Viscosity of Ammonium Nitrate+ Formamide Mixtures

Article pubs.acs.org/jced

Viscosity of Ammonium Nitrate + Formamide Mixtures Milan Vraneš, Sanja Dožić, Aleksandar Tot, and Slobodan Gadžurić* Faculty of Science, Department of Chemistry, Biochemistry and Environmental Protection, University of Novi Sad, Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia ABSTRACT: In this work the viscosity of NH4NO3 + formamide solutions in a wide concentration range up to 0.3703 ammonium nitrate mole and in the temperature range from (298.15 to 348.15) K was determined. The validity of Jones−Dole and Goldsack−Franchetto’s equations were checked and applied to describe the viscosity dependence on concentration. The equation for the viscosity dependence on both the ammonium nitrate mole fraction and temperature is also presented in this paper.

1. INTRODUCTION The study of the transport properties of inorganic salts solutions in different organic solvents in a wide concentration range is extremely complex owing to the presence of different interactions that occur in these systems. One of the key transport properties of the electrolyte solution for many applications in new technological processes is viscosity. Thus, knowledge of an accurate viscosity together with the influences of temperature, pressure, and composition is of a great importance for the engineering community.1,2 Earlier, viscosity was mainly investigated in diluted solutions in the range of validity of the Debye−Hü ckel law3 providing valuable information in diluted solutions regarding ion−dipole interactions.4,5 Since concentrated solutions are widely used in many industrial areas, further studies of the viscosity in the wide electrolyte concentration range in different solvents is justified. This work is the continuation of our systematic investigation of transport properties of ammonium nitrate solutions in different amides, wherein the viscosity is measured over a whole ammonium nitrate concentration range and at various temperatures. Electrical conductivity of ammonium nitrate binary mixtures with lower amides (formamide, N-methylformamide, and N,N-dimethylformamide) and their volumetric properties are studied elsewhere.6−9

Table 1. Provenance and Purity of the Samples chemical name ammonium nitrate formamide

purification method

CAS no.

Merck

6484-52-2

≥ 0.99

none

Merck

75-12-7

≥ 0.995a

distillation

a

After distillation the formamide mass fraction purity remains the same.

investigated binary mixtures in ammonium nitrate concentration ranging from (0 to 0.3703) mole fraction. The spindle type (SC4−18) was immersed and rate per minute (RPM) was set in order to obtain a suitable torque. Measurements were performed in the temperature range from (298.15 to 348.15) K with a rotation speed of 200 rpm for all mixtures and pure formamide (torque range 10 to 20.5). The viscosity data at the corresponding temperatures were recorded automatically on a computer, and then processed in Origin 8.1. Presented experimental values are the mean values of three measurements and the relative standard uncertainty was found to be about 1 %. The densities of the solutions were determined pycnometrically at several temperatures over the whole ammonium nitrate composition range, using a pycnometer with a bulb volume of 10.00 cm3. After the calibration with distilled water at various temperatures, the pycnometer was filled with a mixture and thermostated in a temperature controlled (within ± 0.1 K) and well-stirred water bath for (10 to 20) min to attain thermal equilibrium. The density measurements were measured in the range from (298.15 to 348.15) K. Each experimental density value is the average of three measurements, with the standard uncertainty of ± 0.0002 g·cm−3.

2. EXPERIMENTAL SECTION Ammonium nitrate was used after drying at 353.15 K for 2 h. Formamide (FA) was distilled and the middle fraction was collected and stored in the sealed dark bottle over 4 Å molecular sieves for 3 weeks prior to use. The provenance and purity of these chemicals are given in Table 1. The mixtures for the viscosity measurements were prepared by measuring the appropriate amounts of ammonium nitrate and formamide on a Denver analytical balance. Uncertainty of the mass fraction was less than ± 1·10−4. Viscosity was measured using a Brookfield viscosimeter DVII + Pro connected to a thermostat (accuracy of ± 0.01 K was applied) and filled with about 8 cm3 of all © 2014 American Chemical Society

initial mass fraction purity

provenance

Received: April 14, 2014 Accepted: August 13, 2014 Published: August 21, 2014 3365

