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Original article
13 (
11
); 7759-7772
doi:
10.1016/j.arabjc.2020.09.009

Role of cationic moiety in phosphate fertilizers’ molecules on their solution behavior in terms of volumetric and acoustic parameters at different temperatures and atmospheric pressure

, ,
a Department of Chemistry, Lahore College for Women University, Jail Road, Lahore 54000, Pakistan
b Department of Chemistry, Govt College University, Faisalabad, Pakistan

⁎Corresponding author. bnbsk@yahoo.co.uk (Bushra Naseem)

Received: , Accepted: ,
© The Author(s) 2020
Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

Ultrasonic parameters are very useful tools used to study the physic-chemical behavior and molecular interactions of various liquid mixtures. More than 50% problems of irrigated areas are associated with cultivated land and they frequently occur due to salinity. Application of fertilizers into agricultural land could be a remedy for soil salinity by providing essential nutrients to plants. In this research paper, ultrasonic and volumetric properties of phosphate based fertilizers of different molecular compositions at different temperatures have been studied. This is experimental based work; this knowledge can be employed in formulation of fertilizers according to the nature of their application which could enhance fertilizer’s activity either in terms of nutrients development or to control the salinity of soil. Results obtained from calculated ultrasonic and volumetric parameters indicated presence of strong interactions in aqueous fertilizer solutions which depends upon nature of molecules. Among presently studied phosphate fertilizers i.e. triple superphosphate, nitrophosphate and diammonium phosphate, maximum molecular interactions were observed in aqueous triple super phosphate solutions due to the presence of highly charged cationic specie i.e. calcium ions, which can also be used to control the salinity of soil using electrostatic interactions among saline salts and charged cationic species.

Keywords

Phosphate fertilizers
Ultrasonic parameters
Partial molar expansibility
Compressibility factor
Hydration number
1

1 Introduction

During recent years, the acoustic studies have found extensive applications in characterizing the aspects of physicochemical behavior and to predict the solute–solute, solute–solvent and ion–solvent interactions in aqueous, non-aqueous and mixed solutions. The various parameters derived from measurements of speed of sound are known to give valuable information regarding different types of intermolecular interactions existing in solutions. Also spectral techniques like UV–Visible may be productive in order to explore our knowledge regarding solution behavior and presence of various molecular interactions among different components of mixture.

Fertilizers are mainly used in agricultural land to supply the micro and macro nutrients for crop production, to provide better plant nutrition and to increase the fertility of saline soil (Nunes et al., 2014). Numerous factors are involved in plant response to fertilizers under saline, sodic, or waterlogged conditions so a suitable fertilizer should be used for this purpose. Efficiencies of fertilizers applied to salt – affected soils are lower than when applied to non-saline soils. A decrease in the ability of the plants to absorb K or NH4 usually takes place in saline soils containing excess Na, Mg, or Ca. Also, P absorption may be decreased in presence of excess Cl− or SO4−. Application of K, NH4 or P fertilizers not only corrects their deficiencies but also decreases the adverse effects of Na, Cl, or SO4− on the plants (Naseem and Arif, 2017).

Phosphorus being a macro nutrient is a multivalent element in periodic table with non-metallic characteristics significant for a living system. Phosphorus is found to be an essential element in growth of plants and it plays an important role in physiological functions related to energy transformations (Chien et al., 2011). Application of phosphate (P) to plants in the form of synthetic fertilizers has become very common practice in agro ecosystem (Nunes et al., 2014; Gupta et al., 2014; Cao et al., 2003).

When applied to soil, several types of interactions occur among ions of fertilizer molecules and water. These types of interactions need a thorough investigation, the basis of solute–solute interactions among functional groups of macro molecules may arise from any specific interactions which include dipole-diploe, dipole induced dipole, ion–dipole, hydrogen bonding and charge transfer interactions. It is desirable to employ simple, low cost and rapid techniques such as ultrasonic method to study the miscibility of macromolecular blends. Studies on various types of intermolecular interactions existing among phosphate fertilizers and water molecules in solution using data of thermo physical properties like density and sound velocity of aqueous phosphate fertilizers solutions may provide useful information about the efficiency of different phosphate fertilizers. This knowledge could be helpful in understanding the role of fertilizers to control soil salinity.

A detailed literature survey indicated that the role of fertilizers or pesticides for reducing the toxic effects of heavy metals present in soil and also their role for increasing the crop yield is being studied for many years. Further experiments have been performed for the identification and quantification of specific forms of organic phosphorus in organic fertilizers and soils (Campos, 2002; Thawornchaisit and Polprasert, 2009; Annaheim et al., 2015). Recently, role of a phosphate fertilizer in order to remove or to reduce soil salinity has also been investigated in terms of intermolecular interactions prevailing among fertilizer molecule and saline salts usually present in saline soil (Naseem and Arif, 2017), there is a severe lack of study on interaction of phosphate fertilizers in aqueous solutions.

Therefore, present study is aimed to explore the comparative efficiency of different phosphate fertilizers like triple super phosphate, di ammonium phosphate and nitro phosphate for improving the crop production in terms of intermolecular interactions present in their solutions. Knowledge about thermo physical properties provides an insight into molecular interactions in solutions and effect of different parameters on interactions which could be helpful for choosing a suitable fertilizer for a specific soil under ambient conditions of temperature and pressure. In present study three phosphate fertilizers i.e. di ammonium phosphate (DAP), triple super phosphate (TSP) and nitro phosphate have been used. Chemical structure of three phosphate fertilizers is shown in Fig. 1.

Chemical structures of phosphate fertilizers.
Fig. 1
Chemical structures of phosphate fertilizers.

Volumetric and acoustic parameters of solutions are governed by variation in density and sound velocity passing through solutions. Volumetric properties e.g. apparent and partial molar volume, Hepler’s constant, thermal expansion coefficient and so on, while acoustical properties such as compression factor, hydration number, acoustic impedance and relative association etc. are indicative of intermolecular interactions present in solutions (Sadeghi and Goodarzi, 2008; Omota et al., 2009).

