Densities and Viscosities for Aqueous Solutions of Sodium Chlorate

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Densities and Viscosities for Aqueous Solutions of Sodium Chlorate and Potassium Chlorate + Methanol from (288.15 to 318.15) K at 0.1 MPa Guadalupe Pérez-Durán and Gustavo A. Iglesias-Silva*

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Departamento de Ingeniería Química Tecnológico Nacional de México en Celaya Celaya, Guanajuato, C.P. 38010 México ABSTRACT: In this work, we present densities and viscosities of aqueous solutions of sodium and potassium chlorate from (288.15 to 318.15) K at molalities from (0.1 to 1) and (0.01 to 0.5) for the aqueous solutions of sodium and potassium chlorate, respectively. Also, densities and viscosities of these aqueous solutions of sodium and potassium chlorate + methanol are measured from (288.15 to 318.15) K at concentration from (0.1 to 1, 0.1 to 0.3) m, respectively. Densities are from a vibrating tube densimeter and viscosities are from a rolling ball microviscosimeter. Ternary mixtures are prepared by adding (1 to 20)% volume of methanol to the aqueous solutions. Apparent molar volumes are calculated from the density measurements. Apparent molar volumes have been correlated using an extended Redlich−Rosenfeld− Meyer equation. The values of the parameters indicate that a stronger interaction of solvent−ions occurs in the potassium chlorate solution than in the sodium chlorate aqueous solutions. The equation correlates the data within an average absolute percentage deviation of 3.7%. Limiting apparent molar volumes for the sodium and potassium chlorate aqueous solution from this work agree within 1.9 cm3/mol with the literature values. Solutions of potassium chlorate show an iso-viscosity behavior at the temperatures and concentrations considered in this work. Also, the Dole-Jones equation correlates the viscosity data within an average absolute percentage deviation of 0.29%.

1. INTRODUCTION Thermodynamic properties such as the density and viscosity are important in the design of chemical processes. The density can be useful to determine the characteristic of the material while the viscosity can be used to determine the transport of the material. Sodium and potassium chlorates are oxidizing agents and in combination with other substances can form explosive mixtures. Sodium chlorate is also used in the production of chlorine dioxide.1 Sodium chlorate aqueous solutions can be used as a herbicide but only in an adequate amount of water since the sodium chlorate is susceptible to leaching.2 Sodium chlorate is phytotoxic for all green plants. It has a sterilizing effect to the soil and it can be mixed with other herbicides in aqueous solution as long as the herbicide does not oxidize. Sodium chlorate is a major and stable byproduct present in drinking water, which has been disinfected by chlorine dioxide.3 Hanley et al.4 measured the solubility of NaClO3 and KClO3 and determined the Pitzer parameters for each salt. They performed evaporation rate experiments in a Mars simulation chamber to determine the activity of water for various concentrations. They mention that the chlorate ion is an intermediate oxidation species between the chlorine ion and perchlorate ion both found on Mars, and there exists a possibility that chlorate can be found on Mars. Also, aqueous solutions of potassium chlorate can be used in the veterinary pharmaceutical industry. They are used as a weak astringent antiseptic in stomatitis.5 Therefore, there is a need of thermodynamic properties of chlorates. Crystallization of © XXXX American Chemical Society

potassium salts in water can change drastically by the addition of alcohols such as methanol and ethanol.6 Therefore, the sodium and potassium chlorate in aqueous solution can be crystallized in a drowning out process by the addition of methanol. Linnivov7 uses ethanol for creation of supersaturation in solutions allowed to vary strongly the crystallization process conditions. Aqueous solutions of sodium chlorate with methanol8 are used in chlorine dioxide facilities. They are continuously fed to a vessel that serves as reactor and evaporative crystallizer. On the other hand, potassium chlorate with water + methanol9 can be used in a process of blasting with an inorganic oxidizer. Thermodynamic properties of aqueous solutions of potassium and sodium chlorate reported in the literature are scarce. The solubility of sodium and potassium chlorate in water has been reported by Miyamoto.10 He makes a compilation of solubility data of sodium chlorate with various solvents. In his work, he reports the solubility of sodium chlorate and potassium chlorate in water. Hood11 measure the viscosities of an aqueous solution of potassium chlorate at 298.15 K and at molar concentrations from 0.01 to 0.56. He uses an Ostwald viscosimeter. Jones and Talley12 measure the viscosity of an aqueous solution of potassium Special Issue: Latin America Received: October 31, 2018 Accepted: April 15, 2019

A

DOI: 10.1021/acs.jced.8b01008 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information chemical name

source

CASRN

initial purity mass fraction

purification method

analysis methoda

water methanol sodium chlorate potassium chlorate

Fermont J.T. Baker Sigma-Aldrich Sigma-Aldrich

7732-18-5 67-56-1 7775-09-9 3811-04-9

0.9997 0.9997 0.9997 0.9996

none none none none

GC GC titration titration

a

Gas chromatography or titration provided by the supplier.

dry air as reference fluids.20 In this work, oscillating periods in μs can be represented as τ = 2702.7 + 999.21ρ within 0.05% error. The density must be given in g·cm−3. We estimate the standard uncertainty in the density to be 0.00025 g·cm−3. Viscosities are measured using a rolling ball microviscosimeter (Anton Paar, AVMn). The microviscosimeter uses a small sample quantity (400 μL) in a capillary tube of 1.6 mm therefore temperature equilibrium is achieved rapidly. The temperature is measured using a Pt-100 thermometer with an uncertainty of 0.05 K. The operation principle is based upon measuring the descending time of a rolling ball of a fixed distance inside a capillary tube full of sample. The ball descends due to the difference between the densities of the ball and the fluid and the viscosity can be calculated using a relation between the viscosity, the time, and the densities,

chlorate at 298.15 K at molar concentrations up to 0.1 using also an Ostwald viscosimeter. Oliver and Campbell13 measure the electrical conductivity, viscosity, and density of aqueous solutions of sodium chlorate at 298.15 K. They use a modified pycnometer type Ostwald with a capacity of 45 cm3. Two identical pycnometers are used to corroborate the weight in the procedure. They report an accuracy of ±0001 g/cm3. Later, Roux et al.14 measure heat capacities and apparent molar volumes of electrolyte solutions at 298.15 K. In their work, they include aqueous solutions of potassium and sodium chlorate. They measure density differences with a flow vibrating tube densimeter with a repeatability of ±3 ppm. Densities of sodium chlorate in mixed solvent (water + aniline hydrochloride) have been measured at 303.15 K by Berchiesi et al.15 Harano et al.16 measure the nucleation rate of potassium chlorate from supersaturated aqueous solutions. Unfortunately, there are not measurements of aqueous solutions of sodium and potassium chlorate with methanol reported in the literature. In this work, we present the densities and viscosities of aqueous solutions of potassium and sodium chlorate from (288.15 to 333.15) K and (288.15 to 318.15) K, respectively. For the aqueous solutions, we have considered the concentration range of (0.1 to 1) and (0.01 to 0.5) m. Also, in this work we present the densities and viscosities of these aqueous solutions + methanol. They are measured from (288.15 to 318.15) K at concentrations from (0.1 to 1) and (0.1 to 0.3) m for aqueous solutions of sodium and potassium chlorate, respectively. We have calculated apparent molar volumes for the mixtures. We have used the Redlich− Rosenfeld−Meyer17,18 (RRM) equation and the correlation of Jones and Dole19 to represent the apparent molar volumes and viscosities, respectively.

