth from two locations, namely Ibadan (7º22′N; 3º55′E) and Ogbomoso 

(8º07′N; 4º14′E) in southwestern Nigeria. Prior to incubation, soils were analysed. The pH (H2O) was determined 

with the aid of a pH meter buffered between pH 4 and 7. Total N was determined by macro-kjeldahl method as 

described by Bremner [11].  

Available P was determined by Bray-1 P method [12]. Exchangeable bases (Ca, Mg, K, and Na) were 

determined according to Jackson [13] using a 1M neutral ammonium acetate (1M NH4OAc pH 7.0) solution. 

Available sulphur was determined by turbimetric method [14]. Organic carbon was determined by wet dichromate 

method [15]. Texture was determined by Bouyoucos hydrometer method [16]. The computed textural 

components (% sand, % silt, and % clay) were finally input on texture check menu of Soil Kit App for confirmation 

of the textural class, thereby eliminating the rigour of tracing the textural class on textural triangle. Cattle manure 

(CM) was collected from Institute of Agricultural Research and Training, Ibadan, while cacao pod husk (CPH) was 

collected from fermentatory unit of Cocoa Research Institute of Nigeria (CRIN), Ibadan. The CPH was spread in 

windrow chamber of composting section of the screenhouse at the back of the Agronomy Building, University of 

Ibadan, Nigeria to air-dry for four weeks and was later ground into powder to form Cocoa Pod Powder (CPP). 

Analysis for nutrient contents (N, P, K, Ca, Mg, S, Fe, Mn, Zn, Cu) was done using prescribed procedures of 

Association of Official Analytical Chemist (A. O. A. C.) [17].  

In the incubation study, 50g of soil sample was measured into incubation cups (4 cm diameter x 6.5 cm height) 

and treated with Cattle Manure (CM) at 90 kg N ha-1, CM at 90 kg N ha-1 + sulphur powder (SP) at 30 kg S ha-1, 

Cocoa Pod Powder (CPP) at 90 kg N ha-1, CPP at 90 kg N ha-1 + SP at 30 kg S ha-1, NPK 20-10-10 at 90 kg Nha-1, 

Nitrogen-phosphorus-potassium (NPK) fertilizer grade 20-10-10 at 90 kg N ha-1 + SP at 30 kg S ha-1 and No 

Fertilizer Treatment (NFT). The incubated soils were moistened with distilled water at 60% field capacity thrice 

per week throughout a 105-day incubation period under ambient laboratory conditions (temperature; 22-280C, 



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relative humidity; 82- 89%). The experiment was completely randomized design with three replicates (five 

incubation cups per replicate to cater for five-time incubation periods of 21, 42, 63, 84, and 105 days). Two hundred 

and ten incubation cups (7 fertilizer treatments x 3 replicates x 5 incubation periods x 2 location soils) were used. 

Total N and available S contents of incubated soils were determined at 21, 42, 63, 84 and 105 days of incubation 

(DOI) to ascertain the extent of their release dynamics.  

Furthermore, nitrogen and sulphur release patterns were subjected to kinetics study by fitting their release 

data into zero-, first- and second- order kinetics using the relationship denoted by the equations [18, 19] stated 

below:  

𝑍𝑒𝑟𝑜 − 𝑜𝑟𝑑𝑒𝑟:  𝑞𝑡  =  𝑞0 –  𝑘0𝑡  (1) 

𝐹𝑖𝑟𝑠𝑡 − 𝑜𝑟𝑑𝑒𝑟: 𝑙𝑛(𝑞𝑡)  =  𝑙𝑛 (𝑞0)  −   𝑘1𝑡 𝑜𝑟 𝑙𝑜𝑔𝑒  𝑞𝑡  =  𝑙𝑜𝑔𝑒  𝑞𝑜 – 𝑘1𝑡 𝑜𝑟 𝑞1  =  𝑞0𝑒−𝑘1𝑡  (2) 

𝑆𝑒𝑐𝑜𝑛𝑑 − 𝑜𝑟𝑑𝑒𝑟: 1/𝑞𝑡  =  1/𝑞0 – 𝑘2𝑡    (3) 

Where q0 is the estimated quantity or releasable potential of nutrient initially present in the incubated soil at 

day 1, qt is the amount present after a specific time of incubation, and t is time of incubation (21, 42, 63, 84, 105), 

while k0, k1 and k2 are zero, first- and second- order kinetics constants, respectively. The essence of the kinetics 

study of N and S is to determine whether the release of each of the nutrients is independent of its initial entire 

concentration (zero-order) or dependent on its initial concentration with constant proportion of release (first-order) 

or dependent on concentration of one nutrient and the other (second-order) if they interact. Therefore, a 

mathematical description of N and S release could provide useful indices for estimating their release potentials and 

rates in soils. 