2

2 Materials and methods

2.1

2.1 Materials

Fertilizers (triple superphosphate, di ammonium phosphate and nitro phosphate) used were Sigma Aldrich products. In order to minimize the experimental or purity errors, glassware used in the experiment was washed with de-ionized water and then dried in oven. In present study for preparation of solutions de-ionized water having conductivity of 1.5 × 10−4 Ω−1 m−1 was used.

2.2

2.2 Methods

Instrument used in present study is Anton paar density and sound velocity analyzer (DSA 5000 M) and is very accurate and precise. Density (ρ) and ultrasonic velocity (u) of phosphate fertilizer’s solutions in water was measured at different temperatures with single sample solution. Oscillation frequency of U-shaped tube in instrument determines the density of sample and propagation time technique is used for measuring speed of sound waves passing through the sample being injected into the instrument. Fundamental frequency of instrument for sound velocity measurement is 3 MHz. Thus, the sound velocity is obtained by dividing the known distance between transmitter and receiver by the measured propagation time of the sound waves up to 0.5 m s−1 accuracy and 0.1 ms−1 repeatability. The accuracy and repeatability of DSA 5000 M for density are 5 × 10−6 gcm−3 and 5 × 10−6 gcm−3 respectively. Accuracy in Temperature is ±0.01 K (Rajagopal and Edwin Gladson, 2011). The weighing of chemicals was done by Wiggen Hauser electronic balance (model no. WH180-4) with a precision of ±0.0001 g. The measured densities and ultrasound speeds were utilized in determining volumetric and acoustical properties of solutions. The standard uncertainties in molality (m), density (ρ), sound velocity (u), and temperature (T) and pressure (P) are ±0.000090 mol·kg−1, ±0.66 × 10−6 g·cm−3, ±0.029 m·s−1, ±10−2 K and ±5 kPa respectively

Phosphate fertilizer’s solutions of various concentrations (for TSP 0.0042–0.0384 mol·kg−1, for DAP 0.0075–0.09 mol·kg−1 and for nitro phosphate 0.0069–0.089 mol·kg−1) were prepared in water and then density and speed of sound passing through these solutions were measured using a temperature range of 293.15–313.15 K.

3

3 Results and discussion

3.1

3.1 Density and sound velocity measurements of phosphate fertilizers solutions

Measured data of density and ultrasonic speed of water and aqueous solutions of phosphate fertilizers with different fertilizer concentrations at different temperatures has been given in Table 1, Comparison of measured density and ultrasonic speed data for water with literature reported data showed that measured data is in accordance with data reported in literature (Omota et al., 2009; Rajagopal and Edwin Gladson, 2011; Kapadi et al., 1997; Chauhan and Kumar, 2014).

Table 1 Molality (m) density (ρ) and ultrasonic speed (u) of water and aqueous phosphate fertilizers solutions at different temperatures (T).
m/mol·kg−1 ρ/g·cm−3
293.15 K 298.15 K 303.15 K 308.15 K 313.15 K
Water
0.998202 0.997025 0.995748 0.994258 0.992567
Triple super phosphate
0.0042 0.998627 0.997448 0.996167 0.994671 0.992977
0.0128 0.999487 0.998301 0.997009 0.995512 0.993806
0.0213 1.000317 0.999121 0.997813 0.996311 0.994607
0.0299 1.001137 0.999931 0.998616 0.997111 0.995396
0.0384 1.001927 1.000711 0.999414 0.997881 0.996147
Nitro phosphate
0.0069 0.999569 0.999278 0.997851 0.995741 0.994345
0.0209 0.999780 0.999481 0.998041 0.995921 0.994511
0.0419 1.000091 0.999735 0.998264 0.996132 0.994713
0.0629 1.000402 0.999956 0.998436 0.996301 0.994871
0.0839 1.000713 1.000109 0.998532 0.996378 0.994969
Di ammonium phosphate
0.0075 0.998921 0.997765 0.996364 0.994723 0.993247
0.0227 1.000356 0.999186 0.997763 0.996059 0.994576
0.0450 1.002445 1.001262 0.999802 0.998005 0.996501
0.0680 1.004557 1.003357 1.001885 0.999996 0.998439
0.0900 1.006578 1.005345 1.003857 1.001832 1.000294
u/m·s−1
Water
1482.63 1497.06 1509.57 1519.15 1529.63
Triple super phosphate
0.0042 1503.32 1513.45 1524.56 1536.76 1552.91
0.0128 1509.08 1519.21 1530.32 1542.52 1558.67
0.0213 1514.84 1524.97 1536.08 1548.28 1564.43
0.0299 1520.60 1530.73 1541.84 1554.04 1570.19
0.0384 1526.36 1536.49 1547.60 1559.80 1575.95
Nitro phosphate
0.0069 1487.63 1505.96 1515.23 1521.98 1533.88
0.0209 1494.08 1512.41 1521.68 1528.43 1540.33
0.0419 1500.53 1518.86 1528.13 1534.88 1546.78
0.0629 1506.98 1525.31 1534.58 1541.33 1553.23
0.0839 1513.43 1531.76 1541.03 1547.78 1559.68
Di ammonium phosphate
0.0075 1485.13 1496.71 1512.03 1521.36 1531.23
0.0227 1489.86 1500.72 1516.05 1525.47 1534.24
0.0450 1494.59 1504.73 1520.07 1529.58 1537.25
0.0680 1499.32 1508.74 1524.09 1533.69 1540.26
0.0900 1504.05 1512.75 1528.11 1537.80 1543.27

The standard uncertainties in molality (m), density (ρ), sound velocity (u), and temperature (T) and pressure (P) are ±0.0009 mol·kg−1, ±0.66 × 10−6 g·cm−3, ±0.029 m·s−1, ±10−2 K and ±5 kPa respectively. Expanded uncertainties (k = 2) in density and sound velocity are ±1.32 × 10−6 g·cm−3 and ±0.058 m·s−1 respectively

From data given in Table 1 it is obvious that with increasing concentration of fertilizer’s molecules in solutions, density of solutions also increases which could be due to enhanced molecular interactions between water and fertilizer molecules at higher concentrations while density decreases with rising temperature because at higher temperatures the kinetic energy of the molecules in solutions increases which dominates over binding energy among solution components and hence solution becomes less dense (Rajagopal and Edwin Gladson, 2011; Naseem et al., 2013). Data given in Table 1 shows that the sound velocity of aqueous fertilizer’s solutions increases with increasing concentration of fertilizer’s molecules in solutions due to increased associations between water and phosphate fertilizer’s molecules at higher concentrations of solutions. While at higher temperature, due to loose binding and enhanced degree of collisions in a solution results in an increase in sound velocity (Chauhan and Kumar, 2014).