dx.doi.org/10.1021/je500284p | J. Chem. Eng. Data 2014, 59, 3365−3371

Journal of Chemical & Engineering Data

Article

3. RESULTS AND DISCUSSION Viscosity of the pure FA (Table 2) and studied NH4NO3 + FA binary mixtures were measured at temperatures from (298.15 Table 2. Experimental and Literature Values of Vscosity (η) of Pure Formamide at Specified Temperaturesa T/K

this work

refs

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15

3.23 2.95 2.67 2.43 2.20 1.99 1.82 1.69 1.58 1.52 1.49

3.23b, 3.305c, 3.302d, 3.3220e 2.9663e, 2.941f, 2.8767g, 2.975c 2.59b, 2.640c, 2.6531e 2.36b, 2.361f, 2.420c, 2.4039e 2.2187e 1.966f, 2.001d

Figure 1. Viscosity of the NH4NO3 + FA binary mixtures in the temperature range from (298.15 to 348.15) K for different mole fractions of NH4NO3: ■, 0.3703; □, 0.3333; ●, 0.3000; ○, 0.2499; ▲, 0.1999; △, 0.1667; ▼, 0.1428; ▽, 0.1250; ◆, 0.1111; ◇, 0.0999; ◀, 0.0769; ◁, 0.0624; ▶, 0.0476; ▷, 0.0243; ⬢, 0.0123; ⬡, 0.0050; ★, 0. The lines represent the VFT type fitting of the experimental data with parameters reported in Table 4.

Standard uncertainties are u(x) = 1·10−4, u(T) = 0.01 K. Relative standard uncertainties: RSD (η) = 1 %. bReference 10. cReference 11. d Reference 12. eReference 13. fReference 14. gReference 1. a

η =1+A c ηo

to 348.15) K in the whole ammonium nitrate concentration range, up to 0.3703 mole fraction. These values are given in Table 3 and graphically presented in Figure 1. As it can be seen from this figure, the viscosity of all binary mixtures monotonically decreases with increasing temperature. The experimental results of the viscosity were fitted using the Vogel−Fulcher− Tammann (VFT) equation:15 η = a exp(b /(T − To))

(2)

The coefficient A was shown to be a function of solvent properties and limiting conductivities of ions. For the higher concentrations (between 0.1 and 0.2 mol·dm−3) the limiting law was extended by Jones and Dole,16 introducing the viscosity coefficient B: η = 1 + A c + Bc ηo

(1)

where η is the viscosity, T is the temperature in K, and a, b, and T0 are the coefficients of the VFT equation whose values together with their standard deviations are given in Table 4. For the solutions which contain a single solute dissolved in a single solvent, a limiting law that predicts the relative viscosity of the solution can be expressed as

(3)

where ηo is the viscosity of pure formamide, A√c term is identical to those obtained from a limiting-law theory of longrange electrostatic interactions in a dielectric continuum,17 and coefficient B was found to be an additive property of ions and give a useful measure of ion−solvent interactions. An extended

Table 3. Viscosity (η) of Binary Mixture NH4NO3 + FA as a Function of Ammonium Nitrate Mole Fraction in the Temperature Range from (298.15 to 348.15) K at Atmospheric Pressure (0.1 MPa)a T/K =

298.15

303.15

308.15

313.15

318.15

0.3703 0.3333 0.3000 0.2499 0.1999 0.1667 0.1428 0.1250 0.1111 0.0999 0.0769 0.0624 0.0476 0.0243 0.0123 0.0050 a

323.15

328.15

333.15

338.15

343.15

348.15

6.60 5.92 5.33 4.55 3.82 3.42 3.16 2.96 2.82 2.70 2.46 2.35 2.21 2.02 1.92 1.87

6.00 5.37 4.85 4.15 3.49 3.14 2.91 2.73 2.60 2.50 2.29 2.18 2.05 1.87 1.78 1.73

5.46 4.89 4.42 3.80 3.24 2.91 2.70 2.53 2.41 2.33 2.14 2.03 1.91 1.75 1.67 1.62

5.02 4.50 4.08 3.51 3.02 2.70 2.53 2.38 2.26 2.19 2.02 1.93 1.82 1.67 1.60 1.56

4.63 4.19 3.79 3.27 2.82 2.54 2.38 2.24 2.14 2.06 1.93 1.84 1.75 1.61 1.56 1.52

η/(mPa·s)

x(NH4NO3) 13.01 11.71 10.49 8.79 7.19 6.33 5.76 5.35 5.00 4.83 4.42 4.15 3.91 3.56 3.37 3.31