As regards zero-order kinetics, qt values were plotted against days of incubation (DOI) values for determining 

their coefficients of determination (R2) and equations on regression curves, q0 was estimated from the equation of 

the curve at first day, k0 was derived from the gradient of the curve by dividing the estimated q0 with mean interval 

of DOI. For first-order, ln qt values were plotted against t values with R2 values and equations determined from the 

curve as well; the ln q0 was determined from the equation of the curve for the first day and converted to q0 value as 

elnq0, while k1 was determined by dividing the slope with mean interval of DOI.  

For second-order kinetics, 1/qt values were plotted against t (DOI) values with their R2 values and equations 

displayed by regression curve; 1/q0 was determined from the equation of the curve and converted to q0 value as 

inverse of 1/q0.
 The second-order constant (k2) was determined by dividing the slope with mean interval of DOI as 

well. The release dynamics and kinetics studies are useful for the purpose of determining periodic release level, 

initial releasable potential, and kinetics rate constant prior to growing a crop at the field locations from where such 

soils are collected. 

 

3. RESULTS AND DISCUSSION 

3.1. Pre-Incubation Soil Properties 

The pH (H2O) was 6.1 (slightly acidic) in soil of Ibadan, whereas it was 5.9 (moderately acidic) in soil of 

Ogbomoso (Table 1). The soil of Ibadan had higher organic carbon (12.2 g/kg) than that of Ogbomoso, which was 

valued of 11.7 g/kg. The available phosphorus was above critical level of 10.0 mg/kg stated by Akinrinde and 

Obigbesan [20]. The total N values of soils from the two locations were low (1.3, 1.2) considering the critical 

values of 1.5g/kg [20, 21]. The soils of Ibadan and Ogbomoso had exchangeable potassium of 0.2 cmol/kg, which 

was above critical level of 0.15 cmol/kg according to Akinrinde and Obigbesan [20] and Chude, et al. [21]. 

Available sulphur of soil from Ibadan and Ogbomoso had lower values of 6.1 and 5.6 mg/kg, respectively, than 10 

mg/kg critical level stated by Oseni, et al. [22]. The soils were sandy loam and loamy sand for Ibadan and 

Ogbomoso, respectively.  

 

 



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Table 1. Pre-incubation soil properties of Ibadan and Ogbomoso locations. 

Parameter Ibadan Ogbomoso 

pH (H2O) 6.1 5.9 
Organic C (g/kg) 12.2 11.7 
Total N (g/kg) 1.3 1.2 
Available nutrients (mg/kg) 
P 12.0 13.0 
S 6.1 5.6 
Exchangeable cations (cmol/kg) 
Ca2+ 1.6 1.4 
Mg2+ 1.4 1.2 
K+ 0.2 0.2 
Na+ 0.2 0.1 
Exchangeable acidity (cmol/kg) 0.1 0.2 
ECEC (cmol/kg) 3.5 3.1 
Extractable micronutrients (mg/kg) 
Cu 1.5 3.1 
Fe 21.0 22.0 
Mn 3.5 3.0 
Zn 48.2 50.1 
Particle size analysis (g/kg) 
Sand 673 768 
Silt 131 122 
Clay 196 110 
Textural class Sandy loam Loamy sand 

 

 

Table 2. Nutrient contents of cattle manure, cocoa pod powder and NPK. 

Nutrient Cattle manure Cocoa pod powder NPK 

g/kg 
N 5.0 4.0 200.0 

P2O5 2.0 5.0 100.0 
K2O 4.0 7.0 100.0 

Ca 1.3 1.6 0.0 
Mg 6.0 8.0 0.0 

mg/kg 
S 3.0 7.0 0.0 

Zn 46.0 58.0 0.0 
Cu 22.0 36.0 0.0 
Fe 11.0 7.0 0.0 
Mn 36.0 31.0 0.0 

 

Note: NPK- nitrogen-phosphorus-potassium fertilizer grade 20-10-10. 