3.2

3.2 Acoustic parameters

Ultrasonic or acoustic parameters like compressibility factor, hydration number and intermolecular length are useful tool to study the physicochemical behavior and molecular interactions of various liquid mixtures. Ion-ion and ion–solvent interactions play an important role in solution chemistry (Dhondge et al., 2017).

3.2.1

3.2.1 Apparent and partial molar isentropic compression

Apparent molar isentropic compression (Kϕ) is degree of compression of ions in solution. Kϕ can be calculated from following equation using measured data of density and ultrasonic velocity.

(1)
K ϕ = β s M / ρ + 1000 ( β s ρ o - β s o ρ ) / m ρ ρ o M is molar mass (g·mol−1) of fertilizers, m denotes molality (mol·kg−1)of fertilizer solutions in water, ρ and ρo represents density (g·cm−3) of solutions and solvent respectively and βs is adiabatic compression (Pa−1) of solutions and is calculated using following Newton Laplace equation, (Sharma et al., 2015).
(2)
β s = 1 / u 2 · ρ u is ultrasonic velocity of phosphate fertilizer’s solutions in water.

Calculated data of Kϕ for aqueous phosphate fertilizer’s solutions at different temperatures have been given in Table 2.

Table 2 Molality (m) and apparent molar isentropic compression (Kϕ) of phosphate fertilizers solutions in water at different temperatures (T) and at 101 kPa pressure.
m/mol·kg−1 Kϕ × 10−4/cm3·mol−1·Pa−1
293.15 K 298.15 K 303.15 K 308.15 K 313.15 K
Triple super phosphate
0.0042 −4.99 −4.75 −4.73 −3.15 −2.88
0.0128 −3.75 −3.30 −3.24 −2.70 −2.06
0.0213 −3.51 −2.99 −2.95 −2.61 −1.87
0.0299 −3.39 −2.84 −2.80 −2.56 −1.78
0.0384 −3.32 −2.77 −2.72 −2.52 −1.74
Nitro phosphate
0.0069 −4.83 −4.65 −3.94 −3.53 −2.97
0.0209 −3.13 −3.01 −2.74 −2.59 −2.37
0.0419 −2.23 −2.13 −1.98 −1.90 −1.77
0.0629 −1.93 −1.83 −1.72 −1.66 −1.56
0.0839 −1.78 −1.68 −1.58 −1.53 −1.45
Di ammonium phosphate
0.0075 −4.65 −3.74 −3.42 −2.95 −2.24
0.0227 −3.19 −2.85 −2.69 −2.47 −2.18
0.0450 −2.48 −2.28 −2.18 −2.03 −1.85
0.0680 −2.21 −2.07 −1.98 −1.86 −1.71
0.0900 −2.10 −1.98 −1.90 −1.78 −1.66

The standard uncertainties in molality (m), apparent molar isentropic compression (Kϕ), temperature (T) and pressure (P) are ±0.0009 mol·kg−1, ±0.02 × 10−4 cm3·mol−1·Pa−1, ±10−2 K and ±5 kPa respectively.

Reported results in Table 2 show that with increasing temperature, Kϕ values of phosphate fertilizers in water increases. This can be due to the greater degree of thermal agitation among the solution components at higher temperature, resulting in release of more solvent molecules from solvation shell of fertilizer’s molecules into bulk which positively contribute to overall compression of solution. This is an indication of weaker solute–solvent interactions at higher temperature. Less compressible solutions of phosphate fertilizers in water at higher concentration of fertilizer’s molecules indicated the presence of stronger electrostatic intermolecular interactions in solutions (Dhondge et al., 2017).

Among these fertilizers (triple super phosphate, di ammonium phosphate and nitro phosphate) maximum values of Kϕ at respective temperatures have been observed for aqueous triple superphosphate solutions because of the formation of most compact structure of solute (TSP) molecules in solvent (water) due to presence of stronger intermolecular interactions (hydrogen bonding) among highly charged Ca2+ ions (from TSP) and negatively charged end of polar water molecules than prevailing in nitro phosphate and di ammonium phosphate solutions. Hence observed order of decreasing apparent molar isentropic compression is.

  • Kϕ (Triple superphosphate) > Kϕ (Nitrophosphate) > Kϕ (Diammonium phosphate)

Partial molar isentropic compression Koϕ can be calculated from plots between concentration and Kϕ of fertilizer solutions in water using following equation (George et al., 2002; Naseem et al., 2016).

(3)
K ϕ = K ϕ o + S k m Koϕ is isentropic compression of phosphate fertilizer’s solutions at infinite dilution and gives insight about strength and nature of intermolecular interactions present in solutions. Whereas, slope (Sk) shows pair wise interactions or solute–solute interactions in solutions.

Calculated data for Koϕ and Sk of fertilizers in water have been given in Table 3.

Table 3 Partial molar compression (Kϕo) and slope (Sk) of phosphate fertilizers solutions in water at different temperatures (T) and at 101 kPa pressure.
Fertilizers 293.15 K 298.15 K 303.15 K 308.15 K 313.15 K
Koϕ/cm3·mol−1·Pa−1
Triple super phosphate −0.0005 −0.0004 −0.0003 −0.0003 −0.0002
Nitrophosphate −0.0004 −0.0004 −0.0004 −0.0004 −0.0004
Diammonium phosphate −0.0003 −0.0003 −0.0002 −0.0002 −0.0001
Sk/kg·cm3·mol−2·Pa−1
Triple super phosphate 0.0018 0.0009 0.0004 0.0008 0.0005
Nitrophosphate 0.0003 0.0003 0.0002 0.0002 0.0002
Diammonium phosphate 0.0002 0.0002 0.0001 0.0001 0.0001

The standard uncertainties in Partial molar compression (Kϕo), temperature (T) and pressure (P) are ±0.35 × 10−4 cm3·mol−1·Pa−1, ±10−2 K and ±5 kPa respectively.