η = K1 + K 2t(ρb − ρf )

(1)

where K1 and K2 are calibration constants; t is the rolling time in seconds; ρb and ρf are the densities of the ball and the fluid, respectively. The calibration constants are obtained using the viscosity and the rolling time of n-decane, 1-nonanol, and CANNON viscosity reference standard number S3. The estimated relative standard uncertainty in the viscosity is equal to 0.015. Generally, the molality uncertainty is not presented formally. Here, we calculate molality standard uncertainty considering mi =

nis

=

mTsolv

nis solv

∑l = 1 mlsolv

(2)

where nsi is the moles of solute i; msolv T is the total mass of the solvents in kg; msolv is the l-solvent mass in kilogram. l Considering that the mixture is prepared gravimetrically, the molality is

2. EXPERIMENTAL SECTION Samples. The samples are provided by J.T. Baker for methanol (99.97% in mass fraction), Fermont for water (HPLC), Sigma-Aldrich for potassium chlorate (99.96% in mass fraction) and sodium chlorate (99.97% in mass fraction). Table 1 presents the sample specifications. The mixtures are prepared gravimetrically using an analytical balance (Ohaus, OHAUS00240) with a precision of 0.1 mg. The samples are prepared prior to measurement, placed in sealed containers and mixed thoroughly to guarantee a homogeneous system and total solubility of the salt. Also, preventive measures are taken to avoid exposure to air and evaporation. Apparatuses and Procedures. Densities of binary and ternary mixtures are measured with a vibrating tube densimeter (Anton Paar, DMA 5000). The reproducibility for density and temperature reported by the manufacturer are 1 × 10−6 g·cm−3 and 0.001 K, respectively. The density of the fluid is related to the period of oscillation of the U-tube filled with the sample when the cell is under a harmonic electromagnetic force. The densimeter is calibrated periodically using ultrapure water and

mi = f ({mks}, {mksolv }, {Mk})

(3)

where msk is the k solute mass in grams, msk is the k solvent mass in kg; and Mk is the molar mass in g·g mol−1. The total differential of eq 3 is solutes

dmi =

∑ k=1

ij ∂mi yz jj z dmks jj ∂m s zzz k k {mjs≠k , mTsolv , M

solvents

+

∑ k=1 solutes

+

∑ k=1

ij ∂mi yz jj z dmksolv jj solv zzz ∂ m s solv k k {mT , mj≠k , M , mj≠k

ij ∂mi yz jj z dMk jj ∂M zzz k k {mT , Mj≠k

(4)

Without considering cross terms or covariance, the square of the molality standard uncertainty is B


Journal of Chemical & Engineering Data solutes

∑

(σmi)2 =

k=1

ij ∂mi yz jj z (σmks)2 jj ∂m s zzz k k {mjs≠k , mTsolv , M 2

solvents

∑

+

k=1 solutes

+

Article

∑ k=1

Table 2. Comparison between Experimental Liquid Density and Viscosity for Sodium and Potassium Aqueous Solutions at 298.15 K, m1 = 0.1 mol·kg−1 and Pressure p = 0.1 MPaa

ij ∂mi yz jj z (σmksolv )2 jj solv zzz ∂ m k k {mTs , mjsolv ≠ k , M , mj ≠ k

ρ/g·cm−3

2

ij ∂mi yz jj z (σMk)2 jj ∂M zzz k k {mT , Mj≠k 2

(5)

mis MimTsolv

solvents

Mi ∑i = 1

this work

literature

this work

1.00429 1.00465

1.0040512 1.004439 1.00468810 1.00459812

0.941 0.878

(6)

ij ∂mi yz δ jj z = solvik jj ∂m s zzz mT Mi k k {mjs≠k , mTsolv , M

Then the derivatives are

ij ∂mi yz mis mi jj zz = − = − solv jj solv zz solv 2 (mT ) Mi mT k ∂mk {mTs , mjsolv ≠ k , M , mj ≠ k ij ∂mi yz mis δik δ jj z = − solv = −mi ik jj ∂M zzz 2 M M mT k k k k {mT , Mj≠k

(7)

0.89799 0.888710

2

∑

(10)

For a mixture with a solute and a solvent, the molality uncertainty is given by

(8)

and

2 ij m1 yz ij 1 yz 1 zy ji s 2 solv 2 2 z j z jj jj solv zzz (σm1 ) + jjj− solv zzz (σm1 ) + jjjj− m1 zzzz (σM1) M m M m 1 1{ T { { k k k T 2

σm1 =

2

(11)

(9)

where δik is a kronecker delta. Finally,

and for a mixture with a solute and two solvents,

2 ij 1 yz i y i y jj zz (σm s)2 + jjj− m1 zzz {(σm solv )2 + (σm solv )2 } + jjj−m 1 zzz (σM )2 jj solv zz jj 1 1 2 1 jj 1 M zz solv z z 1{ k k mT M1 { k mT { 2

σm1 =

ij δik yz s 2 jj z jj solv zzz (σmk ) m M k=1 k T i{ 2 solvents ij mi yz zz ∑ (σm solv )2 + jjjj− solv zz k m k=1 T { k 2 solutes ij δ yz + ∑ jjj−mi ki zzz (σMk)2 j Mk z{ k=1 k solutes

(σmi)2 =

misolv

literature

Standard uncertainties: u(ρ) = 2.5·10−4 g·cm−3, ur(η) = 0.015, u(m1) = 0.0008 mol kg−1, u(T) = 0.05 K u(p) = 10 kPa.

mis

=

aqueous solution sodium chlorate potassium chlorate

a

The derivatives can be found from the definition of molality and expressing everything in terms of mass, mi =

η/mPa·s

2

Using eqs 11 and 12, the maximum standard uncertainties for the molality is 0.0008 mol·kg−1. Standard uncertainties for the density, viscosity, and derived properties are calculated using a propagation error formula.21 Preparation of the aqueous solution with alcohol are performed gravimetrically with a methanol content of approximately (1, 5, 15, and 20)% volume.

AAPD =

l N |X exp − X lit orcalc| | o 100 o o o i i m } ∑ exp o o o N o i=1 Xi n ~

(12)

(13)

or calc where Xexp and Xlit are experimental and calculated (or i i literature) densities or viscosities, respectively; and N is the number of experimental data. The comparison with the density of Oliver and Campbell13 is a single point at a molality equal to 1.04. Densities of aqueous solutions of potassium chlorate have been compared with those reported by Hood,11 Jones and Talley,12 and Roux et al.14 and our values agree within an average absolute percentage error of (0.007, 0.005, and 0.006)%, respectively. Unfortunately, densities for aqueous solutions with methanol have not been published in the literature. Tables 5−8 show the densities for the aqueous solutions of sodium chlorate and potassium chlorate with methanol together with the mole fraction of methanol in the mixed solvent (methanol + water). The percentage volumes in the solvent are approximately (1, 5, 15, 20)% We have calculated the apparent molar volume from the experimental densities using

3. RESULTS We have measured the densities of aqueous solutions of sodium and potassium chlorate from (288.15 to 333.15) K and (288.15 to 318.15) K, respectively. We have considered the concentration range of (0.1 to 1) and (0.01 to 0.5) m1 for the aqueous solutions of sodium and potassium chlorate. We have compared our experimental densities for the sodium chlorate aqueous solutions with the density values from Oliver and Campbell13 and Roux et al.14 Our experimental measurements agree with their values within an average absolute percentage deviation of (0.0015 and 0.017)%, respectively. Table 2 shows a comparison of the density and viscosity with literature values at m1 = 0.1 and 298.15 K. Experimental densities are shown in Tables 3 and 4. The average absolute percentage deviation is calculated using