                            

3.3. Influence of Nitrogen and Sulphur Application on Total Nitrogen Across Incubation Periods 

In soils of Ibadan location, all fertilizers improved total N status of the soil across incubation periods, as shown 

in Table 3. Cow dung manure-CM increased total N from 1.75 g/kg at 21 DOI to 2.63 g/kg at 105 DOI (34.6-

102.3%) over initial value of 1.30 g/kg prior to incubation. Soil treated with CM + SP had total N increase of 34.6-

105.4% (1.75–2.67 g/kg). Increments of 52.3–126.1% (1.98–3.07 g/kg) and 40.7–141.5% (1.83–3.14 g/kg) were 

observed in soil treated with CPP and CPP + SP, respectively (Table 3). On the other hand, NPK and NPK + SP 

fertilizers increased total N with percentage values of 66.9–140.8% (2.17–3.13 g/kg) and 63.1–142.3% (2.12–3.15 

g/kg). In soils with NFT, total N was raised from 1.61 g/kg at 21 DOI to 1.90 g/kg at 105 DOI (23.8–53.8%). Up 

to 63 DOI, NPK and NPK + SP treated soils outperformed others. However, as of 84 DOI, NPK and NPK + SP 

were no longer superior to CPP and CPP + SP in terms of N release but to CM and CM + SP, which were better 

than NFT.     

 

 

 



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Table 3. Effects of fertilizers on total nitrogen (g/kg) at successive incubation periods in soils of Ibadan and Ogbomoso locations 

Treatment 
Ibadan Ogbomoso 

Days of incubation 

 21 42 63 84 105 21 42 63 84 105 
CM 1.75d 2.19c 2.58c 2.60d 2.63b 1.64d 2.10c 2.43c 2.49d 2.58b 
CM + SP 1.75d 2.17c 2.62c 2.63d 2.67b 1.60d 2.12c 2.49c 2.48d 2.57b 
CPP 1.98b 2.62b 2.85b 2.88b 3.07a 1.87b 2.42b 2.67b 2.69b 2.89a 
CPP + SP 1.83c 2.65ab 2.87b 2.91ab 3.14a 1.79c 2.46ab 2.69b 2.75ab 2.94a 
NPK 2.17a 2.71a 2.96a 2.99a 3.13a 2.11a 2.56a 2.82a 2.89a 3.10a 
NPK + SP 2.12a 2.67a 2.99a 3.01a 3.15a 2.03a 2.55a 2.78a 2.93a 3.15a 
NFT 1.61e 1.71d 1.82d 1.87e 1.90c 1.52e 1.70d 1.77d 1.82e 1.88c 
Note: CM- cattle manure at 90 kg N/ha, CPP- cattle manure at 90 kg N/ha, NPK20-10-10 – nitrogen phosphorus potassium fertilizer grade 

20-10-10 at 90 kg N/ha, SP- Sulphur powder at 30 kg S/ha.  
Means with similar letter along a column within a group are not significantly different according to Tukey pairwise comparison at 5% 
level of significance. 

 

 

In the soils of Ogbomoso experimental location, all fertilizers enhanced total N of the soil across successive 

incubation periods (3). Treatment CM increased total N from 1.64 g/kg at 21 DOI to 2.58 g/kg at 105 DOI (26.7–

115.0%) over initial value of 1.20 g/kg before incubation. Soil treated with CM + SP had total N rise of 33.3-114.2% 

(1.60–2.57 g/kg). Increases of 55.8 – 140.8% (1.87–2.89 g/kg) and 49.1–145.0% (1.79–2.94 g/kg) were observed in 

soil treated with CPP and CPP + SP, respectively. Likewise, NPK and NPK + SP fertilizers increased total N by 

75.8 – 158.3% (2.11–3.10 g/kg) and 69.2–162.5% (2.03–3.15 g/kg). In NFT soil, total N was raised from 1.52 g/kg 

at 21 DOI to 1.88 g/kg at 105 DOI (26.6–56.7%). At 21 DOI, NPK and NPK + SP outclassed other fertilizers as 

regards N release, but as from 42 DOI, CPP, CPP + SP, NPK, and NPK + SP incubated soils were similar in their 

N release ability till 105 DOI. There was no difference between CM and CM + SP treatments, though higher than 

NFT. 

