Review and Analysis of Thermophysical Properties of a Sulfuric Acid

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

pubs.acs.org/jced

Review and Analysis of Thermophysical Properties of a Sulfuric Acid−Water Electrolyte Laura Oca,*,† Jose Miguel Campillo-Robles,*,‡ and M. Mounir Bou-Ali*,§ Electronics and Computer Science Department, Faculty of Engineering, ‡Elektrokimikako Ikerketa-Taldea, Mekanika eta Ekoizpen Industrialeko Saila, and §Mechanical and Industrial Production Department, Faculty of Engineering, Mondragon Unibertsitatea, 20500 Arrasate, Basque Country, Spain

Downloaded via UNIV OF SOUTH DAKOTA on September 5, 2018 at 09:10:51 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

ABSTRACT: In this work, we have performed a critical review of the thermophysical properties of sulfuric acid−water mixtures. The thermophysical properties analyzed are density, viscosity, refraction index, thermal expansion coefficient, and mass expansion coefficient. The density of the sulfuric acid−water mixture has been measured for different mass fractions (w = 0.1− 0.4) over a broad temperature range (T = 273.15−333.15 K). A new parametrization of the density has been performed using a least-squares method. In this parametrization, the number of coefficients has been reduced with respect to previous works. Moreover, this new equation has been analyzed in an extended region of temperature and concentration in the following ranges: w = 0−0.1, T = (233.15−373.15 K). The coefficients of thermal and mass expansion have also been calculated experimentally, and a linear relation of the density has been determined as a function of the variations in temperature and concentration. In addition, viscosity and refraction index measurements have been performed at 298.15 and 293.15 K, respectively. Our results have been checked against measurements in the literature (review) and show good correspondence. teries,16−18 such as advanced lead-acid batteries.19−21 Electrolytes for this kind of battery are composed of sulfuric acid and water, and the performance and useful life of this battery are affected by the properties of this mixture.22,23 Today, additives for the electrolytes of the lead-acid battery are being studied for the improvement of the thermal physical properties of the electrolytes and the battery’s useful life.24−27 Moreover, small amounts of impurities could severely affect the performance and lifetime of this device.28 Furthermore, the scientific community notices the importance of sulfuric acid in atmospheric processes. Nowadays, atmospheric nucleation processes are being analyzed.29,30 This strong acid plays a key role in the formation of aerosols in the troposphere and the stratosphere.31,32 Sulfuric acid aerosols influence the quality of life through its climatic and health effects. These aerosol particles participate in the formation of acid rain, which pollutes the soil and the groundwater courses of the earth.33 Sulfuric acid aerosols also modify the radiative balance of the atmosphere by scattering and absorbing sunlight.34 This process affects the global temperature and thus the global climate. Indeed, at this moment, research is focused on the possibility of conditioning the CO2 greenhouse effect by means of these aerosols.35 The main objective of this work is to compare and contrast experimental results of the thermophysical properties of the

1. INTRODUCTION Sulfuric acid has been known and used since the Middle Ages. It has many desirable properties that lead to its use in a wide variety of applications.1 For this reason, it has been an important item of commerce since the 17th century.2 Nowadays, sulfuric acid is one of the most important inorganic compounds produced by the chemical industry.3−5 In fact, sulfuric acid is used as a raw material or as a processing agent in the production of nearly all manufactured goods. The major use of sulfuric acid is in the production of fertilizers and in the manufacture of chemicals, but it is also needed for batteries, explosives, derived products of petroleum, detergents, dyes, insecticides, drugs, plastics, steel, and many other products.6 Because of the sulfuric acid demand in emerging countries, worldwide production is in continuous increase.7 The world production of sulfuric acid is estimated to be greater than 260 million tonnes, and all of the forecasts show that it will continue increasing.8 Moreover, sulfuric acid consumption is often cited as an indicator of the general state of the economy of one country.9 The properties of sulfuric acid−water mixtures have been studied systematically from the 19th century.10,11 Therefore, there is an impressive mass of experimental evidence. However, some physicochemical properties of these mixtures are still being studied.12−15 At this moment, the properties of these mixtures are been studied deeply due to the use of the sulfuric acid as an electrolyte in lead-acid batteries and its role in atmospheric processes. Nowadays, the research performed to develop energy storage systems is principally focused on getting advanced bat© XXXX American Chemical Society

Received: June 6, 2018 Accepted: August 24, 2018

A

DOI: 10.1021/acs.jced.8b00466 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Density Measurements of the Sulfuric Acid−Water Solutions Chronologically Ordered in the Literature, Where T Is the Temperature, w Is the Mass Fraction, and ρ Is the Density T/K [number of values or ΔT from previous temperature in K]

w [number of values or Δw in %]

measured magnitudeb

first author

year

Ferguson39 Domke40 Börnstein41 (A) Sullivan42 (B) Sullivan42 Rhodes43 Washburn (editor)44a

1904 1905 1912 1918 1918 1923 1928

288.75 273.15−333.15 [10 K] 288.15, 298.15 273.15−323.15 [10 K] 278.15, 288.15, 298.15 288.75 288.75

0−0.9319 [29] 0−1 [1%] 0−1 [1%] 0−0.9319 [73] 0−0.9319 [29] 0−0.9960 [20] 1−1 [1%]