V⌀ 1 = 1000 C

ρs − ρ m1ρρs

+

M1 ρ

(14) DOI: 10.1021/acs.jced.8b01008 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 3. Experimental Densities, ρ (g·cm−3), Apparent Molar Volumes, Vϕ1 (cm3·mol−1), and Viscosities, η (mPa·s), at Temperature T, and Molality, m1 (mol·kg−1) for Sodium Chlorate Aqueous Solution at Pressure p = 0.1 MPaa m1 mol·kg−1

ρ g·cm−3

0.0000 0.1000 0.2030 0.3010 0.4060 0.5010 0.6100 0.7090 0.8090 0.8920 0.9950

0.999115 1.00654 1.01373 1.02046 1.02769 1.03424 1.04164 1.04827 1.05501 1.06047 1.06722

0.0000 0.1000 0.2030 0.3010 0.4060 0.5010 0.6100 0.7090 0.8090 0.8920 0.9950

0.994037 1.00112 1.00792 1.01439 1.02131 1.02758 1.03468 1.04102 1.04749 1.05269 1.05923

Vϕ1 cm3·mol−1

η mPa·s

ρ g·cm−3

1.122 1.126 1.134 1.142 1.150 1.157 1.165 1.177 1.189 1.200 1.208

0.998216 1.00554 1.01260 1.01924 1.02640 1.03287 1.04018 1.04673 1.05339 1.05878 1.06547

0.719 0.726 0.734 0.742 0.750 0.758 0.765 0.774 0.781 0.788 0.796

0.992218 0.99924 1.00598 1.01238 1.01926 1.02547 1.03251 1.03880 1.04520 1.05036 1.05681

T = 288.15 K 31.955 33.935 34.769 35.036 35.077 35.207 35.341 35.342 35.447 35.543 T = 308.15 K 35.146 37.694 37.888 38.041 38.033 38.090 38.206 38.161 38.271 38.258

Vϕ1 cm3·mol−1

η mPa·s

ρ g·cm−3

0.990 0.996 1.007 1.017 1.025 1.033 1.042 1.050 1.058 1.067 1.076

0.997055 1.00429 1.01124 1.01783 1.02490 1.03129 1.03852 1.04500 1.05159 1.05691 1.06355

0.656 0.663 0.670 0.678 0.685 0.693 0.700 0.708 0.716 0.723 0.729

0.990214 0.99718 1.00388 1.01022 1.01704 1.02320 1.03019 1.03643 1.04278 1.04783 1.05422

T = 293.15K 32.937 35.368 35.789 35.948 35.970 36.076 36.200 36.183 36.289 36.351 T = 313.15 K 35.686 38.202 38.442 38.579 38.572 38.613 38.728 38.682 38.798 38.809

Vϕ1 cm3·mol−1

η mPa·s

ρ g·cm−3

0.882 0.889 0.897 0.908 0.918 0.926 0.933 0.942 0.949 0.957 0.965

0.995654 1.00281 1.00967 1.01621 1.02320 1.02953 1.03669 1.04309 1.04962 1.05488 1.06146

T = 298.15 K 33.782 36.292 36.554 36.739 36.753 36.840 36.955 36.924 37.028 37.063 T = 318.15 K 36.163 38.653 38.920 39.055 39.045 39.073 39.188 39.144 39.325 39.345

Vϕ1 cm3·mol−1

η mPa·s

T = 303.15 K 34.501 37.056 37.262 37.426 37.433 37.502 37.620 37.576 37.681 37.694

0.793 0.801 0.809 0.817 0.827 0.835 0.841 0.849 0.857 0.865 0.873

0.602 0.609 0.616 0.623 0.631 0.637 0.643 0.650 0.657 0.665 0.672

a Standard uncertainties: u(ρ) = 2.5·10−4 g·cm−3, ur(η) = 0.015, u(Vϕ1) = (3.2 at 0.1 m and 0.25 at 1 m) cm3 mol−1, u(m1) = 0.0008 mol kg−1, u(T) = 0.05 K u(p) = 10 kPa.

Table 4. Experimental Densities, ρ (g·cm−3), Apparent Molar Volumes, Vϕ1 (cm3·mol−1), and Viscosities, η (mPa·s), at Temperature T, and Molality, m1 (mol·kg−1) for Potassium Chlorate Aqueous Solution at Pressure p = 0.1 MPaa m1 mol·kg−1

ρ g·cm−3

0.0000 0.0101 0.1001 0.2010 0.3021 0.4009 0.5008

0.999115 0.99992 1.00689 1.01452 1.02210 1.02941 1.03668

0.0000 0.0101 0.1001 0.2004 0.3021 0.4001 0.5008

0.994037 0.99481 1.00150 1.00884 1.01614 1.02318 1.03020

Vϕ1 cm3·mol−1

η mPa·s

ρ g·cm−3

1.122 1.127 1.113 1.105 1.101 1.100 1.105

0.998216 0.99901 1.00589 1.01344 1.02093 1.02817 1.03537

0.719 0.725 0.717 0.717 0.718 0.720 0.725

0.992218 0.99299 0.99962 1.00691 1.01415 1.02115 1.02813

T = 288.15 K 42.706 44.540 45.189 45.421 45.583 45.790 T = 308.15 K 45.811 47.454 48.032 48.191 48.290 48.436

Vϕ1 cm3·mol−1

η mPa·s

ρ g·cm−3

0.990 0.995 0.984 0.979 0.977 0.977 0.983

0.997055 0.99784 1.00465 1.01212 1.01954 1.02671 1.03384

0.656 0.661 0.655 0.656 0.656 0.659 0.665

0.990214 0.99098 0.99757 1.00480 1.01199 1.01896 1.02590

T = 293.15K 43.861 45.450 46.064 46.263 46.398 46.581 T = 313.15 K 46.454 48.030 48.542 48.705 48.775 48.911

Vϕ1 cm3·mol−1

η mPa·s

ρ g·cm−3

0.882 0.888 0.878 0.874 0.873 0.876 0.881

0.995654 0.99644 1.00318 1.01058 1.01794 1.02504 1.03212

T = 298.15 K 44.714 46.235 46.816 46.992 47.110 47.281 T = 318.15 K 46.996 48.504 49.030 49.188 49.217 49.317

Vϕ1 cm3·mol−1

η mPa·s

T = 303.15 K 45.264 46.886 47.460 47.626 47.742 47.885

0.793 0.799 0.789 0.788 0.788 0.791 0.797

0.602 0.607 0.602 0.603 0.604 0.608 0.613

Standard uncertainties: u(ρ) = 2.5·10−4 g·cm−3, ur(η) = 0.015, u(Vϕ1) = (3.2 at 0.1 m and 0.25 at 1 m) cm3 mol−1, u(m1) = 0.0008 mol kg−1, u(T) = 0.05 K u(p) = 10 kPa. a

where M1 is the molar mass of the chlorate, ρ is the density of the solution, ρs is the density of the solvent, and m1 is the molality of the solution. Figures 1 and 2 show the apparent molar volume for the sodium and potassium chlorate solutions. For the calculation of the apparent volume of the chlorates with methanol, densities for the solvent mixture (water + methanol) have been taken from Coquelet et al.22 Standard uncertainty for the apparent molar volume has been calculated

using a propagation error formula. The calculated uncertainty ranges from (3.2 to 0.25) cm3·mol−1 at molalities from (0.1 to 1). Higher values of the apparent molar volumes of potassium chlorate than those of sodium chlorate suggest that the potassium ion has a smaller surface charge than the sodium ion.13 Solvation on both aqueous solutions decreases with increasing concentration (increase in apparent molar volume); however, the decrease of solvation is higher in sodium chlorate D