11.66 10.51 9.37 7.85 6.44 5.70 5.20 4.83 4.54 4.37 3.99 3.77 3.55 3.25 3.09 3.02

10.43 9.25 8.25 6.91 5.69 5.07 4.64 4.31 4.08 3.91 3.56 3.39 3.19 2.94 2.81 2.73

9.19 8.23 7.36 6.19 5.09 4.57 4.19 3.90 3.68 3.53 3.23 3.08 2.90 2.66 2.54 2.47

8.18 7.31 6.54 5.52 4.59 4.10 3.77 3.52 3.34 3.19 2.92 2.79 2.63 2.43 2.30 2.24

7.30 6.53 5.85 5.00 4.15 3.75 3.45 3.22 3.07 2.93 2.68 2.56 2.41 2.20 2.09 2.03

Standard uncertainties are u(x) = 1·10−4, u(T) = 0.01 K. Relative standard uncertainties: RSD (η) = 1 %. 3366



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Table 4. VFT Fitting Parameters for the Viscosity of NH4NO3 + FA Mixtures as a Function of Temperature from (298.15 to 348.15) K with the Deviations of Their Fit (σ)a, Calculated from the Experimental Data Given in Tables 2 and 3 x(NH4NO3)

a·102

b

T0

σ·102

0.3703 0.3333 0.3000 0.2499 0.1999 0.1667 0.1428 0.1250 0.1111 0.0999 0.0769 0.0624 0.0476 0.0243 0.0123 0.0050

1.619 4.293 7.474 10.84 21.00 12.36 15.53 17.27 12.70 20.29 18.34 18.41 19.81 14.43 15.93 17.74

1787.4 1215.5 933.5 745.6 483.0 637.9 545.2 494.5 595.3 423.4 431.9 423.4 383.9 457.4 415.6 370.9

31.25 81.73 109.6 128.7 161.6 136.3 147.5 154.3 136.3 164.8 162.5 162.5 169.7 155.9 162.5 171.8

8.24 6.90 5.08 3.24 3.04 2.66 2.65 2.28 2.29 2.19 2.75 2.65 2.87 3.45 4.24 3.95

Figure 2. Variation of the relative viscosity with ammonium nitrate concentration at: ■, 298.15; □, 308.15; ●, 318.15; ○, 328.15; ▲, 338.15; △, 348.15. Lines are obtained using eq 4.

Table 6. Comparison of the Parameters D Obtained Using eqs 4 and 5 at Different Temperatures

a

In the following equation, n is the number of experimental points and ν is the number of an adjustable parameters: ⎛ ∑ (η exp − η cal )2 ⎞0.5 i i ⎟⎟ ση = ⎜⎜ n v − ⎠ ⎝

version of the Jones−Dole’s equation was proposed by Kaminsky18 and used by several authors19−21 to fit the viscosity results of measurements at higher concentrations: η = 1 + A c + Bc + Dc 2 ηo (4)

T/K

D (eq 4)

D (eq 5)

298.15 308.15 318.15 328.15 338.15 348.15

0.025 0.024 0.022 0.020 0.017 0.015

0.014 0.015 0.016 0.016 0.017 0.018

coefficient B with temperature, namely dB/dT.24 It can be observed from Table 5 that value of the coefficient B is decreasing with the increase of temperature (negative dB/dT variation). This indicates the decreasing trend in ion−solvent interactions and justifies the predominance of ion−ion interactions at higher temperature. This is in accordance with our previous results concerning volumetric properties in the same system.9 The interactions that were not taken into account by parameters A and B are included in the Dc2 term. These interactions may exist at higher concentrations, for example, the long-range Coulombic forces, hydrodynamic effect, and interactions arising from changes in ion−solvent interactions with concentration.21 The parameter D gives valuable information about solute− solute structural interaction term. If the higher terms of the hydrodynamic effect are the leading contribution to Dc2, D