 

3.4. Influence of Nitrogen and Sulphur Application on Available Sulphur (S) Across Incubation Periods 

In soils of Ibadan location, CM application increased the available S from pre-incubation value of 6.1 mg/kg to 

6.89 mg/kg at 21 DOI by 13.0% and continued till 105 DOI when available S value reached 9.66 mg/kg, indicating 

58.3% over the pre-incubation value (Table 4). Across incubation periods, similar increment trends were observed 

for other treatments. Soil treated with CM + SP enhanced S by 25.4–66.4% (7.53–10.41 mg/kg) compared with 

initial value (6.1 mg/kg) before incubation. Incubation of the soil with CPP increased S from 7.25 mg/kg at 21 DOI 

to 10.38 mg/kg at 105 DOI representing 18.9–70.1% increment in comparison with value prior to incubation. The 

fertilizer CPP + SP improved S with range of 23.0–78.3% (7.50–10.88 mg/kg while NPK and NPK + SP fertilizers 

resulted in rise of available S of 13.0 – 28.0% (6.83 – 7.81 mg/kg) and 17.0–48.5% (7.14–9.06 mg/kg), respectively. 

In untreated soil, an increment of 3.6–10.8% (6.32–6.76 mg/kg) was observed. The order of S enhancement was 

CPP + SP/CPP > CM + SP > CM/NPK + SP > NPK > NFT.In soils of Ogbomoso, CM application increased the 

available S from pre-incubation value of 5.2 mg/kg to 6.05 mg/kg at 21 DOI by 8.0% and continued till 105 DOI 

when the value reached 9.02 mg/kg, signifying 61.1 % when compared with the pre-incubation value of 5.7 mg/kg. 

Soil treated with CM + SP enriched S by 16.4–78.4% (6.52-9.99 mg/kg) when matched with initial value prior to 

incubation. Incubation of the soil with CPP increased S from 6.04 mg/kg at 21 DOI to 9.84 mg/kg at 105 DOI, 

signifying 14.3–75.3% increment in comparison with value before incubation. The fertilizer CPP + SP improved S 

with range of 12.9–78.9% (7.50–10.88 mg/kg whereas soil incubated with NPK and NPK + SP resulted in an 

increase of available S by 6.1.0–26.6% (5.84–7.09 mg/kg) and 6.3 – 35.7% (6.25–7.6 mg/kg) respectively. Untreated 

soil had an increment of 3.6–10.8% (6.32–6.76 mg/kg). The order in which S enhancement occurred was CPP + 

SP/CPP/CM + SP > CM > NPK + SP > NPK > NFT. 

 

 
 
 



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Table 4. Effects of fertilizers on available Sulphur (mg/kg) at successive incubation periods in soils of Ibadan and Ogbomoso locations 

Treatment 
Ibadan Ogbomoso 

Days of incubation 

 21 42 63 84 105 21 42 63 84 105 
CM 6.89de 7.59c 9.10b 9.76b 9.66e 6.05bc 6.35bc 8.66ab 9.02b 9.02b 
CM + SP 7.53a 7.89ab 9.45a 10.15b 10.14b 6.52a 6.82b 8.98a 9.85a 9.99a 
CPP 7.25bc 7.76bc 9.28ab 10.88a 10.88a 6.04bc 6.30c 8.42bc 9.42ab 9.84a 
CPP + SP 7.50ab 8.03a 9.54a 10.95a 10.88a 6.32ab 7.55a 8.70ab 9.62a 10.02a 
NPK 6.83e 7.03d 7.57d 7.79d 7.81d 5.64d 5.98e 6.96de 7.01d 7.09d 
NPK + SP 7.14cd 7.62c 8.81c 8.81c 9.06d 5.95c 6.13de 7.24cd 7.46c 7.60c 
NFT 6.32f 6.29e 6.54e 6.75e 6.76e 6.05bc 6.35bc 8.66ab 9.02b 9.02b 

 

Note: CM- cattle manure at 90 kg N/ha, CPP- cattle manure at 90 kg N/ha, NPK20-10-10 – nitrogen phosphorus potassium fertilizer grade 20-10-10 at 
90 kg N/ha, SP- Sulphur powder at 30 kg S/ha.  
Means with similar letter along a column are not significantly different according to Tukey pairwise comparison at 5% level of significance. 