Article

Table 5. Experimental Densities, ρ (g·cm−3), Apparent Molar Volumes, Vϕ1 (cm3·mol−1), and Viscosities, η (mPa·s), at Temperature T, and Molality, m1 (mol·kg−1) for Sodium Chlorate in a (Water + Methanol) Solution and at Pressure p = 0.1 MPaa m1 mol·kg−1

xmeth

ρ g·cm−3

0.1000 0.3000 0.5085 0.8055 1.0054

0.0044 0.0045 0.0045 0.0045 0.0045

1.00500 1.01899 1.03344 1.05314 1.06591

0.1000 0.3000 0.5085 0.8055 1.0054

0.0044 0.0045 0.0045 0.0045 0.0045

1.00116 1.01474 1.02869 1.04775 1.06014

0.1009 0.3018 0.5014 0.8014 1.0094

0.0228 0.0229 0.0232 0.0228 0.0229

0.99987 1.01428 1.02729 1.04701 1.06051

0.1009 0.3018 0.5014 0.8014 1.0094

0.0228 0.0229 0.0232 0.0228 0.0229

0.99573 1.00989 1.02246 1.04155 1.05462

Vϕ1 cm3·mol−1 T = 288.15 K 17.501 29.363 31.709 33.592 34.486 T = 303.15 K 18.662 31.022 33.610 35.528 36.384 T = 288.15 K 26.765 31.189 34.194 35.445 35.738 T = 303.15 K 26.877 31.954 35.480 36.996 37.362

η mPa·s

ρ g·cm−3

1.153 1.164 1.188 1.221 1.217

1.00390 1.01779 1.03206 1.05152 1.06415

0.815 0.827 0.847 0.875 0.875

0.99947 1.01291 1.02674 1.04562 1.0579

1.257 1.277 1.299 1.330 1.325

0.99866 1.01304 1.02589 1.04538 1.05872

0.872 0.891 0.912 0.938 0.937

0.99400 1.00800 1.02046 1.03938 1.05234

Vϕ1 cm3·mol−1 T = 293.15K 17.640 29.713 32.250 34.211 35.111 T = 308.15 K 20.288 31.996 34.398 36.230 37.047 T = 293.15K 26.612 31.205 34.506 35.914 36.258 T = 308.15 K 27.609 32.693 36.126 37.598 37.939

η mPa·s

ρ g·cm−3

1.019 1.029 1.052 1.083 1.082

1.00264 1.01637 1.03047 1.04972 1.06222

0.739 0.750 0.769 0.794 0.795

0.99759 1.01091 1.02461 1.04334 1.05565

1.101 1.122 1.144 1.173 1.170

0.99725 1.01157 1.02427 1.04355 1.05675

0.786 0.803 0.823 0.848 0.848

0.99207 1.00606 1.01829 1.03706 1.04992


η mPa·s 0.906 0.919 0.940 0.970 0.969 0.674 0.685 0.703 0.727 0.728 0.975 0.995 1.016 1.045 1.043 0.713 0.730 0.749 0.780 0.773

Standard uncertainties: u(ρ) = 2.5·10−4 g·cm−3, ur(η) = 0.015, u(Vϕ1) = (3.2 at 0.1 m and 0.25 at 1 m) cm3 mol−1, u(m1) = 0.0008 mol kg−1, u(xmeth) = 0.0005, u(T) = 0.05 K u(p) = 10 kPa. Solvent: methanol + water, xmeth + xwater = 1

a

Table 6. Experimental Densities, ρ (g·cm−3), Apparent Molar Volumes, Vϕ1 (cm3·mol−1), and Viscosities, η (mPa·s), at Temperature T, and Molality, m1 (mol·kg−1) for Sodium Chlorate in a (water + methanol) solution and at Pressure p = 0.1 MPaa m1 mol·kg−1

xmeth

ρ g·cm−3

0.1029 0.3001 0.5002 0.8007 1.0003

0.0724 0.0728 0.0729 0.0728 0.0725

0.98735 1.00031 1.01369 1.03335 1.04607

0.1029 0.3001 0.5002 0.8007 1.0003

0.0724 0.0728 0.0729 0.0728 0.0725

0.98261 0.99511 1.00806 1.02713 1.03954

0.1014 0.3005 0.4998 0.8031 1.0038

0.1000 0.1002 0.1001 0.1000 0.0992

0.98211 0.99439 1.00729 1.02755 1.03978

0.1014 0.3005 0.4998 0.8031 1.0038

0.1000 0.1002 0.1001 0.1000 0.0992

0.97686 0.98855 1.00119 1.02077 1.03266


η mPa·s

ρ g·cm−3

1.560 1.585 1.600 1.618 1.611

0.98622 0.99878 1.01200 1.03144 1.04403

1.039 1.063 1.082 1.101 1.100

0.98060 0.99300 1.00583 1.02474 1.03695

1.709 1.727 1.752 1.764 1.765

0.98056 0.99262 1.00540 1.02544 1.03756

1.1248 1.1413 1.1647 1.1825 1.1923

0.97472 0.98626 0.9986 1.01822 1.02998

Vϕ1 cm3·mol−1 T = 293.15K 35.390 38.865 38.362 38.218 38.339 T = 308.15 K 35.753 39.419 39.430 39.505 39.735 T = 293.15K 25.970 37.974 38.647 37.815 38.620 T = 308.15 K 22.779 38.640 39.909 39.070 39.984

η mPa·s

ρ g·cm−3

1.346 1.373 1.391 1.409 1.409

0.98444 0.99704 1.01012 1.02936 1.04187

0.926 0.949 0.967 0.985 0.986

0.97843 0.99071 1.00344 1.0222 1.03451

1.473 1.488 1.512 1.542 1.534

0.97881 0.99068 1.00334 1.02312 1.03517

1.000 1.015 1.036 1.054 1.064

0.97239 0.98381 0.99551 1.01550 1.02713

Vϕ1 cm3·mol−1 T = 298.15 35.920 38.867 38.630 38.621 38.736 T = 313.15 36.324 39.988 39.954 40.005 40.023 T = 298.15 24.220 38.021 38.906 38.289 39.067 T = 313.15 23.131 39.156 41.557 39.576 40.521

η mPa·s

K 1.177 1.203 1.219 1.239 1.239 K 0.831 0.853 0.870 0.889 0.890 K 1.279 1.296 1.321 1.337 1.344 K 0.893 0.908 0.929 0.947 0.957

Standard uncertainties: u(ρ) = 2.5·10−4 g·cm−3, ur(η) = 0.015, u(Vϕ1) = (3.2 at 0.1 m and 0.25 at 1 m) cm3 mol−1, u(m1) = 0.0008 mol kg−1, u(xmeth) = 0.0005, u(T) = 0.05 K u(p) = 10 kPa. Solvent: methanol + water, xmeth + xwater = 1.

a

E



Article

Table 7. Experimental Densities, ρ (g·cm−3), Apparent Molar Volumes, Vϕ1 (cm3·mol−1), and Viscosities, η (mPa·s), at Temperature T, and Molality, m1 (mol·kg−1) for Potassium Chlorate in a (Water + Methanol) Solution and at Pressure p = 0.1 MPaa m1 mol·kg−1

xmeth

ρ g·cm−3

0.1009 0.2018 0.3057

0.0045 0.0045 0.0045

1.00548 1.01312 1.02092

0.1009 0.2018 0.3057

0.0045 0.0045 0.0045

1.00177 1.00914 1.01674

0.1077 0.2006 0.3008

0.0229 0.0229 0.0226

1.00034 1.00725 1.01512

0.1014 0.3005 0.4998

0.0229 0.0229 0.0226

0.99650 1.00307 1.01081

Vϕ1 cm3·mol−1 T = 288.15 29.271 37.470 40.278 T = 303.15 29.204 38.720 41.692 T = 288.15 43.432 45.047 44.216 T = 303.15 40.795 45.239 44.798