where Dc 2 is adjustable empirical constant. Obtained coefficients A, B, and D are given in Table 5. In Figure 2 the reduced viscosity dependence of the ammonium nitrate concentration is presented. The coefficient A depends on the long-range Coulombic interactions between the ions, and it is observed that these A values are negative, indicating very weak ion−ion interactions.19,22 The coefficient B is a function of viscosity effects as Coulombic interaction, size, and shape of effects or Einstein effect, orientation of polar molecules in the ionic field, and distortion of the solvent structure. The positive values of the coefficient B indicate strong ion−solvent interactions and structure-making effect (ions ordering) in the system.23 Better criteria to describe structure-making or structure-breaking tendency in the system is variation of the

Table 5. Jones−Dole’s Equation Fitting Parameters for the Viscosity of NH4NO3 + FA Solutions in the Temperature Range from (298.15 to 348.15) K with the Deviations of Their Fit (σ) and Regression Coefficient (R2) T

A

B

D

K

(dm3/2·mol−1/2)

(dm3·mol−1)

(dm6·mol−2)

298.15 308.15 318.15 328.15 338.15 348.15

−0.035 −0.047 −0.038 −0.006 −0.002 −0.027

± ± ± ± ± ±

0.005 0.007 0.006 0.003 0.003 0.005

0.162 0.159 0.157 0.155 0.151 0.144

± ± ± ± ± ±

0.015 0.012 0.010 0.009 0.008 0.007

0.025 0.024 0.022 0.020 0.017 0.015 3367

± ± ± ± ± ±

−4

3.0·10 4.7·10−4 4.1·10−4 3.2·10−4 3.3·10−4 3.4·10−4

σ

R2

0.005 0.009 0.007 0.006 0.009 0.010

0.9997 0.9992 0.9993 0.9995 0.9994 0.9992



Article

Table 7. Experimental Density Values of Ammonium Nitrate + Formamide Mixtures, as a Function of Ammonium Nitrate Mole Fraction (x) in the Temperature Range from (298.15 to 348.15) K at Atmospheric Pressure (0.1 MPa)a T/K =

298.15

308.15

318.15

0.3703 0.3333 0.3000 0.2499 0.1999 0.1667 0.1428 0.1250 0.1111 0.0999 0.0769 0.0624 0.0476 0.0243 0.0123 0.0050 a

328.15

338.15

348.15

1.2907 1.2730 1.2573 1.2349 1.2124 1.1953 1.1835 1.1721 1.1670 1.1603 1.1468 1.1384 1.1301 1.1172 1.1104 1.1049

1.2835 1.2655 1.2497 1.2275 1.2046 1.1880 1.1755 1.1643 1.1586 1.1522 1.1388 1.1305 1.1221 1.1087 1.1019 1.0963

1.2764 1.2581 1.2421 1.2201 1.1969 1.1807 1.1675 1.1564 1.1502 1.1442 1.1308 1.1226 1.1140 1.1001 1.0935 1.0884

d/(g·cm−3)

x(NH4NO3) 1.3121 1.2953 1.2802 1.2570 1.2354 1.2176 1.2071 1.1963 1.1912 1.1844 1.1712 1.1626 1.1547 1.1424 1.1343 1.1296

1.3049 1.2879 1.2725 1.2496 1.2279 1.2099 1.1994 1.1879 1.1838 1.1763 1.1627 1.1543 1.1462 1.1342 1.1274 1.1219

1.2978 1.2804 1.2649 1.2422 1.2201 1.2026 1.1915 1.1799 1.1754 1.1683 1.1547 1.1463 1.1381 1.1257 1.1189 1.1137

Standard uncertainties are u(d) =2·10−4 g·cm−3, u(x) = 1·10−4, u(T) = 0.01 K.

o≠ o≠ o≠ Table 8. Values of Vo1, Vo2, Δμo≠ 1 , Δμ2 , TΔS2 and ΔH2 for NH4NO3 + FA Solutions at Different Temperatures

a

parameter

T/K = 298.15

T/K = 308.15

T/K = 318.15

T/K = 328.15

T/K = 338.15

T/K = 348.15

Vo2·106/(m3·mol−1)a Vo2·106/(m3·mol−1)a −1 Δμo≠ 1 / (kJ·mol ) −1 Δμo≠ / (kJ·mol ) 2 −1 TΔSo≠ / (kJ·mol ) 2 −1 ΔHo≠ 2 / (kJ·mol )