 

3.5. Kinetics of Nitrogen (N) Release from Fertilizers across Incubation Periods 

Figures 1, 2, and 3 present zero, first- and second-order kinetics evaluations of N, respectively, throughout the 

incubation periods in soils of Ibadan and Ogbomoso locations. In soil of Ibadan location, the data fitted into 

regression curves indicated that N release from all fertilizers complied with zero, first, and second order kinetics 

considering the values of their respective significant coefficients of determination (R2) within the ranges of 0.58 – 

0.94, 0.58 – 0.91, and 0.57 – 0.96, while their release kinetics constants (k0, k1, k2) ranged from 0.0053 to 0.0175, 

0.0008 to 0.0056, and 2.9 x 10-10 to 0.0007 g/kg/day, respectively for zero, first, and second order kinetics along 

with their estimated releasable quantity-q0 of 1.17 – 200.92, 1.18 – 200.92, and 1.19 – 200.0 g/kg (Table 5). In soils 

of Ogbomoso location, N release from incubated soils was suitably described by zero, first, and second-order 

kinetics models with R2 values ranging from 0.50–0.89. As regards first and second order kinetics, all treatments 

conformed to respective R2 values of 0.86–0.92 and 0.86–0.95, respectively. Kinetics constants ranged from 0.0054 

to 0.0165, 0.0009 to 0.0038, and 2.85 x 10-10 to 0.0085 g/kg/day, respectively, for zero, first- and second-order 

kinetics (Table 6). The estimated releasable quantities (q0) were of the ranges 0.98–200.81, 0.90–200.82 and 0.79– 

200.0 g/kg for zero, first- and second-order kinetics, respectively (Table 6). 

 

 
Figure 1. Zero order kinetics of nitrogen in soils of Ibadan and Ogbomoso locations. 

Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, 
SP- Sulphur powder. 

 



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Figure 2. First order kinetics of nitrogen in soils of Ibadan and Ogbomoso locations. 

Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, SP- Sulphur powder. 

 

 
Figure 3. Second order kinetics of nitrogen in soils of Ibadan and Ogbomoso locations. 

Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, SP- Sulphur powder. 

 

 

 

 

 



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Table 5. Releasable potential of nitrogen (q0), kinetics constants (k0 k1 & k2) and R2 for zero, first and second order kinetics in 
soil of Ibadan location. 

Fertilizer 

Zero order First order Second order 

q0 
g/kg 

k0 
g/kg/Day 

R2 
q0 

g/kg 
k1 

g/kg/Day 
R2 

q0 
g/kg 

k2 
g/kg/Day 

R2 

CM 6.11 0.013 0.877 6.11 0.0024 0.887 6.12 0.0054 0.631 
CM+SP 6.12 0.0135 0.939 6.13 0.0025 0.893 6.13 0.0004 0.901 
CPP 5.27 0.0119 0.611 5.33 0.0027 0.591 5.40 0.0006 0.570 
CPP+SP 5.34 0.0135 0.718 5.41 0.0031 0.684 5.51 0.0007 0.648 
NPK 200.81 0.0175 0.577 200.80 0.0009 0.576 200.0 2.9×10-10 0.574 
NPK+SP 200.92 0.0166 0.847 200.92 0.0008 0.848 200.0 2.9×10-10 0.849 
NFT 1.17 0.0053 0.859 1.18 0.0056 0.914 1.19 0.0062 0.955 
SE ± 36.2 0.002 0.053 36.2 0.0007 0.056 40.9 0.001 0.061 

 

 

Table 6. Releasable potential of nitrogen (q0), kinetics constants (k0 k1 & k2) and R2 for zero, first and second order 
kinetics in soil of Ogbomoso location. 

Fertilizer 

Zero order First order Second order 

q0 
g/kg 

k0 
g/kg/ 
Day 

R2 
q0 

g/kg 
 

k1 
g/kg/ 
Day 

R2 
q0 

g/kg 
k2 

g/kg/Day 
R2 

CM 5.96 0.0127 0.888 5.98 0.0025 0.919 6.05 0.0055 0.950 
CM+SP 6.03 0.0134 0.882 6.03 0.0025 0.892 6.04 0.0046 0.901 
CPP 4.91 0.0152 0.870 4.91 0.0036 0.897 4.92 0.0085 0.921 
CPP+SP 4.94 0.0160 0.883 4.95 0.0038 0.908 4.97 0.0230 0.930 
NPK 200.81 0.0165 0.856 200.82 0.0009 0.857 200.0 2.86 × 10-10 0.858 
NPK+SP 200.80 0.0167 0.894 200.80 0.0009 0.894 200.0 2.85 × 10-10 0.894 
NFT 0.98 0.0054 0.496 0.90 0.0006 0.349 0.79 0.0080 0.184 
SE ± 36.2 0.0020 0.055 36.2 6 × 0-4 0.078 36.1 0.002 0.104 

 Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, SP- Sulphur powder, NFT-
No fertilizer treatment. 