η mPa·s

ρ g·cm−3

1.135 1.151 1.140

1.00449 1.01202 1.01975

0.803 0.820 0.813

1.00008 1.00739 1.01493

1.263 1.260 1.248

0.99930 1.00608 1.01390

0.877 0.879 0.875

0.99477 1.00127 1.00896

Vϕ1 cm3·mol−1 T = 293.15K 28.364 37.537 40.514 T = 308.15 K 30.746 39.794 42.583 T = 293.15K 41.664 44.725 44.175 T = 308.15 K 41.495 45.999 45.415

K

K

K

K

η mPa·s

ρ g·cm−3

1.002 1.017 1.010

1.00324 1.01069 1.01835

0.728 0.741 0.739

0.99768 1.00546 1.01294

1.108 1.107 1.096

0.99802 1.00469 1.01246

0.792 0.792 0.788

0.99284 0.99927 1.00693

Vϕ1 cm3·mol−1 T = 298.15 28.381 37.960 41.000 T = 313.15 38.278 41.128 43.653 T = 298.15 40.806 44.810 44.380 T = 313.15 42.826 47.057 46.210

η mPa·s

K 0.893 0.907 0.904 K 0.664 0.676 0.675 K 0.982 0.982 0.975 K 0.719 0.721 0.719


a

Table 8. Experimental Densities, ρ (g·cm−3), Apparent Molar Volumes, Vϕ1 (cm3·mol−1), and Viscosities, η (mPa·s), at Temperature T, and Molality, m1 (mol·kg−1) for Potassium Chlorate in a (Water + Methanol) Solution and at Pressure p = 0.1 MPaa m1 mol·kg−1

ρ g·cm−3

xmeth

0.1004 0.2006 0.3004

0.0728 0.0728 0.0729

0.98715 0.99442 1.00194

0.1004 0.2006 0.3004

0.0728 0.0728 0.0729

0.98246 0.98940 0.99678

0.1032 0.2010 0.3006

0.1001 0.1002 0.0994

0.98138 0.98866 0.99565

0.1032 0.2010 0.3006

0.1001 0.1002 0.0994

0.97600 0.98299 0.98988

Vϕ1 cm3·mol−1 T = 288.15 55.718 52.068 49.560 T = 303.15 50.630 51.221 49.393 T = 288.15 53.379 49.832 50.534 T = 303.15 49.661 49.414 50.610

η mPa·s

ρ g·cm−3

K 1.585 1.566 1.579

0.98580 0.99295 1.00041

1.058 1.050 1.064

0.98048 0.98734 0.99468

1.723 1.703 1.685

0.97979 0.98696 0.99392

1.109 1.127 1.123

0.97384 0.98075 0.98761

K

K

K

Vϕ1 cm3·mol−1 T = 293.15K 53.205 51.459 49.303 T = 308.15 K 50.477 51.543 49.715 T = 293.15K 51.471 49.422 50.362 T = 308.15 K 49.608 49.748 50.954

η mPa·s

ρ g·cm−3

1.369 1.355 1.370

0.98424 0.99127 0.99869

0.942 0.936 0.950

0.97832 0.98511 0.99242

1.478 1.469 1.455

0.97799 0.98506 0.99199

1.003 1.002 1.000

0.97150 0.97835 0.98518

Vϕ1 cm3·mol−1 T = 298.15 51.536 51.188 49.256 T = 313.15 50.969 52.142 50.186 T = 298.15 50.296 49.305 50.391 T = 313.15 50.134 50.349 51.444

η mPa·s

K 1.198 1.187 1.202 K 0.846 0.842 0.856 K 1.286 1.281 1.273 K 0.897 0.897 0.896


a

than in potassium chlorate.13 The Redlich-Rosenfeld-Meyer (RRM) equation17,18 has been used to correlate the apparent molar volumes at dilute concentrations (m < 0.2). In this work, we have correlated the apparent molar volumes using an extended RRM equation,23 V⌀ 1 = V ⌀0 + SV m10.5 + BV m1 + CV m11.5

where vi and zi are the stoichiometric number and absolute charge of ion i, respectively. AV values for aqueous solutions of 1:1 electrolytes at different temperatures have been already calculated by Ananthaswamy and Atkinson.24 Table 9 shows the parameters for eq 15. We have fixed the value of SV as given by eq 16; therefore, we have only three adjusting parameters. Obviously, if one considers SV an adjusting parameter, eq 16 correlates better the apparent molar volume at the expense of losing physical meaning. Figures 1 and 2 show correlations behavior. We can compare our values for V0⌀ for the aqueous solutions only at 298.15 K. For the potassium chlorate aqueous solution, we found a value of V0⌀ equal to 44.5229 cm3 mol−1 at 298.15 K. This value agrees with the partial molar volume at infinite dilution of (45.667, 46, and 43.5) cm3 mol−1 reported by Redlich and Bigeleisen,25 Millero26 and Fajans and

(15)

where V0⌀ is the limiting apparent molar volume, BV and CV are adjustable parameter, and SV is the Pitzer−Debye−Huckel limiting slope for the volume molar volume calculated by ÄÅ ÅÅ 1 Å SV = AV ÅÅÅ ÅÅ 2 ÅÇ

∑ i

ÉÑ3/2 ÑÑ

2Ñ Ñ vz i i Ñ ÑÑ

ÑÑÖ

(16) F



Article

strong solute−solute interactions. In our case, the solute− solute interactions slightly increase with temperature. The same behavior occurs for the potassium chlorate solution with the exception at 298.15 K. For the sodium and potassium chlorate mixed solvent solutions, we have calculated AV in eq 16 using,30 AV = NA2e 3(8π 2εo3RT )−1/2 ε−3/2[(∂ lnε /∂P)T − κT /3] (17)

where NA is the Avogadro number, e is the unit proton charge, εo is the electrical permittivity at vacuum, ε is the relative permittivity (dielectric constant) of the solvent, R is the universal gas constant, P is pressure, T is the temperature in kelvins, and κT is the isothermal compressibility of the solvent. Marcus and Hefter31 give an expression for the limiting slope at atmospheric pressure and 1:1 electrolyte solutions, Figure 1. Apparent molar volumes for sodium chlorate aqueous solutions: ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; △, 303.15 K; ■, 308.15 K; □, 313 K; ⧫, 318.15 K; , RRM equation; ---, unweighted RRM equation.