40.03 36.89 14.33 24.17 −2.82 21.34

40.32 38.55 14.34 24.33 −2.92 21.41

40.62 39.22 14.31 24.45 −3.01 21.43

40.93 39.82 14.27 24.56 −3.11 21.45

41.24 40.95 14.33 24.60 −3.20 21.40

41.56 41.78 14.60 24.65 −3.30 21.35

Calculated from ref 6.

Table 9. Values of the Parameters E, V, B′, ΔGsalt * and ΔGo* with Regression Coefficient R2 E V R2 B′a ΔG*o /(kJ·mol−1) ΔGsalt * /(kJ·mol−1) a

T/K = 298.15

T/K = 308.15

T/K = 318.15

T/K = 328.15

T/K = 338.15

T/K = 348.15

8.416 ± 0.082 5.061 ± 0.039 0.9992 0.153 14.32 49.50

8.054 ± 0.074 4.658 ± 0.036 0.9996 0.154 14.33 49.30

7.692 ± 0.065 4.259 ± 0.034 0.9992 0.156 14.30 48.95

7.550 ± 0.058 4.091 ± 0.029 0.9992 0.157 14.26 49.11

7.197 ± 0.045 3.762 ± 0.027 0.9991 0.156 14.32 48.87

6.636 ± 0.032 3.704 ± 0.018 0.9997 0.133 14.59 48.39

Calculated using eq 13.

should always be positive, and can be predicted using the Thomas relation:25 D = 10.05·10−6(V 2o)2

Δμ2o ≠ = Δμ1o ≠ +

RT (1000B + V 2o − V1o) V1o

(6)

where B is the viscosity coefficient obtained from eq 4, Δμo≠ 2 is the ionic activation energy at infinite dilution, and Vo1 is the

(5)

partial molar volumes of the solvent at infinite dilution calculated from our previous work.6 Experimental density values used for this calculation at 298.15 K and from our previous work are presented in Table 7. Δμo≠ 1 represents the free energy of activation of viscous flow per mole of the pure solvent and is given by the relation:

where Vo2 is the partial molar volume of the solute at infinite dilution obtained from our previous work.6 The coefficient 10.05 in eq 5 accounts for the hydrodynamic interactions of spheres, and the effect of doublet formation due to collision was determined by Later, Manley, and Mason.26 The values of the parameter D obtained using eqs 4 and 5 show good agreement (Table 6) and indicate that it is necessary to take into account the hydrodynamic interaction of particles, particle rotation, and collision between particles, which describes the parameter D. It was interesting to analyze experimental viscosity data on the basis of transition state theory of relative viscosity,5 using the following expression:

⎛ η V1o ⎞ Δμ1o ≠ = RT ln⎜ o ⎟ ⎝ hNA ⎠

(7)

where NA is Avogadro’s number, h is Planck constant, η0 is the viscosity of the solvent, R is the universal gas constant, and T is absolute temperature. The values of Δμo≠ and Δμo≠ are 1 2 o≠ reported in Table 8. It can be seen that Δμ1 is practically 3368



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ΔH2o ≠ = Δμ2o ≠ + T ΔS2o ≠

(9)

o≠ The values of TΔSo≠ 2 and ΔH2 are reported in Table 8. On the basis of Eyring’s absolute rate theory, Goldsack and Franchetto28 have proposed a model for calculating the viscosity of concentrated solutions of 1:1 electrolytes:

η=

ηoe XE (10)

1 + XV +

NO3−

where X is the mole fraction of NH4 or ions in the solution. The parameter E is defined by the molar free energy of activation for viscous flow of the anion (ΔGa*), cation (ΔGc*), and solvent particles (ΔGo*): E = (ΔGc* + ΔGa* − 2ΔGo*)/(RT )

The parameter V from eq 10 represents the absolute ionic hydration number and is defined by the volume of the anion, cation, and pure solvent (formamide) particles:

Figure 3. Comparison of the viscosity data obtained by using eq 10 and the experimental values at 298.15 K.