ρ(T, 288.75 ρ(T, 288.15 ρ(T, 277.15 ρ(T, 288.75 ρ(T, 288.75 ρ(T) ρ(T, 277.15

Forsythe (editor)45

1954

1965

(B) Fasullo46

1965

Haase47

1966

(A) D’Ans48 (B) D’Ans48 Bode49

1967 1967 1977

277.55 288.65−422.05 288.75 273.15 273.15−323.15 [10 K], 298.15

(A)Weast (editor)50 (B)Weast (editor)50

1981 1981

273.15−303.15 [10 K] 288.15, 298.15, 323.15, 348.15, 373.15

Kaye51 Maksimova52a

1986 1987

273.15−348.15 [25 K] 273.15−323.15 [25 K]

Beyer53

1996

0−0.98 [1%] 0.4, 0.7 0.3−0.7 [10%] 0.2−0.7 [10%] 0−0.9 [10%] 0−1 [10%] 0−0.6498 [53] 0.65−1 [0.1%] 0.03929−0.7706 [16] 0.03929−0.8593 [19] 0.02−1 [5%] 0.05−1 [12] 0−0.5 [ 2%] 0.5−1 [5%] 0−1 [1%] 0−0.1 [0.5%] 0.1−0.2 [1%] 0.2−1 [2%] 0.01731−1 [65] 0.1−0.3 [10%] 0.3−0.8 [5%] 0.389, 0.630 0.523, 0.886 0.3−0.76 [2%] 0.02−1 [2%] 0.04−1 [2%] 0.1−0.8 [2%] 0.01−1 [1%] 0.123 0.291 0.503 0.585 0.672 0.765 0−0.597 [11] 0−0.5 [2%] 0.5−0.6 [5%] 0.0746−0.3994 [22]

ρ(T, 277.15 K)

(A) Fasullo46a

273.15−348.15 [25 K] 273.15−333.15 [10 K] 288.15, 298.15, 353.15, 373.15 293.15 233.15 244.25, 255.35 266.45

(A) Aseyev54 (B) Aseyev54

1996 1996

(C) Aseyev54 Perry55 Myhre56a

1996 2008 2003

Salkind57 Pavlov58

2002 2017

293.15 293.15 293.15 233.15−283.15 [10 K] 323.15, 343.15, 363.15 195.15 221.15 233.15−273.15 [5 K] 273.15−318.15 [5 K] 323.15−373.15 [5 K] 273.15−363.15 [5 K] 273.15−333.15 [10 K] 288.15, 298.15, 353.15, 373.15 262.15−300.15 [13] 241.15−303.15 [14]

Liu59a

2012

221.15−301.15 [13]

K) K) K) K) K) g·cm−3 K)

ρ(T)

measured/sourcec

units

lb·ft−3

ρ(T, 288.75 K)

yes yes no/Domke no/Ferguson no/Ferguson yes no/Domke and different sources no/Domke

NI

no/Ferguson

ρ(T)

kg·L−1

no/Washburn

ρ(T) ρ(T) ρ(T, 277.15 K)

g·cm−3 g·cm−3

no/Washburn no/Rhodes no/Washburn

ρ(T, 277.15 K) ρ(T, 277.15 K) ρ(T, 293.15 K) ρ(T) ρ(T) ρ(T) ρ(T) ρ(T) ρ(T) ρ(T, 277.15 K) ρ(T)

no/Washburn no/Washburn

kg·m−3 g·cm−3

NI yes yes

g·mL−1 kg·m−3 kg·m−3 kg·m−3 kg·m−3

no/different sources NI NI no/Washburn yes

ρ(T, 288.15 K) ρ(T, 277.15 K)

no/Domke no/Washburn

ρ(T, 298.15 K)

yes

These authors generated the data used for the comparison of our experimental work and fitting. NI, no information found. bDensity ρ(T) and relative density ρ(T, 288.75 K) are differentiated, in which the relative density represents a unitless value in relation to a density at a certain temperature (i.e., 288.15 K). cClarification of which works contain original measurements and which ones referred only to others’ measurements, where yes indicates direct measurements and no/source explains from which source the presented values are taken. a

sulfuric acid−water mixture with measurements of this work and provide a historic overview of those properties. To reach that goal, the experimental density, coefficient of thermal expansion, coefficient of mass expansion, dynamic viscosity, and refraction index values have been measured. To checking the previous results, we have performed a systematic measurement of the thermophysical properties previously analyzed of these mixtures as a function of temperature and concentration. Moreover,

density parametrizations of the literature have been analyzed, and we have proposed a new simple parametrization based on our experimental results, which could be useful for the modeling of different systems.

2. DENSITY The sulfuric acid−water electrolyte density has been measured extensively over wide temperature and concentration ranges. As B



Article

Table 2. Parametrizations of the Density of Sulfuric Acid−Water Solutions Chronologically Ordered in the Literaturea first author

year

T/K

w

Novotny65 Aseyev54

1988 1996

273.15−373.15 273.15−363.15

0−1 0.1−0.8

ρ = ρwater(T) + Ax + BxT + CxT2 + Dx3/2 + Ex3/2T + Fx4/2T2 ρ = ρwater(T) + Aw + BwT + Cw2