AV = 69862.911T −1/2ε−3/2[(∂lnε /∂P)T − κT /3]ρ1/2 (18)

where ρ is the density of the solvent in kg/dm3, values of AV are in cm3 kg1/2 mol−3/2, and T in kelvins. The temperature dependence of the relative permittivity with pressure has been estimated using the correlation developed by Marcus and Hefter31 (∂lnε/∂P)T , P0 = 1.039κT − 0.920κT /ε(P0)

(19)

where ε(P0) is the relative permittivity at atmospheric pressure and eq 19 gives the (∂ lnε/∂P)T,P0 in GPa−1 with a standard deviation of 0.13 GPa−1. The values of the relative permittivity for methanol + water mixtures are taken from Albright and Gosting.32 Values of the dielectric constant have been correlated using a quadratic function of the mole fraction. The volume percentage of (1, 5, 15, and 20) of methanol corresponds to an approximately mole fraction of (0.0045, 0.0229, 0.0728, and 0.1) of methanol in the mixed solvent (water + methanol). The isothermal compressibility of the mixture is calculated using standard equations of state from REFPROP.33 Table 9 shows an average value of SV for the mixtures. We have found the parameters of eq 15 using a weighted least-squares method. The data have been weighted using the uncertainty of the apparent molar volume. The addition of a small quantity of methanol in both aqueous solutions reduces the value of the apparent molar volume; however, at higher methanol concentrations the apparent molar volume increases. This behavior at high concentrations of alcohol has been shown by Bateman34 for strontium chloride in ethanol−water. The same behavior is shown in the limiting apparent molar volume. At a fixed molality and temperature, the decrease in apparent molar volume with the concentration of methanol indicates an increase of solvation but then there is a decrease at higher methanol concentration. Negative BV values imply an increase of solute−solute interactions.34 Limiting apparent molar volumes have been correlated using

Figure 2. Apparent molar volumes for potassium chlorate aqueous solutions: ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; △, 303.15 K; ■, 308.15 K; □, 313 K; ⧫, 318.15 K, , RRM equation; ---, unweighted RRM equation.

Johnson,27 respectively. Our value of V0⌀ at 298.15 K for the sodium chlorate aqueous solution is 32.9364 cm3 mol−1. This value agrees with the partial molar volume at infinite dilution (34.9 cm3 mol−1) reported by Couture and Laidler.28 For the systems considered in this work, at infinite dilution each ion is surrounded by water or a mixed solvent, and this occurs at an infinitely large distance from the other ions. Therefore, V0⌀ only measures the ion−solvent interaction. The values of V0⌀ for both aqueous solutions decrease with increasing temperature. For the potassium chlorate aqueous solutions, V0⌀ values are greater than those for sodium chlorate indicating stronger ion− solvent interactions. Table 9 shows that V⌀0 magnitude increases with temperature for both aqueous solutions. This indicates an increase of ion−solvent interactions. These strong ion solvent interactions in the potassium chlorate solution will increase the apparent molar volume less than in the sodium chlorate solution. BV values for sodium chlorate aqueous solutions are positive and decrease with increasing temperature. Bahadur et al.29 mention that positive values indicate

V ⌀0 = a1 + a 2T + a3T 2

(20)

where ai is the adjusting parameters. Table 10 shows the value of the parameters. The limiting apparent molar expansibility can be found from the above equation G



Article

Table 9. Parameters for the Redlich−Rosenfeld−Meyer Equation aqueous system potassium chlorate

sodium chlorate

sodium chlorate + methanol (xmeth ≈ 0.0045)




T/K

V0⌀ (cm3·mol−1)

SVa (cm3·mol−1·5kg0.5)

BV (cm3·mol−2·kg)

CV (cm3·mol−2.5·kg1.5)

σ(V⌀) cm3·mol−1

AAPD %

288.15 293.15 298.15 303.15 308.15 313.15 318.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 288.15 293.15 298.15 303.15 308.15 313.15 288.15 293.15 298.15 303.15 308.15 313.15 288.15 293.15 298.15 303.15 308.15 313.15 288.15 293.15 298.15 303.15 308.15 313.15

42.5326 43.6732 44.5229 45.0699 45.6098 46.2513 46.7695 30.8009 32.0460 32.9364 33.6787 34.3243 34.8473 35.3309 20.7658 20.7120 20.9686 21.7994 23.2776 24.9238 24.3999 23.8902 23.8897 24.0685 24.9112 25.5527 38.0654 37.5878 37.6627 37.8315 38.0771 38.8537 36.5309 36.2975 36.2441 36.1704 36.8426 38.3829

1.7150 1.7922 1.8743 1.9616 2.0547 2.1540 2.2601 1.7150 1.7922 1.8743 1.9616 2.0547 2.1540 2.2601 1.8045 1.8198 1.8415 1.8683 1.9027 1.9447 1.8528 1.8713 1.8963 1.9267 1.9648 2.0208 1.9921 2.0196 2.0542 2.0952 2.1446 2.2026 2.0599 2.0893 2.1261 2.1698 2.2221 2.2833

18.3188 15.4727 14.3489 15.2395 15.2684 13.9119 13.4330 15.4255 14.2523 13.7157 13.3704 13.0371 12.8074 12.2890 35.3501 37.6028 39.1216 38.7953 36.1695 33.9543 32.7837 35.6978 37.2585 38.6094 37.8891 38.1057 −2.2353 −1.3146 −1.0062 −0.7703 −0.5098 −1.0236 −0.5396 0.1093 0.6134 1.0770 0.8229 −0.2814

−20.5613 −17.6151 −16.6015 −17.8911 −18.1015 −16.8359 −16.6584 −12.7418 −12.0937 −11.8083 −11.6575 −11.4902 −11.3458 −10.8892 −23.5230 −25.1132 −26.2769 −26.1696 −24.3879 33.9543 −23.3261 −25.2310 −26.2711 −27.2747 −26.8569 −27.1778 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.2518 0.2065 0.1988 0.2163 0.2210 0.2124 0.1881 0.3548 0.4483 0.4618 0.4744 0.4758 0.4740 0.4776 4.7321 4.7218 4.8844 4.8401 4.5961 4.0407 0.6364 0.5849 0.5083 0.6863 0.7170 0.4734 1.1742 1.9598 1.6480 2.0330 2.1066 2.2202 6.2406 7.8171 9.0538 9.7977 10.5389 11.3551

0.370 0.304 0.289 0.306 0.310 0.290 0.257 0.810 0.942 0.930 0.929 0.919 0.912 0.925 8.502 8.416 8.625 8.170 7.178 5.725 1.048 1.009 0.900 1.130 1.128 0.690 1.315 1.914 1.536 1.821 1.918 1.8728 7.202 9.457 11.427 12.882 14.020 15.195

a

Fixed parameter.

Values of E0⌀ are depicted in Table 11, respectively. The values of E0⌀ decrease with an increase of temperature for the aqueous solutions and increase with temperature for the mixed solvent solutions. The positive values indicate that solvent molecules are removed from the solvated sphere of ions.35 Hepler36 interprets the structure making/breaking of a solute by the calculation of the derivative of E0⌀ with temperature. The ∂E0⌀/ ∂T is negative for a structure-breaking solute. In this work, ∂E0⌀/∂T = 2a3, then sodium and potassium chlorate in aqueous solution are structure-breaking. On the other hand the addition of methanol becomes sodium chlorate structure-making in the mixed solvent. Viscosities for the aqueous solutions of potassium chlorate are reported in the literature at 298.15 K. Our experimental viscosities measurements agree with viscosity values from Hood2 and Jones and Telley3 within an average absolute percentage of (2.01 and 0.72)%, respectively. For the potassium chlorate aqueous solution, Hood11 mentions that the mixture presents negative viscosities at low concentrations; that is, viscosities less than the viscosity of

Table 10. Parameters for eq 20 aqueous system potassium chlorate sodium chlorate sodium chlorate + methanol (xmeth ≈ 0.0045) sodium chlorate + methanol (xmeth ≈ 0.0229) sodium chlorate + methanol (xmeth ≈ 0.0728) sodium chlorate + methanol (xmeth ≈ 0.1)

a1 a2 a3 (cm3·mol−1) (cm3·mol−1·K−1) (cm3·mol−1·K−2) −178.289 −266.340 835.297

1.3385 1.8325 −5.5820

−0.001984 −0.002780 0.009562

597.901

−3.8694

0.006521

477.037

−2.9548

0.004967

777.523

−4.9938

0.008408

ij ∂V 0 yz E⌀0 = jjj ⌀ zzz = a 2 + 2a3T j ∂T z k {P

(21)