Obtained negative values of Koϕ for phosphate fertilizer’s solutions in water indicated the presence of strong solute -solvent (phosphate fertilizers-water) interactions in solutions. At higher temperature, due to discharge of solvent molecules from second hydration layer of fertilizer’s molecules, compressibility of bulk water molecules increases and hence Koϕ, values become less negative. Positive Sk values for aqueous phosphate fertilizers solutions are indicative of weak solute–solute interactions in solutions (Naseem et al., 2016).

3.2.2

3.2.2 Hydration number

Hydration number; another acoustic parameters is defined as the number of water molecules which on addition of a solute in solution get bounded with incoming solute molecules. Hydration numbers reveal the dynamic situation of ions as they move in solution. In this way number of water molecules moving freely in solutions decreases which in result cause a decrease in the overall compressibility of solution because bonding or formation of rigid links of water molecules with solute molecules has resulted into a decrease in distance between interacting. From the obtained compressibility data, hydration number for phosphate fertilizers is being calculated using following relation (Burakowski and Gliński, 2007).

(4)
n h = n 1 / n 2 1 - β s / β s o n1 represents number of water molecules and n2 are the number of solute molecules present in solution. Positive or negative values of nh indicate the structure making or breaking ability of solute molecules in the solutions respectively and their magnitude provide an insight about strength of intermolecular interactions present in solutions (Kharat, 2013). Obtained values of nh have been given in Table 4.
Table 4 Molality (m) and hydration number (nh) of phosphate fertilizers in water at different temperatures (T) and at 101 kPa pressure.
m/mol·kg−1 nh
293.15 K 298.15 K 303.15 K 308.15 K 313.15 K
Triple super phosphate
0.0042 67.89 65.91 64.89 47.89 45.22
0.0128 53.06 48.10 48.03 42.32 34.78
0.0213 50.20 44.52 44.87 41.10 32.45
0.0299 48.68 42.67 41.68 40.74 31.54
0.0384 47.79 41.78 40.18 39.89 30.99
Nitro phosphate
0.0069 65.70 64.90 56.62 51.80 45.34
0.0209 44.95 44.41 41.51 39.79 37.51
0.0419 34.01 33.49 32.09 31.10 29.83
0.0629 30.27 29.79 28.73 28.15 27.19
0.0839 28.33 27.80 26.89 26.41 25.66
Di ammonium phosphate
0.0075 60.24 49.68 46.59 41.53 32.92
0.0227 41.85 38.24 37.05 35.10 32.08
0.0450 32.83 30.95 30.25 29.10 27.47
0.0680 29.40 28.11 27.60 26.73 25.57
0.0900 27.88 26.87 26.45 25.68 24.78

The standard uncertainties in molality (m), temperature (T) and pressure (P) are ±0.0009 mol·kg−1, ±10−2 K and ±5 kPa respectively.

Reported results show that for all used phosphate fertilizers, nh values are positive indicating the structure making behavior of phosphate fertilizers in their aqueous solutions. With increasing concentration of phosphate fertilizers in their solutions, nh values decrease. This suggests the presence of strong intermolecular interactions of phosphate fertilizers with water molecules. Presence of strong intermolecular interactions in aqueous phosphate fertilizer’s solution leads to decrease in compressibility of solutions which results in decreasing hydration number. As all phosphate fertilizers are of electrolytic nature, decrease in hydration number with increasing solute concentration can also be explained according to Pasynski suggestions, who states that in electrolytic solutions due to electrostatic field of ions, water molecules experience electrostrictive compression which acts like very high static pressure and renders the solutions very less compressible (or even non compressible at all) that in turn leads to decrease in hydration number (Burakowski and Gliński, 2008).

Electrostatic interactions at higher temperature become weaker and water molecules are released into the bulk leading to decreased compressibility of water molecules around solute molecules. Hence hydration number is observed to be decreasing with increasing temperature (Kharat, 2013).

Hydration number for aqueous TSP solutions is greater than its value for aqueous nitro phosphate and di ammonium phosphate solutions; highly hydrated molecule has greater nh values and in present case TSP is more hydrated molecule due to presence of greater charge Ca2+ ions. Hydration number for these phosphate fertilizers has the following trend.

  • Triple superphosphate > Nitrophosphate > Di ammonium phosphate.

3.2.3

3.2.3 Intermolecular free length (Lf)

Intermolecular free length is another acoustical parameter describing the nature and strength of molecular interactions present in a solution and is referred to as distance among the surfaces of two molecules. Molecules of liquid are assumed to be spherical and the average value of distance that ultrasonic waves travel between two molecules is called intermolecular free length (Lf). It could be evaluated from isentropic compressibility (βs) using following equation.

(5)
L f = K β s where K = Jacobson temperature-dependent constant. Its value is [(93.875 + 0.375)T × 10−8]/K and T is absolute temperature.

Nature and extent of molecular interactions present in solution affects the values of Lf. When isentropic compressibility decreases, free length also decreases and vice versa. Generally, Lf is affected by different parameters like temperature and concentration of solution components etc. Using measured sound velocity data at different temperatures Lf was calculated and that data is given in Table 5. Graphical presentation of variation of intermolecular free length with molality of phosphate fertilizers is shown in Figs. 2–4.