 

 

3.6. Kinetics of Sulphur (S) Release from Fertilizers across Incubation Periods 

The zero and first and second order kinetics analysis of S across the incubation periods in soil of Ibadan and 

Ogbomoso locations are shown in Figures 4 and 5, respectively. In soils of Ibadan location, S release in soils 

incubated with various fertilizers was in conformity with zero, first- and second-order kinetics when put into 

consideration the values of their corresponding coefficients of determination (R2) which fell within the ranges of 

0.78–0.95, 0.31–0.96 and 0.77–0.95.  

 

 
Figure 4. (a)  Zero order and  (b) first order; kinetics of sulphur in soils of Ibadan and Ogbomoso locations. 



Current Research in Agricultural Sciences, 2024, 11(2): 64-75 

 

 
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© 2024 Conscientia Beam. All Rights Reserved. 

Kinetics constants (k0, k1, k2) ranged from 0.005 to 0.038, 0.0015 to 0.0089 and 0.00009 to 0.0007 mg/kg/day, 

respectively for zero, first- and second-order kinetics, while their estimated initial (releasable) quantity (q0) had the 

range of 8.9 – 27.97, 5.88–28.02 and 5.91–28.09 g/kg in soil of Ibadan location (Table 7).  

 

 
Figure 5. Second order kinetics of sulphur in soils of Ibadan and Ogbomoso locations. 

Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, SP- Sulphur powder. 

 

Table 7. Releasable potential of sulphur (q0), kinetics constants (k0 k1 & k2) and R2 for zero, first and second order kinetics in soil of Ibadan 
location. 

Fertilizer 

Zero order First order Second order 

q0 
mg/kg 

k0 
mg/kg/Day 

R2 
q0 

mg/kg 
k1 

mg/kg/Day 
R2 

q0 
mg/kg 

k2 
mg/kg/Day 

R2 

CM 8.98 0.035 0.947 9.08 0.0049 0.952 9.24 0.00070 0.952 
CM+SP 23.75 0.038 0.943 13.62 0.0055 0.313 23.81 0.00008 0.953 
CPP 13.10 0.049 0.962 18.28 0.0089 0.785 13.57 0.00009 0.940 
CPP+SP 27.97 0.052 0.890 28.02 0.0029 0.877 28.09 0.00047 0.863 
NPK 15.87 0.016 0.917 5.88 0.0032 0.940 5.91 0.00063 0.916 
NPK+SP 20.78 0.029 0.913 20.05 0.0015 0.919 20.79 0.00008 0.923 
NFT 6.02 0.005 0.775 6.02 0.0009 0.771 6.02 0.00014 0.765 
SE ± 3.01 0.006 0.020 3.10 0.0009 0.090 3.38 0.00001 0.026 
Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, SP- Sulphur powder, NFT- No fertilizer 

treatment. 
 

 

In soil of Ogbomoso location, S release from fertilizers complied with the various kinetics orders, with R2 values 

ranging from 0.88–0.98, 0.87–0.99 and 0.88-0.99 for zero, first and second order kinetics models. Kinetics constants 

ranged from 0.012 to 0.046, 0.001 to 0.0058 and 0.00007 to 0.0009 mg/kg/day, respectively for zero, first- and 

second-order kinetics, respectively (Table 8).  

 

Table 8. Releasable potential of sulphur (q0), kinetics constants (k0 k1 & k2) and R2 for zero, first and second order kinetics in soil 
of Ogbomoso location. 