H



Article

Table 11. Limiting Apparent Molar Expansibility (E0⌀) at Different Temperatures aqueous System potassium chlorate sodium chlorate sodium chlorate + methanol sodium chlorate + methanol sodium chlorate + methanol sodium chlorate + methanol

(xmeth (xmeth (xmeth (xmeth

≈ ≈ ≈ ≈

0.0045) 0.0229) 0.0728) 0.1)

288.15 K

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

0.1951 0.2304 −0.0714 −0.1113 −0.0923 −0.1483

0.1753 0.202 0.0242 −0.0461 −0.0426 −0.0642

0.1554 0.1748 0.1198 0.0191 0.0070 0.0199

0.1356 0.1470 0.2154 0.0843 0.0567 0.1040

0.1158 0.1192 0.3111 0.1495 0.1064 0.1881

0.0959 0.0914 0.4067 0.2147 0.1560 0.2721

0.0761 0.0636

water. On the other hand, Jones and Talley12 measure the viscosity of this solution at concentrations from 0.002 to 0.1, and they show that the viscosity increases and then decreases as the concentration increases. In this work, our viscosities for the potassium chlorate solution show the same behavior of that of the Jones and Talley12 results. Also, the aqueous potassium chlorate solutions show an iso-viscosity behavior at each temperature, as shown in Figure 3. This viscosity behavior is

η = 1.64562 − 0.04508t + 6.869 × 10−4t 2 − 4.404 × 10−6t 3

1%Vmeth

(24)

η = 1.64562 − 0.04508t + 6.869 × 10−4t 2

5%Vmeth (25)

η = 1.64562 − 0.04508t + 6.869 × 10−4t 2

15%Vmeth (26)

η = 1.64562 − 0.04508t + 6.869 × 10−4t 2

20%Vmeth (27)

Figure 3. Iso-viscosity behavior as a function of temperature for potassium chlorate aqueous solutions: ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; △, 303.15 K; ■, 308.15 K; □, 313 K; ⧫, 318.15 K. , eq 22; ---, Dale-Jones equation.

Figure 4. Iso-viscosity behavior as a function of temperature for potassium chlorate aqueous solutions + methanol: ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; △, 303.15 K; ■, 308.15 K; □, 313 K; ⧫, 318.15 K. , 1% Vmeth, eq 24; ---, 5% Vmeth, eq 25; −·−·−·, 15% Vmeth, eq 26; ···, 20% Vmeth, eq 27.

within the standard uncertainty of the property. Therefore, a single equation can be used to represent the viscosity measurements η = 1.64562 − 0.04508t + 6.869 × 10−4t 2 − 4.404 × 10−6t 3

(22)

Figure 4 shows this iso-viscosity behavior. Viscosities of sodium chlorate aqueous solutions have been correlated using the Jones−Dole19 equation

where t is the temperature in degrees Celsius. The above equation is valid in the molality interval of 0.01 ≤ m1 ≤ 0.5. Parameters of eq 22 are statistically valid within the 95% confidence interval. Equation 22 correlates the viscosity within an average absolute percentage deviation of 0.45% and a standard deviation of 0.0053 defined as ÄÅ N É ÅÅ ∑ (X exp − X lit orcalc)2 ÑÑÑ1/2 ÅÅ i = 1 i ÑÑ i ÑÑ σ = ÅÅÅ ÑÑ ÅÅ N−n (23) ÅÇ ÑÑÖ

η = η0 + Am10.5 + Bm1

(28)

where η0, A, and B are characteristic parameters obtained from the experimental data at each temperature. The above equation correlates the viscosity data within an average absolute percentage error of 0.29%. Table 12 shows the values of the parameters η0, A, and B together with the standard deviation and the average absolute percentage deviation. Also, we have correlated the viscosities with methanol content using eq 28. The average absolute percentage deviation is (0.544, 0.391, 0.242, and 0.2)% for aqueous solutions with (1, 5, 15, and 20)% methanol, respectively. Falkenhagen and Vernon37 relate

In the above equation n is the number of fitting parameters. We have also represented the viscosities of the aqueous solutions of potassium chlorate with methanol with a single equation, I



Article

Table 12. Parameters for eq 28 for Aqueous Solutions of Sodium Chlorate aqueous system potassium chlorate

sodium chlorate

sodium chlorate + methanol (xmeth ≈0.0045)




T/K

η0 (mPa·s)

A (mPa·s mol−0.5·kg0.5)

B (mPa·s· mol−1·kg)

σ(η) mPa·s

AAPD %

288.15 293.15 298.15 303.15 308.15 313.15 318.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 288.15 293.15 298.15 303.15 308.15 313.15 288.15 293.15 298.15 303.15 308.15 313.15 288.15 293.15 298.15 303.15 308.15 313.15 288.15 293.15 298.15 303.15 308.15 313.15

1.13643 1.00296 0.89622 0.80555 0.73165 0.66725 0.61199 1.12303 0.98949 0.88122 0.79287 0.71893 0.65599 0.60219 1.11365 0.98039 0.86953 0.78051 0.70658 0.64231 1.22219 1.06646 0.94200 0.83901 0.75546 0.68433 1.53246 1.31643 1.14411 1.00476 0.89357 0.80083 1.67920 1.44050 1.24760 1.09297 0.96959 0.86396

0.06831 0.07435 0.09524 0.09852 0.09248 0.09843 0.08109 −0.03317 −0.00054 0.00293 0.00169 −0.00188 −0.00276 −0.00121 0.10802 0.10426 0.10263 0.09686 0.09057 0.08756 0.10900 0.10961 0.10493 0.10360 0.09534 0.09087 0.09518 0.10330 0.10635 0.10699 0.10087 0.09476 0.09326 0.10102 0.10000 0.09987 0.09417 0.09256

−0.10074 −0.08677 −0.09224 −0.08348 −0.07557 −0.07284 −0.05724 0.11825 0.08695 0.08176 0.07844 0.07930 0.07688 0.07049 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.0090 0.0079 0.0084 0.0074 0.0073 0.0067 0.0058 0.0025 0.0012 0.0015 0.0011 0.0005 0.0007 0.0010 0.0091 0.0081 0.0071 0.0065 0.0060 0.0055 0.0080 0.0069 0.0063 0.0060 0.0054 0.0087 0.0096 0.0063 0.0068 0.0066 0.0054 0.0040 0.0063 0.0092 0.0043 0.0038 0.0038 0.0040

0.2869 0.2863 0.3146 0.3112 0.2929 0.3577 0.2989 0.1385 0.0740 0.1057 0.0859 0.0400 0.0628 0.1048 0.5324 0.5488 0.5364 0.5438 0.5512 0.5529 0.3494 0.3486 0.3522 0.3904 0.3671 0.5409 0.2542 0.2178 0.2167 0.2406 0.2688 0.2510 0.2179 0.3588 0.1865 0.1452 0.1364 0.1557

water40 mixtures show an increase of the viscosity in the rich water composition until it reaches a maximum and then decreases. This could be ascribed to a solid-like enhancement of the water in methanol. In this work, viscosities of sodium and potassium chlorate with alcohol are greater than those in the aqueous solution. Therefore, our results could indicate a solid-like behavior of the water in the mixed solvent. The molality interval for the potassium chlorate aqueous solutions + methanol is restricted by crystallization of the salt. In the molality and temperature interval considered in this work, crystallization of the salt does not appear during the density and viscosity measurements.