Table 5 Molality (m), Acoustic impedance (Z), Relative association (RA) and Intermolecular free length (Lf) of phosphate fertilizers solutions in water at different temperatures (T) and at 101 kPa pressure.
T/K m/(mol·kg−1) Z/(kg·m−2·s−1) RA Lf × 10−3/(m)
Triple super phosphate
0.0042 1501.70 0.996126 7.018
0.0128 1509.62 0.996286 6.954
293.15 0.0213 1518.54 0.997099 6.887
0.0299 1527.53 0.997937 6.821
0.0384 1536.41 0.998685 6.756
0.0042 1510.07 0.997047 6.932
0.0128 1517.97 0.997204 6.866
298.15 0.0213 1526.89 0.998016 6.804
0.0299 1535.87 0.998848 6.739
0.0384 1544.72 0.999575 6.675
0.0042 1519.02 0.997272 6.841
0.0128 1526.90 0.997417 6.780
303.15 0.0213 1535.78 0.998205 6.716
0.0299 1544.75 0.999037 6.652
0.0384 1553.57 0.999761 6.589
0.0042 1536.61 0.995201 6.674
0.0128 1544.41 0.995302 6.616
308.15 0.0213 1553.18 0.996015 6.554
0.0299 1562.03 0.996773 6.493
0.0384 1570.67 0.997379 6.434
0.0042 1548.38 0.993352 6.563
0.0128 1556.18 0.993457 6.507
313.15 0.0213 1564.94 0.994161 6.446
0.0299 1573.73 0.994882 6.387
0.0384 1582.42 0.995517 6.329
Nitro phosphate
0.0069 1486.99 0.999882 7.162
0.0209 1493.75 0.999682 7.099
293.15 0.0419 1500.67 0.999456 7.036
0.0629 1507.59 0.999222 6.973
0.0839 1514.51 0.998961 6.912
0.0069 1504.87 1.000432 6.991
0.0209 1511.63 1.000395 6.929
298.15 0.0419 1518.46 1.000327 6.869
0.0629 1525.24 1.000253 6.810
0.0839 1531.93 1.000145 6.752
0.0069 1511.97 0.999821 6.915
0.0209 1518.71 0.999781 6.855
303.15 0.0419 1525.48 0.999704 6.796
0.0629 1532.18 0.999628 6.738
0.0839 1538.77 0.999549 6.681
0.0069 1515.50 1.000225 6.869
0.0209 1522.22 1.000171 6.810
308.15 0.0419 1528.94 1.000076 6.751
0.0629 1535.63 0.999984 6.693
0.0839 1542.17 0.999864 6.637
0.0069 1525.21 0.999028 6.772
0.0209 1531.88 0.999208 6.714
313.15 0.0419 1538.6 0.99936 6.657
0.0629 1545.26 0.999501 6.601
0.0839 1551.83 0.999604 6.546
Di ammonium phosphate
0.0075 1483.09 1.000264 7.193
0.0227 1489.11 0.999033 7.141
293.15 0.0450 1495.06 0.997910 7.091
0.0680 1501.02 0.996794 7.042
0.0900 1506.95 0.995685 6.990
0.0075 1492.89 1.000212 7.091
0.0227 1498.17 0.998991 7.046
298.15 0.0450 1503.41 0.997828 7.003
0.0680 1508.64 0.99664 6.961
0.0900 1513.83 0.995391 6.918
0.0075 1506.23 1.000806 6.956
0.0227 1511.52 0.999582 6.914
303.15 0.0450 1516.75 0.998395 6.872
0.0680 1521.98 0.997166 6.830
0.0900 1527.21 0.995868 6.789
0.0075 1513.25 1.001165 6.882
0.0227 1518.62 0.999935 6.839
308.15 0.0450 1523.94 0.998744 6.797
0.0680 1529.26 0.997518 6.755
0.0900 1534.54 0.996208 6.714
0.0075 1520.48 0.999828 6.805
0.0227 1524.74 0.998597 6.772
313.15 0.0450 1528.96 0.997409 6.741
0.0680 1533.17 0.996185 6.709
0.0900 1537.32 0.994908 6.678

The standard uncertainties in molality (m), Acoustic impedance (Z), intermolecular free length (Lf), Relative association (RA), temperature (T) and pressure (P) are ±0.0009 mol·kg−1, ±0.02 × 104 (kg·m−2·s−1), ±0.002 × 10−3 m, ±0.000010, ±10−2 K and ±5 kPa respectively.

Plot between molality (m) and intermolecular free length (Lf) of triple super phosphate solutions in water at 293.15 K (♦), 298.15 K (□), 303.15 K (▲), 308.15 K (○) and 313.15 K (×).
Fig. 2
Plot between molality (m) and intermolecular free length (Lf) of triple super phosphate solutions in water at 293.15 K (♦), 298.15 K (□), 303.15 K (▲), 308.15 K (○) and 313.15 K (×).
Plot between molality (m) and intermolecular free length (Lf) of nitro phosphate solutions in water at 293.15 K (♦), 298.15 K (□), 303.15 K (▲), 308.15 K (○) and 313.15 K (×).
Fig. 3
Plot between molality (m) and intermolecular free length (Lf) of nitro phosphate solutions in water at 293.15 K (♦), 298.15 K (□), 303.15 K (▲), 308.15 K (○) and 313.15 K (×).
Plot between molality (m) and intermolecular free length (Lf) of di ammonium phosphate solutions in water at 293.15 K (♦), 298.15 K (□), 303.15 K (▲), 308.15 K (○) and 313.15 K (×).
Fig. 4
Plot between molality (m) and intermolecular free length (Lf) of di ammonium phosphate solutions in water at 293.15 K (♦), 298.15 K (□), 303.15 K (▲), 308.15 K (○) and 313.15 K (×).

It was found that values decrease with increase in concentration of phosphate fertilizers (solute), and temperature. The decrease in free length with increase in solute concentration indicates that molecular interactions among solution components get stronger on addition of solute molecules in solutions. This is because more number of solute molecules become available for solvent molecules to interact with. The presence of phosphate fertilizer in solution causes visible change in sound velocity values, which increases with increasing concentration of the phosphate fertilizers. Ultrasonic velocity depends on intermolecular free length Lf. With the decrease in free length, velocity increases and vice versa. Such dependency is clearly observed in studied solutions, the highest sound velocity data found in triple super phosphate solutions correlates the smallest Lf data among other studied phosphate fertilizers. The intermolecular length of three studied phosphate fertilizers in water lies in following order: di ammonium phosphate > nitro phosphate > Triple super phosphate. This is due to presence of stronger molecular interactions (hydrogen bonding) between highly charged Ca2+ ions (from TSP) and negatively charged end of polar water molecules than prevailing in nitro phosphate and di ammonium phosphate solutions.