Myhre66

1998

273.15−323.15

0.1−0.9

ρ=

expression

10

no. of coefficients

ρ

T

kg m−3 kg m−3

°C °C

21 11

kg m−3

K

35

kg m−3

°C

8−10

g cm−3 g cm−3 kg m−3 g cm−3

°C K °C K

5 21 4 95

4

∑ ∑ Aijwi(T − 273.15) j i=0 j=0

Kulmala67

1998

233.15−298.15

0.1−1

Walrafen68 Vehkamäki69 Hyvärinen70 Clegg37

2000 2002 2005 2011

293.15 273.15−373.15 297.35 273.15−373.15

0.7−1 0−1 0−1 0.06−1

(T − 273.15) 60 ρ1 = A + Bw − Cw2 + Dw3 − Ew4; ρ2 = F + Gw − Hw2 + Iw3 − Jw4 ρ = A + Bx + Cx2 + Dx3+Ex4 + Fx5 ρ = A(w) + B(w)T + C(w)T2 ρ = ρwater + Aw + Bw2 + Cw3 + Dw4 ρ(T, w) = ρ(Tr, w) + (T − Tr)(Q1(Tr, w)) − TrQ2(Tr, w) + Q2(Tr, w)(T2 − Tr2)/2 ρ = ρ1 + (ρ2 − ρ1)

A, B, and C are coefficients used to adjust the equation. T is temperature, w is the mass fraction of sulfuric acid, ρ is the density, and x corresponds to the molar fraction (with units of mol dm−3 in Novotny65 and mole % in Walrafen68). a

This kind of equations is often needed in numerical algorithms of chemical engineering and physical chemistry. Therefore, different kinds of parametrization of the density have been developed in the literature.60 One example of technological importance is the electrolyte of the lead-acid batteries. In this practical case, the temperature and density of the electrolyte are measurable parameters. A numerical relation between concentration and these two parameters is necessary because some of the governing equations of the battery electrochemistry are functions of the electrolyte concentration.61−64 In this section, first, bibliographical research on the parametrization of sulfuric acid−water mixtures has been done. Then, a comparison of our experimental data and with the literature has been performed. Finally, a new and simple parametrization based on our experimental data has been proposed. 2.2.1. Review of Parametrizations. The identified parametrizations are collected in Table 2. Novotny and Söhnel justified an empirical equation for describing the density of binary aqueous solutions.65 This equation is a polynomial expansion with six adjustable constants and one term related to the density of the water. This term is an empirical equation of temperature that has three nonadjustable parameters. Novotny and Söhnel tested the validity of the equation for more than 300 binary aqueous solutions. In the case of sulfuric acid−water mixtures, they fitted data of Domke and Bein,40 Washburn,44 and D’Ans and Lax.48 Because of the special behavior of the mixture, they performed three different fits between 273.15 and 373.15 K in these concentration ranges (w): 0−0.7, 0.71−0.9, and 0.91−1. Later, Aseyev and Zaytsev54 presented another polynomial expansion with three adjustable constants and one term related to the density of the water. This last term is a function of temperature, which has nine nonadjustable parameters and is valid in the region w = (0.1− 0.8), T = (273.15−363.15 K). These authors take the experimental data from Domke and Bein,40 Washburn,44 and D’Ans and Lax.48 In 1998, Myhre et al. performed another polynomial fitting of the density of the sulfuric acid−water mixtures in the w = (0.1−0.9), T = (210.15−323.15 K) region.66 They fitted their measurements of density at low temperatures (Table 2) to the data of Washburn.44 The parametrization developed by Myhre et al. had 35 adjustable terms. However, this equation contained errors resulting in minor inaccuracies at low temperatures. For this reason, afterward, in 2003, Myhre and

a result, there is a great amount of experimental data available. Three review works attempted to order and compare these density measurements.36−38 In 1960, Timmerman collected data from 19 density measurements and cited another 34 works dismissing them.36 Later, in 1975, Potter et al. collected 11 measurements in a bibliographic review of components of geothermal waters.38 Finally, in 2011, Clegg et al. published another review with 16 density measurements.37 These two review works are useful in taking a quick survey of the experimental literature. All in all, we believe that a wider comparison between the most remarkable measurements is needed. Therefore, in this document we present a systematic review of the most cited works on the density of the sulfuric acid−water electrolyte. 2.1. Critical Review of Density. To review the selection of data available in the bibliography, some criteria have to be defined. On the one hand, we have rejected data before 1900 as a result of insufficient accuracy or because experimental methods and units are confusing. This criterion agrees with Timmermans.36 In addition, measurements by Timmermans36 in 1960 were discarded because the author claims that these data have only historical value and are not accurate enough. On the other hand, measured density values have been included. Added to that, authors that have taken values from other sources have been identified. Moreover, reviews of measurements that other authors consider of great importance have also been taken into account. Table 1 collects the most remarkable information about the measurements of the bibliography. In order to compare the literature values with our work, the authors indicated in Table 1 have been selected. Five references have been roughly compared with our experimental values: first Washburn,44 because many authors take this book as a reference.47−50 In this work, values are mostly taken from Domke and Bein40 although values at 353.15 and 373.15 K have been taken from different sources. Second, Fasullo, 46 Maksimova et al.,52 and Myhre et al.56 measurements have been analyzed because they have values at low and high temperatures (below 273.15 K and over 333.15 K and with a wide range of concentrations). Finally, Liu’s and Li’s measurements have been compared because they have characterized the lead-acid battery electrolyte.59 2.2. Density Parametrization. The parametrization of the density data of liquids as a single function of the concentration and the temperature is a key factor from a practical point of view. C