⎛ V + Va ⎞ V=⎜ c ⎟−2 ⎝ Vo ⎠

constant at all compositions and temperatures, implying that o Δμo≠ 2 depends mainly on the viscosity coefficient B and the V2 5 o o≠ o≠ − V1 term in eq 6. According to Feakins et al., if Δμ2 > Δμ1 the coefficient B will be positive for electrolyte solutions. This indicates stronger ion−solvent interactions and suggests a weakening of the intermolecular forces in the solvent structure. The higher value of Δμo≠ 2 will effect a stronger tendency for the electrolyte to form a structure.27 The entropy of activation for electrolytic solutions has been calculated from ΔS2o ≠ = −

(12)

where Vc is molar volume of the cation, Va is molar volume of the anion, and V0 is the molar volume of the pure formamide. The obtained results from eq 10 are listed in Table 9 at five selected temperatures: 308.15, 318.15, 328.15, 338.15, and 348.15 K. The parameters E and V are related to the Jones− Dole’s viscosity coefficient B′ by the following relation: B′ =

d(Δμ2o ≠ ) dT

(11)

(E − V ) 22.02

(13)

The equation applies to formamide solution on the molal scale, since there are 22.02 mol of formamide per kilogram of formamide. Calculated values of the coefficient B using eq 13 are in a good agreement with those obtained using Jones− Dole’s eq 3, as it can be seen by comparing the B values listed in Tables 5 and 9.

(8)

ΔSo≠ 2

where has been obtained from the negative slope of the plots of Δμo≠ 2 versus T, using last squares treatment. The activation enthalpy has been calculated from

Figure 4. Variation of relative viscosity with ammonium nitrate mole fraction and temperature. 3369



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to aqueous, non- aqueous and methanol + water systems. J. Chem. Soc. Faraday Trans. 1974, 70, 795−806. (4) Wang, P.; Anderko, A.; Young, R. D. Modeling viscosity of concentrated and mixed-solvent electrolyte systems. Fluid Phase Equilib. 2004, 226, 71−82. (5) Roy, M. N.; Bhattacharjee, A.; Das, R. K. Studies on molecular interactions of oxalic acid and its salts in co-aqueous solutions of 1,3dioxolane by volumetric and viscometric measurements at T = (298.15, 308.15, and 318.15) K. J. Mol. Liq. 2010, 156, 146−153. (6) Gadzuric, S.; Vranes, M.; Dozic, S. Electrical conductivity and density of ammonium nitrate + formamide mixtures. J. Chem. Eng. Data 2011, 56, 2914−2918. (7) Dožić, S.; Vraneš, M.; Zec, N.; Gadžurić, S. Transport properties of ammonium nitrate in N-methylformamide and N,N-dimethylformamide. J. Mol. Liq. 2014, 195, 99−104. (8) Dožić, S.; Vraneš, M.; Gadžurić, S. Volumetric properties of ammonium nitrate in N-methylformamide. J. Mol. Liq. 2014, 193, 189−193. (9) Vraneš, M.; Dožić, S.; Djerić, V.; Gadžurić, S. Volumetric properties of ammonium nitrate in N,N-dimethylformamide. J. Chem. Thermodyn. 2012, 54, 245−249. (10) Cases, A. M.; Gómez Marigliano, A. C.; Bonatti, C. M.; Sólimo, H. N. Density, viscosity, and refractive index of formamide, three carboxylic acids, and formamide + carboxylic acid binary mixtures. J. Chem. Eng. Data 2001, 46, 712−715. (11) Almasi, M. Densities and viscosities of the mixtures (formamide + 2-alkanol): Experimental and theoretical approaches. J. Chem. Themordyn. 2014, 69, 101−106. (12) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents, Physical Properties and Methods of Purification, 4th ed.; Wiley Interscience: New York, 1986. (13) Nain, A. K. Ultrasonic and viscometric studies of molecular interactions in binary mixtures of formamide with ethanol, 1-propanol, 1,2-ethanediol and 1,2-propanediol at different temperatures. J. Mol. Liq. 2008, 140, 108−116. (14) Campos, V.; Gómez Marigliano, A. C.; Sólimo, H. N. Density, viscosity, refractive index, excess molar volume, viscosity, and refractive index deviations and their correlations for the (formamide + water) system. Isobaric (vapor + liquid) equilibrium at 2.5 kPa. J. Chem. Eng. Data 2008, 53, 211−216. (15) Fulcher, G. S. Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc. 1925, 8, 339−355. (16) Jones, G.; Dole, M. The viscosity of aqueous solutions of strong electrolytes with special reference to barium chloride. J. Am. Chem. Soc. 1929, 51, 2950−2964. (17) Onsager, L.; Fuoss, R. M. Irreversible processes in electrolytes. Diffusion, conductance and viscous flow in arbitrary mixtures of strong electrolytes. J. Phys. Chem. 1932, 36, 2689−2778. (18) Kaminsky, M. The concentration and temperature dependence of the viscosity of aqueous solutions of strong electrolytes. III. KCl, K2SO4, MgCl2, BeSO4, and MgSO4 solutions. Z. Phys. Chem. Neue Folge 1957, 12, 206−231. (19) Abdulagatov, I. M.; Azizov, N. D. Experimental study of the effect of temperature, pressure, and concentration on the viscosity of aqueous KBr solutions. J. Solution Chem. 2008, 37, 3−26. (20) Lencka, M. M.; Anderko, A.; Sanders, S. J.; Young, R. D. Modeling viscosity of multicomponent electrolyte solutions. Int. J. Thermophys. 1998, 19, 367−378. (21) Magerramov, M. A.; Abdulagatov, A. I.; Abdulagatov, I. M.; Azizov, N. D. Viscosity of tangerine and lemon juices as a function of temperature and concentration. Int. J. Food Sci. Technol. 2007, 42, 804−818. (22) Roy, M. N.; Bhattacharjee, A.; Chakraborty, P. Investigation on molecular interactions of nicotinamide in aqueous citricacid monohydrate solutions with reference to manifestation of partial molar volume and viscosity B-coefficient measurements. Thermochim. Acta 2010, 507−508, 135−141.