3.2.4

3.2.4 Relative association (RA)

Relative association (RA) is another acoustic parameter which helps in understanding the intermolecular interactions, i.e. extent of association in solution relative to association existing in water. It is associated with following two types of effects taking place in solution:

  • The breaking of solvent molecules on addition of solute to it, which tends to decrease the RA value.

  • Simultaneous solvation of solute by solvent molecules which leads to increase in magnitude of RA.

RA can be calculated using following formula

(6)
R A = ρ / ρ o u o / u 3

Calculated data of RA for phosphate fertilizers solutions in water is given in Table 5, which show that RA values decrease with increasing fertilizer concentration indicating that in addition to solute molecules in solution breaking of solvent molecules occurs developing strong inter-ionic interactions in solutions. Among three phosphate fertilizers lowest RA values have been observed for TSP solutions in water than those obtained for nitro phosphate and di ammonium phosphate. This can be explained on the basis of presence of stronger rmolecular interactions (hydrogen bonding) among highly charged Ca2+ ions (from TSP) and negatively charged end of polar water molecules than those present in aqueous nitro phosphate and di ammonium phosphate solutions.

3.2.5

3.2.5 Specific acoustic impedance (Z)

Specific acoustic impedance is the product of ultrasonic velocity and density of solution. It is a measure of resistance offered by the medium for the propagation of sound waves through it. It is directly proportional to ultrasonic velocity and inversely proportional to adiabatic compressibility. Acoustic impedance (Z), explains molecular interactions present in the solution and is dependent on both temperature and concentration of solution. Acoustic impedance (Z) can be calculated using this equation.

(7)
Z = u × ρ

The calculated data of acoustic impedance is given in Table 5. It is observed that value of Z increases with increasing concentration of phosphate fertilizers in aqueous solutions suggesting the presence of stronger molecular interactions due to closer packing structure of solute and solvent molecules. Increase in specific acoustic impedance with increasing fertilizer concentration and variation with increase of temperature show that molecular interactions in aqueous phosphate fertilizers solutions is associative. This also indicates the possibility of strong molecular interactions among the components present in the mixture.

The variation of Z in different fertilizer solutions lies in following order: triple super phosphate > nitro phosphate > di ammonium phosphate, due to presence of stronger intermolecular interactions (hydrogen bonding) among highly charged Ca2+ ions (from TSP) and negatively charged end of polar water molecules than prevailing in nitro phosphate and di ammonium phosphate solutions.

3.3

3.3 Volumetric parameters

Volumetric parameters e.g. molar volume, expansibility factor and its temperature derivative give detailed information about strength and nature of intermolecular interactions present in solutions and have been calculated in the present study in order to support the results of ultrasonic or acoustic parameters about strength and nature of intermolecular interactions in solutions (Ameta et al., 2013; Awasthi and Awasthi, 2012).

3.3.1

3.3.1 Apparent molar volume (Vϕ)

Apparent molar volume (Vϕ); an important volumetric parameter gives information about intermolecular interactions in solutions and manifests the behavior of solutes in solution with change in temperature and can be calculated using following mathematical relation (Iqbal and Verrall, 1989).

(8)
V ϕ = M / ρ - 1000 ρ - ρ o / m ρ ρ o

M is molar mass of fertilizers (for triple superphosphate 234.05 g·mol−1, for nitro phosphate 140.99 gmol−1, for di ammonium phosphate 132.07 g·mol−1). m is the molality (mol·kg−1) of phosphate fertilizer’s solutions in water. ρ is density of fertilizer’s solution and ρo is density of pure solvent, i.e. water respectively.

Calculated values of Vϕ for aqueous fertilizer’s solutions are given in Table 6. Representative 3-D plots of Vϕ vs. concentration in terms of molality (m) of phosphate fertilizer’s solutions in water as a function of temperature have been shown in Figs. 5–7.

Table 6 Molality (m) and apparent molar volume (Vϕ) of phosphate fertilizers solutions in water at different temperatures (T) and at 101 kPa pressure.
m/mol·kg−1 Vϕ/cm3·mol−1
293.15 K 298.15 K 303.15 K 308.15 K 313.15 K
Triple super phosphate
0.0042 131.90 134.57 138.65 144.54 153.83
0.0128 137.94 138.07 140.73 146.48 154.13
0.0213 138.59 141.52 144.45 147.64 158.88
0.0299 139.12 143.58 146.37 148.00 160.84
0.0384 140.43 144.18 147.15 149.50 161.11
Nitro phosphate
0.0069 126.95 127.42 128.30 129.57 131.05
0.0209 127.60 128.16 129.19 130.26 131.54
0.0419 128.56 129.53 130.87 131.83 132.77
0.0629 129.42 130.49 132.23 133.01 133.87
0.0839 130.73 131.77 133.82 134.70 135.15
Di ammonium phosphate
0.0075 36.67 37.67 38.67 40.63 43.64
0.0227 37.15 38.05 39.31 41.36 43.96
0.0450 37.56 38.28 39.70 42.08 44.53
0.0680 38.28 38.98 40.07 42.81 45.37
0.0900 38.57 39.45 40.44 44.09 45.71

The standard uncertainties in molality (m), apparent molar volume (Vϕ) temperature (T) and pressure (P) are ±0.0009 mol·kg−1, ±0.03 cm3·mol−1, ±10−2 K and ±5 kPa respectively.

Graphical representation of variation of apparent molar volume (Vϕ) with molality (m) of aqueous nitro phosphate solutions at different temperatures.
Fig. 5
Graphical representation of variation of apparent molar volume (Vϕ) with molality (m) of aqueous nitro phosphate solutions at different temperatures.
Graphical representation of variation of apparent molar volume (Vϕ) with molality (m) of aqueous triple super phosphate solutions at different temperatures.
Fig. 6
Graphical representation of variation of apparent molar volume (Vϕ) with molality (m) of aqueous triple super phosphate solutions at different temperatures.
Graphical representation of variation of apparent molar volume (Vϕ) with molality (m) of aqueous di ammonium phosphate solutions at different temperatures.
Fig. 7
Graphical representation of variation of apparent molar volume (Vϕ) with molality (m) of aqueous di ammonium phosphate solutions at different temperatures.