Article

co-workers improved their fitting of the data. They obtained an equation with 32 adjustable constants for the same concentration and temperature ranges.56 Kulmala et al.68 provide another parametrization taken from Jaecker-Voirol.71 Walrafen68 fitted with a fifth-degree least-squares polynomial the density values for the range of 70−100 mol % for Kaye and Laby51 with five constants. Vehkamäki et al. presented another parametrization of the density.70 In this case, they used only 21 adjustable constants to fit the densities of Washburn.44 This parametrization well reproduced the low-temperature (220.15− 300.15 K) densities of Myhre et al.56 Hyvärinen et al.71 studied the densities of ternary H2SO4 + NH3 + H2O solutions. Sulfuric acid−water mixture regression can be determined when NH3 is zero at a constant temperature of 297.35 K. Finally, Clegg et al.37 provided a fitting equation with 95 terms to adjust. All in all, this fitting can accurately respond over the whole concentration and temperature ranges. 2.2.2. Density Measurements. The sulfuric acid−water mixtures analyzed in the present work were prepared using the chemical sample given in Table 3.

preparation and relaxation times. We have prepared mixtures with mass fraction ranging from 0.1 to 0.4 for a mass fraction of the densest component. In this range, we have prepared 17 samples, with a difference of concentration between them of approximately w = 0.02. Before the measurements, all of the samples have been shaken vigorously, and then an ultrasonic bath with temperature control has been applied for degassing. The density of the sulfuric acid−water mixtures has been measured using a vibrating quartz U-tube density meter (Anton Paar DMA 5000). The density determination is based on measuring the period of oscillation of the vibrating U-shaped tube which is filled with the sample liquid.72 This density meter measures the density with an accuracy of ±5 × 10−3 kg m−3 and the temperature with an accuracy of ±0.01 K. The temperature control in this device is carried out accurately by means of the Peltier effect. The density meter was calibrated using air and water at 293.15 K following the procedure of the density meter. The density has been measured three times for each concentration and temperature, and then the average density was calculated. The temperature of the measurements has ranged from 273.15 to 333.15 K, with a difference in temperature between each measurement of 283.15 K. In addition, the density at 298.15 K has been measured because it is a reference temperature in the battery world.72 We have measured the density of sulfuric acid−water mixtures in the next temperature and concentration range of w = (0.1−0.4), T = (273.15−333.15 K). The experimental density values of this work are shown in Table 4. The experimental values of the density obtained in this work have been compared to the work of authors selected from Table 1. The results are in good agreement with the previous results of the other researchers in the measured concentration and temperature ranges. For example, Figure 1 shows all of these experimental density values at 273.15, 298.15, and 323.15 K. The experimental values of the density of sulfuric acid solution have been found to vary linearly with temperature in the temperature range of the measurement. Densities of values from

Table 3. Chemical Sample Information chemical name sulfuric acid distilled watera

source Merck

initial mole fraction purity

purification method

0.95−0.97

water still Pobel 909

CAS number 7664-93-9

bidistillation

a

The maximum conductivity of the distilled water used in this work is 0.66 0.02−0.76 [2 w]

first author Rhodes

43

Vinal79 Das80 Aseyev81 Walrafen69

w [number of values or Δw in %]

μ techniques viscometer (cylindrical glass bulb with 2 × 10−4 m3 capacity, glass capillary tube of 0.08 and 0.001 m internal diameter) timing the discharge of a fixed volume solution on pyrex glass of ratio 100 Cannon-Ubbelohde suspended-level viscometer not measured, multiple sources. not measured, Rhodes46

a

Note that Aseyev has not measured all of the mass fractions at all temperatures. At low temperatures, the measured mass fractions are {w (0.1 to 0.22, T (>263.15 K); w (0.24), T (>258.15 K); w (0.26 and 0.6 to 0.66), T (>253.15 K); w (0.28 and 0.68), T (>248.15 K); and w (0.70), T (>243.15 K)}.

Table 9. Measured Dynamic Viscosity (μ ×10−3) of Sulfuric Acid−Water Electrolyte Samples at 298.15 K for Different Mass Fractions of Sulfuric Acid w at 298.15 K and Atmospheric Pressure (1020 ± 20 hPa)a w

μ/Pa s

w

μ/Pa s

0.097 0.115 0.137 0.154 0.173 0.192 0.211

1.07 1.11 1.16 1.22 1.24 1.32 1.36

0.230 0.241 0.269 0.288 0.307 0.327 0.346

1.46 1.48 1.59 1.69 1.78 1.88 2.06

phenomena (e.g., lead-acid battery monitoring82 and atmospheric nucleation processes83). Indeed, the measurement of the refractive index can be used as an indirect method to determine the concentration of the electrolyte. For this reason, the characterization of the refraction index of the sulfuric acid− water electrolyte for different concentrations is interesting. Although the properties of the sulfuric acid−water electrolyte were intensively studied a long time ago, the refractive index of this mixture has not been studied so thoroughly. Initial measurements of the refractive index of the sulfuric acid− water electrolyte started in 1974.84 Table 10 shows a review of the refractive index data of the literature, with more remarkable information about the measurements. A RFM340 series refractometer of Bellingham and Stanley has been used to perform the refraction index measurements (wavelength of 589.3 nm). We have used electrolyte samples of 1 mL. The temperature of the sample remained constant at 293.15 K during measurements. The experimental values of the refractive index are shown in Table 11. Our measured values of the refractive index exhibit linear behavior with mass fraction. Figure 9a shows this linear behavior of the refractive index. Therefore, we can linearly correlate the refractive index with mass fraction, as shown in eq 8:

a Standard uncertainties u are u(T) = 0.1 K, u(μ) = 0.01, u(w, balance) = 10−8 kg, and u(w, chemical composition) = 0.01. Therefore, the combined expanded uncertainty is Uc(μ) = 0.02 × 10−3 Pa s with a level of confidence of 95%.