Fertilizer 

Zero order First order Second order 

q0 
mg/kg 

k0 
mg/kg/ 

Day 
R2 

q0 
mg/kg 

k1 
mg/kg/ 

day 
R2 

q0 
mg/kg 

k2 
mg/kg/ 

Day 
R2 

CM 8.77 0.038 0.882 8.92 0.0058 0.877 9.15 0.00090 0.876 
CM+SP 23.66 0.046 0.936 23.73 0.0022 0.936 23.87 0.00010 0.934 
CPP 13.00 0.046 0.937 13.20 0.0045 0.935 13.48 0.00040 0.930 
CPP+SP 27.60 0.045 0.983 27.65 0.0018 0.985 28.78 0.00007 0.987 
NPK 5.64 0.016 0.889 5.67 0.0034 0.887 5.71 0.00070 0.884 
NPK+SP 20.50 0.020 0.894 20.51 0.0010 0.897 20.53 0.00005 0.899 
NFT 5.61 0.012 0.930 5.80 0.0023 0.930 5.65 0.00047 0.930 
SE ± 3.39 0.006 0.014 3.38 0.0006 0.014 3.48 0.00001 0.017 
Note: CM- Cattle manure, CPP- Cocoa pod powder, NPK- Nitrogen phosphorus potassium fertilizer 20-10-10, SP- Sulphur powder, 

NFT- No fertilizer treatment. 
 



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The estimated releasable potentials (q0) were of the ranges 5.61 – 27.6, 5.67 – 27.65 and 5.65 – 28.78 g/kg for 

zero, first- and second-order kinetics, respectively. The release dynamics and kinetics analysis provided basis of 

estimation for release pattern prior to field evaluation in that the releasable rate constant could be used to estimate 

the potentiality of soil N and S status of the field at a particular day even besides specified days of incubation. The 

kinetics evaluation indicated that pre-incorporation of sole and S-augmented CM and CPP could be done 21 days 

prior to field trials. 

In the incubation study, all fertilizers (sole and sulphur-augmented cattle manure-CM, cocoa pod powder-CPP 

and NPK) enhanced total N and available S of the soil across successive incubation periods in soils of Ibadan and 

Ogbomoso locations. This can be ascribed to periodic release of the elements in the fertilizer over time. The release 

dynamics revealed that N enhancement followed the order: NPK + SP/NPK/CPP + SP/CPP > CM + SP/CM > 

NFT in soils of the two locations, implying that NPK and NPK + SP treatments were comparable to those of CPP 

+ SP and CPP even though they had higher values of N contents at the end of the incubation period. The orders of 

S enhancement were CPP+SP/CPP > CM+SP > CM/NPK+SP > NPK> NFT and CPP+SP/CPP/CM+SP > CM 

> NPK+SP > NPK > NFT in soils of Ibadan and Ogbomoso, respectively. Among fertilizer treatments, it was 

evident that NPK was least in terms of S enhancement. This can be ascribed to the fact that NPK did not contain 

sulphur, unlike other fertilizer sources, even though it is not unexpected that N constituent of NPK would interact 

with the inherent soil S to an extent. In soil of Ibadan and Ogbomoso locations, kinetics of N and S release of all 

fertilizers conformed with zero, first, and second order kinetics considering the values of their respective significant 

coefficients of determination (R2) within the range of 0.20–0.99 across location soils. The implication is that 

releasable potentials of N and S did not depend on initial contents of the elements in incubated soils, and their 

release rates differed from one another with occurrence of interaction between N and S. Ghafoor, et al. [23] had 

earlier reported that zero and first-order kinetics equations suitably described K release from various organic 

manures. According to Dey, et al. [19] zinc release from vermicompost and biochar was in conformitywith first-

order release kinetics like that of magnesium from farmyard manure, whereas S release from vermicompost, 

farmyard manure, mushroom compost, poultry manure, biogas slurry, biochar, and Lantana spp suitably fitted well 

into second-order kinetics in addition to zero and first-orders. 

 

4. CONCLUSION 

This study established that N and S release from sole and sulphur-augmented cattle manure, cocoa pod powder, 

and NPK 20-10-10 suitably fitted well into zero, first- and second-order kinetics, thus determining periodic release 

level, initial releasable potential, as well as kinetic rate constant, all of which could serve as bases for timing of pre-

planting soil incorporation of the fertilizer materials for crop growth, which require N and S for optimal 

performance. Sulphur-augmented cattle manure and cocoa pod powder are substitutes of sulphur-augmented NPK 

for production of crops with high N and S demand and could be applied at least 21 days before planting. 

 

Funding: This study received no specific financial support.    
Institutional Review Board Statement: Not applicable. 
Transparency: The authors state that the manuscript is honest, truthful, and transparent, that no key 
aspects of the investigation have been omitted, and that any differences from the study as planned have been 
clarified. This study followed all writing ethics. 
Competing Interests: The authors declare that they have no competing interests. 
Authors’ Contributions: All authors contributed equally to the conception and design of the study. All 
authors have read and agreed to the published version of the manuscript. 

 

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