Vϕ values increase with rising temperature and molality of fertilizer solutions which is shown by color of plots as the color of plots changes from blue to red. The dark blue color represents lowest value of Vϕ at low temperature and red color represents the highest Vϕ value at highest temperature i.e. 313.15 K. From these results it is obvious that with concentration of fertilizer’s molecules in aqueous solutions, apparent molar volume (Vϕ) increases which show the presence of strong intermolecular interactions in solutions due to enhanced degree of hydration of ions of fertilizer molecules with water molecules. As a result interactions of water with fertilizer molecules tend to increase (Golabiazar and Sadeghi, 2014). Vϕ increases with rising temperature of the solution because expansion in volume occurs due to removal of water molecules from outermost hydration layer of solute molecules into bulk at elevated temperatures (Chadha et al., 2016). Results given in table also show that the values of Vϕ are maximum for triple super phosphate solutions among all fertilizers used which could be due to molecular weight of TSP which is greater as compared to other fertilizers used. According to previous knowledge i.e. increasing molecular weight of solute causes increase in Vϕ values of solutions (Nain and Pal, 2013). Hence observed order of increasing Vϕ for three phosphate fertilizers in water is:

  • Vϕ (Di ammonium phosphate) < Vϕ (Nitro phosphate) < Vϕ (Triple super phosphate)

All fertilizers used have same anionic group (phosphate ion) but with different cations; the Vϕ value is highest in the solution of fertilizer having higher cationic charged specie than the fertilizer with lower charge on their cationic specie (Shamil et al., 1989; Godhani et al., 2014; Anwar and Nain, 1996; Naderi and Sadeghi, 2016). This trend could be explained due stronger intermolecular interactions between highly charged Ca2+ (dissociated from TSP molecules) and polar water molecules as compared to those present in case of NO2+ and NH4+ (produced from the dissociation of nitro phosphate and di ammonium phosphate) in water. Therefore due to greater degree of hydrogen bonding, Ca2+ ions from triple super phosphate tend to attract more OH– ends of water molecules in solutions as compared to NO2+ and NH4+ ions from nitro phosphate and di ammonium phosphate solutions respectively. Hence at each respective temperature for a fixed concentration of fertilizer, Ca2+ ions from triple super phosphate get more hydrated in their solutions and have larger apparent molar volume than the hydrated ions of NO2+ from nitro phosphate and NH4+ from di ammonium phosphate fertilizer in their solutions.

3.3.2

3.3.2 Partial molar volume (Voϕ)

Limiting or partial molar volumes for aqueous phosphate fertilizers molecules have been obtained using following Masson equation (Anwar and Nain, 1996).

(9)
V ϕ = V ϕ o + S v m

Voϕ is the partial molar volume and gives information regarding solute–solvent interactions present in aqueous fertilizer solutions because at infinite dilution solute molecules are far away from each other and are surrounded only by solvent (water) molecules. Therefore, Voϕ is not found to be affected by solute–solute interactions. The term Sv in above Eq. (2) is the slope of plots of molality and Vϕ of aqueous phosphate fertilizer solutions and it suggests the solute- solute interactions present in solutions. Voϕ and Sv values have been given in Table 7.

Table 7 Partial molar volume (Vϕo) and slope (Sv) of phosphate fertilizers solutions in water at different temperatures (T) and at 101 kPa pressure.
Fertilizers 293.15 K 298.15 K 303.15 K 308.15 K 313.15 K
Voϕ/cm3·mol−1
Triplesuper phosphate 130.64 133.02 135.17 140.10 144.02
Nitrophosphate 127.14 127.24 127.77 128.99 130.54
Diammonium phosphate 36.55 37.49 38.69 42.57 43.40
Sv/kg·cm3·mol−1
Triplesuper phosphate 131.71 110.46 106.63 114.24 128.88
Nitrophosphate 11.16 56.31 71.86 66.32 53.97
Diammonium phosphate 23.35 21.34 20.16 25.81 26.49

The standard uncertainties in partial molar volume (Vϕo), temperature (T) and pressure (P) are ±0.77 cm3·mol−1, ±10−2 K and ±5 kPa respectively.

It is obvious from data that Voϕ increases with increasing temperature. It may also be considered that two terms shown in equation given below may contribute to overall partial molar volume of solutions (Anwar and Nain, 1996). V ϕ o = V ϕ o i n t + V ϕ o ( e l e c t )

Voϕ (elect) represents the partial molar volume due to electrostriction of water molecules, i.e. reduction in volume of solution, when solute molecules in solutions are hydrated. While Voϕ (int) is the intrinsic molar volume and may be due to weak van der waals forces and caging effects or hydrophobic character of solute (fertilizers) molecules. Voϕ (int) becomes almost negligible with increasing temperature (Singla et al., 2014). Therefore, at higher temperature, due to loss of hydration sheath of solute molecules Voϕ increases. For phosphate fertilizers used, the observed order of Voϕ values is:

  • Voϕ (Di ammonium phosphate) < Voϕ (Nitrophosphate) < Voϕ (Triple super phosphate)

This order of Voϕ for phosphate fertilizers in their aqueous solutions may be due to stronger intermolecular interactions between Ca2+ ions dissociated from TSP and polar water molecules as compared to those in aqueous nitro phosphate and di ammonium phosphate solutions where NO2+ and NH4+ have lower charge density being bulky groups in size and with large steric hindrance can interact with less water molecules as compared to Ca2+ ions.

3.3.3

3.3.3 Partial molar expansion

Limiting or partial molar expansion (Eoϕ) is another important volumetric parameter which indicates the structure promoting or breaking ability of fertilizer molecules in solutions in terms of their hydrophobic character. Following polynomial equation is being used to express the variation of limiting molar volumes (Vοϕ) with temperature (Sharma et al., 2016).

(11)
V ϕ o = a + b T + c T 2

In Eq. (4), a, b and c are empirical constants and their obtained values have been reported in Table 8. Eoϕ values have been calculated using following mathematical equation.