n(w) = 1.3 × 10−3w + 1.3325

(8)

Combining eqs 1 and 8, it is possible to find a similar relation between the refractive index and the density, which exhibits similar linear behavior. These linear relations are valid only for concentrations lower than 0.4 w, as proven by Beyer.87 For this mass fraction range, our measurements are in agreement with the values in the literature (Figure 9b). Figure 8. Comparison of experimental viscosity values in this work μ and in the bibliography at 298.15 K. ○, Rhodes;46 △, Vinal;79 ◇, Aseyev;81 and ■, this work.

6. CONCLUSIONS The sulfuric acid−water electrolyte is a chemical of great industrial importance. The aim of this work is to compare and

Table 10. Refractive Index of the Sulfuric Acid−Water Solutions Chronologically Ordered in the Literature first author

year

T/K

w

λ/nm

Querry84 Remsberg85 Palmer86 Beyer87 Born88 Niedziela89 Biermann90 Krieger91 Lund-Myhre92

1974 1974 1975 1996 1999 1999 2000 2000 2003

300.15 296.15 300.15 298.15 288.15 200.15−300.15 183.15−293.15 213.15−303.15 220.15−300.15

0.25 0.75, 0.9 0.25, 0.38, 0.5, 0.75, 0.845, 0.956 0, 0.398, 0.523, 0.63, 0.787, 0.886 0, 0.1998, 0.3976, 0.5998, 0.801, 1 0.32−0.87 ≤0.8 0, 0.1004, 0.1741, 0.217, 0.351, 0.4, 0.434, 0.5015, 0.651 0.12−0.81

2000−20 000 6000−13 000 357−2500 214, 254, 308, 313, 365 589 2632 357−2500 351.0, 533.5, 632.9, 782.6 ≥1333

I



Article

Table 11. Measured Refractive Index n of Sulfuric Acid− Water Electrolyte Samples at 293.15 K (λ = 589.3 nm) and Atmospheric Pressure (1020 ± 20 hPa)a w

n

w

n

0.000 0.099 0.121 0.150 0.161 0.179 0.200 0.221 0.240

1.33297 1.34523 1.34761 1.35162 1.35276 1.35510 1.35744 1.36047 1.36249

0.260 0.280 0.300 0.321 0.339 0.362 0.381 0.400 0.423

1.36566 1.36812 1.37054 1.37277 1.37596 1.37853 1.38042 1.38311 1.38683

used resource is that of the International Critical Tables. However, some measurements have increased the information for dilute solutions and low temperatures. We have chosen five of the literature data sets to compare with our density measurements and a new optimized parametrization of the density developed from our measurements. The extrapolation of the new parametrization has defined the working range of the equation in these regions: {w = (0−0.5), T = (273.15−373.15 K)} and {w = (0.12−0.67), T = (221.15−273.15 K)}. We have found a maximum difference between the parametrization and the experimental densities of less than 1%. We have also calculated the coefficients of thermal and mass expansions of the sulfuric acid−water mixtures using our measurements. There are few values of the thermal expansion coefficient in the literature, but they show good agreement with our values. There are no reported values of the mass expansion coefficient. However, in order to check our values, we have correlated them using the Boussinesq approximation, and the agreement is good. We have also measured two other important properties of the electrolyte: the dynamic viscosity (298.15 K) and the refraction index (293.15 K). In both cases, the new measured values agree with literature values.

a

Standard uncertainties u are u(T) = 0.1 K, u(n) = 0.00005, u(w, balance) = 10−8 kg, and u(w, chemical composition) = 0.01. Therefore, the combined expanded uncertainty is Uc(n) = 0.00005 with a level of confidence of 95%.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Laura Oca: 0000-0002-1361-0508 Jose Miguel Campillo-Robles: 0000-0002-2565-6343 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge D. Soler and E. Zarate for help with the development of the density parametrization. We acknowledge the financial support of the Research Group Program (IT 1009-16) and μ4F (KK-2017/00089) of the Basque Government.

■

REFERENCES

(1) King, M. J.; Davenport, W. G.; Moats, M. S. Sulfuric Acid Manufacture: Analysis, Control and Optimization; Elsevier: Amsterdam, 2013. (2) Kreps, T. J. The Economics of the Sulfuric Acid Industry; Stanford University Press: Stanford, CA, 1938. (3) Louie, D. K. Handbook of Sulfuric Acid Manufacturing, 2nd ed.; DKL Engineering: Thornhill, Ontario, Canada, 2008. (4) Ashar, N. G.; Golwalkar, K. R. A Practical Guide to the Manufacture of Sulfuric Acid, Oleums and Sulfonating Agents; Springer: Heidelberg, 2013. (5) Kemf, E., Ed.; Global Chemicals Outlook - Towards Sound Management of Chemicals; United Nations Environment Programme, 2013. (6) Heydorn, B.; Aguiar, D.; Ferguson, A. Sulfuric Acid. Chemical Economics Handbook; SRI International: Menlo Park, CA, 1987. (7) Mccoy, M. The Acid Touch. Rising Prices for Sulfuric Acid Have Widespread Industrial Impact. Chem. Eng. News 2008, 86, 27−29. (8) Sulfuric Acid Market - Global Industry Analysis, Size, Share, Growth, Trends and Forecast 2017 − 2023; Transparency Market Research, 2018.