Variation of the viscosity with temperature in concentrated electrolyte solutions can be explained by comparing the temperature dependence of the parameters E and V from eq 13. The temperature dependence of these parameters reveals two types of ionic behavior: structure-making ions (if E > V) and structure-breaking ions (if E < V). According to our results (Table 9), the ammonium nitrate + formamide system exhibits a structure-making type of ionic behavior. The free energy of activation for viscous flow of the solvent, ΔG*o , can be determined from the following equation: ⎛ η Vo ⎞ ΔGo* = RT ln⎜ o ⎟ ⎝ hNA ⎠

(14)

where Vo is the molar volume of the solvent (formamide). Combining Vo with eqs 11 and 14 and the parameter E shown in Table 9, the total salt free energy of activation, ΔGsalt * can be calculated as * = ΔGc* + ΔGa* ΔGsalt

(15)

Calculated data are listed in Table 9, and their fit is graphically presented in Figure 3. The combined effect of temperature and concentration on the viscosity over a wide range of ammonium nitrate concentration may be expressed by the following relation: Ax B x2 ⎛ η x⎞ = o + o + exp⎜CoT + Do ⎟ ⎝ T T T⎠ ηo

(16)

where x is a mole fraction of ammonium nitrate, Ao, Bo, Co, and Do are parameters of the fit 327.77 ± 5.29, 725.56 ± 19.27, −1.098 ± 0.094, and 1302.99 ± 15.52, respectively. The results obtained using this equation are in good agreement with the experimental results, as can be seen from Figure 4. The largest deviations from the experimental values are reported at 348.15 K at high ammonium nitrate concentration level. The maximum relative error is 3.98 % at ammonium nitrate mole fraction of 0.3703, and the average relative error of the fit obtained using this equation is found to be 1.3 %.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +381 21 4852744. Fax: +381 21 454065. E-mail: [email protected]. Funding

This work was financially supported by the Ministry of Education, Science and Technological Development of Republic of Serbia under contract number ON172012 and The Provincial Secretariat for Science and Technological Development of APV. Notes

The authors declare no competing financial interest.

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REFERENCES

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Viscosity of Ammonium Nitrate+ Formamide Mixtures

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