(12)
E ϕ o = ∂ V ϕ o / ∂ T p = b + 2 c T
(13)
E ϕ o = E ϕ o E l e c t + E ϕ o ( s t r )
Table 8 Coefficients a, b and c of Eq. (4) for phosphate fertilizers (Nitro phosphate, TSP and DAP) in aqueous solutions.
Fertilizers a/(cm3·mol−1) b/(cm3·mol−1·K−1) c/(cm3·mol−1·K−2)
Triplesuper phosphate 1469.2 −9.4744 0.0167
Nitro phosphate 1034.7 −6.0479 0.0104
Diammonium phosphate 576.58 −3.9201 0.0071

The standard uncertainties in temperature (T) and pressure (P) are ±10−2 K and ±5 kPa respectively.

Eoϕ (Elect) is the expansion contributed due to the hydration of solute molecules by water molecules i.e. electrostriction changes, while expansion due to structural changes is termed as Eoϕ (str) and is more prominent at low or room temperature. While at higher temperature, electrostriction component Eoϕ (Elect) is dominant and affects the outermost solvated water molecule’s layer (Dhondge et al., 2017). Calculated values of Eoϕ for phosphate fertilizers in water at different temperatures have been reported in Table 9.

Table 9 Limiting apparent molar expansion (Eoϕ) and temperature derivative of limiting apparent molar expansion (∂Eoϕ/∂T) for three phosphate fertilizers at different Temperatures (T) and at 101 kPa pressure.
T/K Eoϕ × 10−2/cm3·mol−1·K−1 (∂Eoϕ/∂T)/cm3·mol−1·K−2
Triple super phosphate
293.15 48.38
298.15 51.68
303.15 65.08 0.0334
308.15 81.78
313.15 98.48
Di ammonium phosphate
293.15 24.26
298.15 31.36
303.15 38.46 0.0142
308.15 45.56
313.15 52.66
Nitro phosphate
293.15 4.96
298.15 15.36
303.15 25.76 0.0208
308.15 36.16
313.15 46.56

The standard uncertainties in Limiting apparent molar expansion (Eoϕ), temperature (T) and pressure (P) are ±0.008 cm3·mol−1·K−1, ±10−2 K and ±5 kPa respectively.

Values of Eoϕ shown in Table 5 are positive for all of the three fertilizer solutions. Positive values of Eoϕ indicate that at higher temperature due to release of some water molecules into bulk, volume of solution increases than that of pure solvent. Greater values of Eoϕ at higher temperature showed that structural hydrophobic hydration of solute (fertilizers) molecules is dominant over electrostriction of solvent (water) molecules. Such behavior of solute molecules in solutions may be due to the presence of ‘caging effect’ or ‘packing effect’ of solute (fertilizers) molecules in solutions and do not behave as common electrolytes because of having some hydrophobic character (Sharma et al., 2015; Dhondge et al., 2017). It means that the fertilizer molecules by occupying the interstitial spaces in their solution indicate their structure making/hydrophobic character.

From calculated results it is obvious that triple super phosphate has greater values of Eoϕ than di ammonium phosphate and nitro phosphate, indicating that triple super phosphate has maximum hydration due to greater degree of hydrogen bonding in its aqueous solutions at higher temperature. While lowest values of Eoϕ in aqueous di ammonium phosphate solutions indicate the maximum electrostriction of solute molecules in its solutions.

3.3.4

3.3.4 Hepler’s constant

Temperature dependent derivatives of the limiting molar expansion give information about hydrophobic character of any solute molecule in the solution (George et al., 2002). Later on quantitative information regarding hydration of solute molecules in solutions was obtained using Hepler’s constant, which is obtained using following relation (Sharma et al., 2015).

(14)
∂ E ϕ o / ∂ T = ∂ 2 V ϕ o / ∂ T 2 p = 2 c

The sign of (∂Eoϕ/∂T)P determines the structure making or breaking tendency of dissolved solute in a solvent. Positive values of (∂Eoϕ/∂T)P values are indicative of structure making ability of solute molecules, while reverse happens for structure breaking behavior of solute molecules (Sharma et al., 2016). Calculated values of (∂Eoϕ/∂T)P for these phosphate fertilizers in their aqueous solutions have been given in Table 2. Reported data showed that values of (∂Eoϕ/∂T)P are positive for all three phosphate fertilizers indicating their structure making tendency in solutions. Among three fertilizers triple super phosphate has most positive value of (∂Eoϕ/∂T)P which shows that among these phosphate fertilizers, TSP has maximum structure making ability in its aqueous solution. Observed order of increasing structure making ability of three studied phosphate fertilizers is given below.

  • Di ammonium phosphate < Nitro phosphate < Triple super phosphate

4

4 Conclusions

In present work, for aqueous phosphate fertilizer solutions, volumetric (e.g. apparent molar volume and partial molar expansion) and acoustic parameters (like compression factor and hydration number) were calculated from measured data of density and ultrasonic velocity at different temperatures (293.15–313.15)K. Apparent molar volume for fertilizer solutions is positive and is found to be increasing as temperature of solutions rises and also with increasing concentration of fertilizers in their aqueous solutions. It indicated that solute–solvent interactions are dominate solute–solute interactions with increasing solute content in solutions. Values of apparent molar isentropic compression (Kϕ) an acoustical parameter for fertilizer’s aqueous solutions become less negative with an increase in concentration of phosphate fertilizers in their aqueous solutions. This indicates that water molecules are less compressible around fertilizer molecules than in bulk which shows stronger intermolecular interactions in solutions. Moreover, obtained results from partial molar expansion, Hepler’s constant and hydration number indicate the structure making ability of phosphate fertilizers in water. Calculated volumetric and acoustical parameters show that among three phosphate fertilizers triple super phosphate develops maximum interactions in solutions due to greater degree of hydrogen bonding and electrostatic interactions with polar water molecules in its aqueous solutions which indicate the prominent effect of nature of fertilizer molecule on its behavior in solutions. This knowledge can be helpful in improving fertilizer activity according to targeted application (e.g. soil salinity treatment) by changing the nature of its molecule. Thermo-acoustic studies could also be used successfully in this regard.

Acknowledgments

Authors gratefully acknowledge Lahore College for Women University, Lahorefor for providing chemicals used in this study.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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