Figure 9. Electrolyte refractive index. (a) Linear relationship between our measured refractive index and the concentration and density of the electrolyte at 293.15 K. ●, n; ■, ρ. (b) Comparison between our measured refractive index values at 293.15 K and those in the literature. ◇, Palmer,86 300.15 K/702 nm; △, Palmer,86 300.15 K/556 nm; ▷, Palmer,86 300.15 K/449 nm; ☆, Born,88 288 K/589 nm; ⬠, Krieger,91 294 K/533.5 nm; ■, this work.

contrast literature values of the thermophysical properties of this electrolyte with newly measured values, providing a historic overview of those properties. For this purpose, we have collected and compared literature values of the density, coefficient of thermal expansion, dynamic viscosity, and refractive index of this electrolyte. Moreover, we have also collected density parametrizations from the literature to compare with a new and more simple equation developed in this work. The exhaustive review of density values shows that there is plenty of measured data available in the literature. The most J



Article

(9) Strickland, R. W., Kent, J. A., Eds.; Sulfur and Sulfuric Acid. Riegel’s Handbook of Industrial Chemistry; Springer: Heidelberg, 2003; pp 481− 505. (10) Sullivan, T. J. Sulfuric Acid Handbook; McGraw-Hill: New York, 1918. (11) Fasullo, O. T. Sulfuric Acid Use and Handling; McGraw-Hill: New York, 1965. (12) Fraenkel, D. Structure and Ionization of Sulfuric Acid in Water. New J. Chem. 2015, 39, 5124−5136. (13) Fraenkel, D. Electrolytic Nature of Aqueous Sulfuric Acid. 1. Activity. J. Phys. Chem. B 2012, 116, 11662−11677. (14) Fraenkel, D. Electrolytic Nature of Aqueous Sulfuric Acid. 2. Acidity. J. Phys. Chem. B 2012, 116, 11678−11686. (15) Niskanen, J.; Sahle, C. J.; Juurinen, I.; Koskelo, J.; Lehtola, S.; Verbeni, R.; Müller, H.; Hakala, M.; Huotari, S. Protonation Dynamics and Hydrogen Bonding in Aqueous Sulfuric Acid. J. Phys. Chem. B 2015, 119, 11732−11739. (16) Huggins, R. A. Advanced Batteries, Materials Science Aspects; Springer: Heidelberg, 2009. (17) Rahn, C. D.; Wang, C.-Y. Battery Systems Engineering; John Wiley & Sons: Chichester, 2013. (18) Menictas, C., Skyllas-Kazacos, M., Lim, T. M., Eds.; Advances in Batteries for Medium- and Large-Scale Energy Storage; Elsevier: Cambridge, 2014. (19) McKeon, B. B.; Furukawa, J.; Fenstermacher, S. Advanced Lead− Acid Batteries and the Development of Grid-Scale Energy Storage Systems. Proc. IEEE 2014, 102, 951−963. (20) Cattaneo, E.; Riegel, B. Advanced Industrial Lead-Acid Batteries; Elsevier, 2016. (21) Garche, J., Karden, E., Moseley, P. T., Rand, D. A. J., Eds.; LeadAcid Batteries for Future Automobiles; Elsevier: Amsterdam, 2017. (22) Pavlov, D.; Petkova, G.; Rogachev, T. Influence of H2SO4 Concentration on the Performance of Lead-Acid Battery Negative Plates. J. Power Sources 2008, 175, 586−594. (23) Pavlov, D.; Naidenov, V.; Ruevski, S. Influence of H2SO4 concentration on lead-acid performance. H-type and P-type batteries. J. Power Sources 2006, 161, 658−665. (24) Ikeda, S.; Iwata, S.; Nakagawa, K.; Kozuka, Y.; Kozawa, A. Change in Specific Gravity of the Acid Electrolyte in the Lead Acid Battery upon Repeated Charge-Discharge Cycles. Journal of Asian Electric Vehicles 2005, 3, 763−766. (25) Rezaei, B.; Mallakpoux, S.; Taki, M. Application of Ionic Liquids as an Electrolyte Additive on the Electrochemical Behaviour of Lead Acid Battery. J. Power Sources 2009, 187, 605−612. (26) Bhattacharya, A.; Basumallick, I. N. Effect of Mixed Additives on Lead−Acid Battery Electrolyte. J. Power Sources 2003, 113, 382−387. (27) Hou, S. J.; Ikeda, H.; Takai, Y.; Minami, S.; Kozawa, A.; Sugawara, M.; Nishina, T. Experimental Study on the Optimum Density of ITE Additives for a Lead-acid Battery’s Life Prolongation. Journal of Asian Electric Vehicles 2006, 4, 939−946. (28) Rocha, F. R. P.; Nóbrega, J. A. Overcoming the Schlieren Effect in Flow Injection Spectrophotometry by Introduction of Large Sample Volumes. Determination of Chloride in the Electrolyte of Lead-acid Batteries. J. Braz. Chem. Soc. 1997, 8, 625−629. (29) Kulmala, M. How Particles Nucleate and Grow. Science 2003, 302 (5647), 1000−1001. (30) Sipilä, M.; Berndt, T.; Petäjä, T.; Brus, D.; Vanhanen, J.; Stratmann, F.; Patokoski, J.; Mauldin, R. L.; Hyvärinen, A.-P.; Lihavainen, H.; Kulmala, M. The Role of Sulfuric Acid in Atmospheric Nucleation. Science 2010, 327 (5970), 1243−1246. (31) Clarke, A. D.; Varner, J. L.; Eisele, F.; Mauldin, R. L.; Tanner, D.; Litchy, M. J. Particle Production in the Remote Marine Atmosphere: Cloud Outflow and Subsidence During ACE 1. Geophys. Res. 1998, 103, 16397−16409. (32) McGouldrick, K.; Toon, O. B.; Grinspoon, D. H. Sulfuric Acid Aerosols in the Atmospheres of the Terrestrial Planets, Planetary and Space. Planet. Space Sci. 2011, 59, 934−941. (33) Lane, C. N. Acid Rain: Overview and Abstracts; Nova Science Pub Inc: New York, 2003.