the A parameter to a contribution due to interionic electrostatic forces. The B coefficient measures the order and disorder caused by the ions in the solvent structure (ion− solvent interaction). In this work, the B coefficient is negative for the potassium aqueous solution and positive for the sodium chlorate aqueous solution which indicates that potassium chlorate and sodium chlorate are structure-breaking and structure-making solutes, respectively. The result for the potassium chlorate solution agrees with our findings using the Hepler method. Also, the sign of the B coefficient agrees with the result obtained by Jones and Talley12 for the potassium chlorate aqueous solution at 298.15 K. Accascina38 mentions that the sodium ion is structure making while the chlorate anion is structure breaking. They conclude that sodium chlorate is a structure making solute. The same behavior is shown by our viscosity data. Unfortunately, our viscosity results for the mixed solvent solutions are not sufficiently extensive to obtain the B coefficient. However, Franks and Ives39 have stated that a small addition of t-butanol in water enhances the solid-like characteristics of water indicating an increase of the viscosity.38 The methanol +

4. CONCLUSIONS In this work we have measured the densities and viscosities of aqueous solutions of sodium chlorate and potassium chlorate from (288.15 to 318.15) K at molalities from of (0.1 to 1) and (0.01 to 0.5), respectively. Also, we have measured the densities and viscosities of the aqueous solutions of sodium chlorate and potassium chlorate with different percentage volume content of methanol (1, 5, 15, and 20). We have J



Article

(11) Hood, G. R. The Viscosity of Potassium Chlorate in Aqueous Solution. J. Rheol. 1932, 3, 326−332. (12) Jones, G.; Talley, S. K. The Viscosity of Aqueous Solutions as a Function of Concentration. J. Am. Chem. Soc. 1933, 55, 624−642. (13) Oliver, B. G.; Campbell, A. N. Conductances, Densities, and Viscosities of Concentrated Solutions of Lithium Chlorate and of Sodium Chlorate in Water-Dioxane mixtures, at 25 °C. Can. J. Chem. 1969, 47, 4207−4211. (14) Roux, A.; Musbally, G. M.; Perron, G.; Desnoyers, J. E.; Singh, P. P.; Woolley, E. M.; Hepler, L. G. Apparent molar heat capacities and volumes of aqueous electrolytes at 25 °C: NaClO3, NaClO4, NaNO3, NaBrO3, NaIO3, KClO3, KBrO3, KIO3, NH4NO3, NH4Cl, and NH4ClO4. Can. J. Chem. 1978, 56, 24−28. (15) Berchiesi, M. A.; Berchiesi, G.; Vitali, G. Density and Compressibility of Solutions of NaCIO3, NaNO3, KNO3, and RbNO3, in the Mixed Solvent C6H5NH3Cl (1.0001 m)-H2O at 30 °C. J. Chem. Eng. Data 1979, 24, 213−214. (16) Harano, Y.; Nakano, K.; Saito, M.; Imoto, T. Nucleation Rate of Potassium Chlorate from Quiscent Supersaturated Aqueous Solution. J. Chem. Eng. Jpn. 1976, 9, 373−377. (17) Redlich, O.; Rosenfeld, P. Zur Theorie des Molvolumens gelöster Elektrolyte II. Z. Elektrochem. 1931, 37, 705−711. (18) Redlich, O.; Meyer, D. M. The Molar Volumes of Electrolytes. Chem. Rev. 1964, 64, 221−227. (19) 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. (20) Spieweck, F.; Bettin, H. Ü bersicht: Bestimmung der Dichte von Festkorpern und Flussigkeiten. Tech. Mess. 1992, 59, 285−292. (21) Hall, K. R.; Kirwan, D. J.; Updike, O. L. Reporting Precision of Experimental Data. Chem. Eng. Educ. 1975, 9, 24. (22) Coquelet, C.; Valtz, A.; Richon, D. Volumetric Properties of Water + Monoethanolamine + Methanol Mixtures at Atmospheric Pressure from 283.15 to 353.15 K. J. Chem. Eng. Data 2005, 50, 412− 418. (23) Trevani, L. N.; Balodis, E. C.; Tremaine, P. R. Apparent and Standard Partial Molar Volumes of NaCl, NaOH, and HCl in Water and Heavy Water at T = 523 and 573 K at p = 14 MPa. J. Phys. Chem. B 2007, 111, 2015−2024. (24) Ananthaswamy, J.; Atkinson, G. Thermodynamics of Concentrated Electrolyte Mixtures. 4. Pitzer-Debye-Huckel Limiting Slopes for Water from 0 to 100 °C and from 1 atm to 1 kbar. J. Chem. Eng. Data 1984, 29, 81−87. (25) Redlich, O.; Bigeleisen, J. Molar Volumes of Solutes. VI. Potassium Chlorate and Hydrochloric Acid. J. Am. Chem. Soc. 1942, 64, 758−760. (26) Millero, F. J. Water and Aqueous Solutions Horne, R. A., Ed.; Wiley: New York, 1971. (27) Fajans, K.; Johnson, O. Apparent Volumes of Individual Ions in Aqueous Solution. J. Am. Chem. Soc. 1942, 64, 668−678. (28) Couture, A. M.; Laidler, K. J. The Partial Molar Volumes of Ions in Aqueous Solution: I. Dependence on Charge and Radius. Can. J. Chem. 1956, 34, 1209−1216. (29) Bahadur, I.; Deenadayalu, N.; Ramjugernath, D. Effects of Temperature And Concentration on Interactions in Methanol + Ethyl Acetate and Ethanol + Methyl Acetate or Ethyl Acetate Systems: Insights from Apparent Molar Volume and Apparent Molar Isentropic Compressibility Study. Thermochim. Acta 2014, 577, 87−94. (30) Marcus, Y.; Hefter, G. Standard Partial Molar Volumes of Electrolytes and Ions in Nonaqueous Solvents. Chem. Rev. 2004, 104, 3405−3452. (31) Marcus, Y.; Hefter, G. On the Pressure and Electric Field Dependencies of the Relative Permittivity of Liquids. J. Solution Chem. 1999, 28, 575−592. (32) Albright, P. S.; Gosting, L. J. Dielectric Constants of the Methanol-Water System from 5 to 55°. J. Am. Chem. Soc. 1946, 68, 1061−1063. (33) Lemmon, E. W., Huber, M. L., McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and

correlated the apparent molar volumes using the RRM equation. Our partial molar volumes at infinite dilution obtained from the RRM equation agree with the literature values within 1.9 cm3/mol. Potassium chlorate aqueous solutions show stronger interaction with water than sodium chlorate. The limiting apparent molar expansibilities show that solvent molecules are removed from the solvated sphere of ions at temperatures above 298.15 K. Solutions with potassium chlorate have an iso-viscosity behavior at a given temperature. This viscosity behavior with concentration is within the uncertainty of the measurements. The Jones-Dole equation correlates the viscosity of the sodium chlorate and potassium chlorate solutions within a maximum average absolute percentage deviation of 0.29%. Our viscosity results indicate that potassium and sodium chlorate are structure breaking and structure making solutes in water, respectively. However, the Hepler method shows that sodium chlorate becomes structure making with the addition of methanol.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: gais@iqcelaya. itc.mx. Tel.: 011 52 461 611 7575. Fax: 011 52 461 611 7744. ORCID

Gustavo A. Iglesias-Silva: 0000-0001-7260-2308 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Tecnológico Nacional de México (TecNM) for providing financial support for this work through project 6662.18-P. We thank Consejo Nacional de Ciencia and Tecnologiá (CONACyT) for financial support to G.P.-D.

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Densities and Viscosities for Aqueous Solutions of Sodium Chlorate

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