(34) Johnson, B. T.; Shine, K. P.; Forster, P. M. The Semi-Direct Aerosol Effect: Impact of Absorbing Aerosols on Marine Stratocumulus. Q. J. R. Meteorol. Soc. 2004, 130, 1407−1422. (35) Robock, A.; Marquardt, A.; Kravitz, B.; Stenchikov, G. Benefits, risks, and costs of stratospheric geoengineering. Geophys. Res. Lett. 2009, 36, L19703. (36) Timmermans, J. The Physico-Chemical Constants of Binary Systems in Concentrated Solutions; Interscience Publishers: New York, 1960; Vol. IV. (37) Clegg, S. L.; Wexler, A. S. Densities and Apparent Molar Volumes of Atmospherically Important Electrolyte Solutions. 1. The Solutes H2SO4, HNO3, HCl, Na2SO4, NaNO3, NaCl, (NH4)2SO4, and NH4Cl from 0 to 50 °C, Including Extrapolations to Very Low Temperature and to the Pure Liquid State, and NaHSO4, NaOH, and NH3 at 25 °C. J. Phys. Chem. A 2011, 115, 3393−3460. (38) Potter, R. W.; Shaw, D. R.; Haas, J. L., Jr. Annotated Bibliography of Studies on the Density and Other Volumetric Properties for Major Components in Geothermal Waters 1928−74; Geological Survey Bulletin 1417; United States Government Printing Office: Washington, D.C., 1975. (39) Ferguson, W. C.; Talbot, H. P. Table accepted by the Manufacturing Chemists’ Association of the United States, 1904. (40) Domke, J.; Bein, W. Ü ber dichte und Ausdehnung der schwefelsäure in wässeriger Lösung. Z. Anorg. Chem. 1905, 43, 125− 181. (41) Landolt, H.; Börnstein, R. Physikalisch-Chemische Tabellen; Springer: Berlin, 1912. (42) Sullivan, T. J. Sulphuric Acid Handbook; McGraw Hill: London, 1918. (43) Rhodes, F. H.; Barbour, C. B. The viscosities of mixtures of sulfuric acid and water. Ind. Eng. Chem. 1923, 15, 850−852. (44) Washburn, E. W., Ed.; International Critical Tables of Numerical Data, Physics, Chemistry and Technology; McGraw-Hill: New York, 1928; Vol. III, pp 56−57. (45) Forsythe, W. E., Ed. Smithsonian Physical Tables; Smithsonian Institution: Washington, D.C., 1954. (46) Fasullo, O. T. Sulfuric Acid: Use and Handling; McGraw-Hill: New York, 1965. (47) Haase, R.; Sauermann, P. F.; Dücker, K. H. Conductivity of concentrated electrolyte solutions. V. Sulfuric acid. Z. Phys. Chem. 1966, 48, 206−212. (48) D’ Ans, J.; Lax, E. Taschenbuch für Chemiker und Physiker; Springer: Berlin, 1967; Vol. I, 807, 1419. (49) Bode, H. Lead Acid Batteries; John Wiley & Sons: New York, 1977. (50) Weast, R. C.; Astle, M. J. Handbook of Chemistry and Physics; CRC Press: Boca Raton FL, 1981. (51) Kaye, G. W.; Laby, T. H. Tables of Physical and Chemical Constants and Some Mathematical Functions; Longman: London, 1986. (52) Maksimova, I. N.; Pach, J. S.; Pravdin, N. N. Electrolyte Properties: A Handbook; Metallurgy Press: Moscow, 1987. (53) Beyer, K. D.; Ravishankara, A. R.; Lovejoy, E. R. Measurements of UV refractive indices and densities of H2SO4/H2O and H2SO4/ HNO3/H2O solutions. J. Geophys. Res. 1996, 101, 14519−14524. (54) Aseyev, G. G.; Zaytsev, I. D. Volumetric Properties of Electrolyte Solutions: Estimation Methods and Experimental Data; Begell House: New York, 1996. (55) Perry, R. H. Perry’s Chemical Engineers’ Handbook, 8th ed.; McGraw-Hill: New York, 2008. (56) Myhre, C. E. L.; Christensen, D. H.; Nicolaisen, F. M.; Nielsen, C. J. Spectroscopic study of aqueous H2SO4 at different temperatures and compositions: variations in dissociation and optical properties. J. Phys. Chem. A 2003, 107, 1979−1991. (57) Salkind, A. J.; Cannone, A. G.; Trumbure, F. A. In Handbook of Batteries, 3th ed.; Linden, D.; Reddy, T. B., Eds.; McGraw Hill: New York, 2002; Chapter 23. (58) Pavlov, D. Lead-acid batteries: science and technology. A Handbook of Lead-Acid Battery Technology and Its Influence on the Product, 2nd ed.; Elsevier: Oxford, 2017. K



Article

(81) Aseyev, G. G. Electrolytes Transport Phenomena. Methods for Calculation of Multicomponent Solutions and Experiment; Begell House: New York, 1998. (82) Patil, S. S.; Labadeb, V. P.; Kulkarnib, N. M.; Shaligram, A. D. Analysis of refractometric fiber optic state-of-charge (SOC) monitoring sensor for lead acid battery. Optik 2013, 124, 5687−5691. (83) Hsu, J.; Prather, M. J.; Cameron-Smith, P.; Veidenbaum, A.; Nicolau, A. A radiative transfer module for calculating photolysis rates and solar heating in climate models, Solar-J v7.5. Geosci. Model Dev. 2017, 10, 2525−2545. (84) Querry, M. R.; Waring, R. C.; Holland, W. E.; Earls, L. M.; Herrman, M. D.; Nijm, W. P.; Hale, G. M. Optical constants in the infrared for K2SO4, NH4H2PO4 and H2SO4 in water. J. Opt. Soc. Am. 1974, 64, 39−46. (85) Remsberg, E. E.; Lavery, D.; Crawford, B., Jr. Optical Constants for Sulfuric and Nitric Acids. J. Chem. Eng. Data 1974, 19, 263−265. (86) Palmer, K. F.; Williams, D. Optical constants of sulfuric acid; Application to the clouds of Venus. Appl. Opt. 1975, 14, 208−219. (87) Beyer, K. D.; Ravishankara, A. R.; Lovejoy, E. R. Measurements of UV refractive indices and densities of H2SO4/H2O and H2SO4/ HNO3/H2O solutions. J. Geophys. Res. 1996, 101, 14519−14524. (88) Born, M.; Wolf, E. Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light; Cambridge University Press: Cambridge, 1999; p 89. (89) Niedziela, R. F.; Norman, M. L.; DeForest, C. L.; Miller, R. E.; Worsnop, D. R. A temperature- and composition-dependent study of H2SO4 aerosol optical constants using Fourier transform and tunable diode laser infrared spectroscopy. J. Phys. Chem. A 1999, 103, 8030− 8040. (90) Biermann, U. M.; Luo, B. P.; Peter, T. Absorption spectra and optical constants of binary and ternary solutions of H2SO4, HNO3, and H2O in the mid infrared at atmospheric temperatures. J. Phys. Chem. A 2000, 104, 783−793. (91) Krieger, U. K.; Mössinger, J. C.; Luo, B.; Weers, U.; Peter, T. Measurement of the refractive indices of H2SO4−HNO3−H2O solutions to stratospheric temperatures. Appl. Opt. 2000, 39, 3691− 3703. (92) Lund-Myhre, C. E.; Christensen, D. H.; Nicolaisen, F. M.; Nielsen, C. J. Spectroscopic study of aqueous H2SO4 at different temperatures and compositions: Variations in dissociation and optical properties. J. Phys. Chem. A 2003, 107, 1979−1991.

(59) Liu, J.; Li, G. Frequency and temperature characteristics of an ultrasonic method for measuring the specific gravity of lead-acid battery electrolyte. Jpn. J. Appl. Phys. 2012, 51, 026601. (60) Horvath, A. L. Handbook of Aqueous Electrolyte Solutions: Physical Properties, Estimation and Correlation Methods; Ellis Horwood Limited: Chichester, 1985. (61) Esperilla, J. J.; Félez, J.; Romero, G.; Carretero, A. A full model for simulation of electrochemical cells including complex behaviour. Simul. Pract. Theory 2007, 15, 82−97. (62) Cugnet, M.; Laruelle, S.; Grugeon, S.; Sahut, B.; Sabatier, J.; Tarascon, J.-M.; Oustaloup, A. A mathematical model for the simulation of new and aged automotive lead-acid batteries. J. Electrochem. Soc. 2009, 156, A974−A985. (63) Kashkooli, A. G.; Farhad, S.; Fung, A. S.; Chen, Z. Effect of convective mass transfer on lead-acid battery performance. Electrochim. Acta 2013, 97, 278−288. (64) Esfahanian, V.; Kheirkhah, P.; Bahramian, H.; Ansari, A. B.; Ahmadi, G. The effects of electrode parameters on lead-acid battery performance. Adv. Mater. Res. 2013, 651, 492−498. (65) Novotny, P.; Söhnel, O. Densities of binary aqueous solutions of 306 inorganic substances. J. Chem. Eng. Data 1988, 33, 49−55. (66) Myhre, C. E. L.; Nielsen, C. J.; Saastad, O. W. Density and surface tension of aqueous H2SO4 at low temperature. J. Chem. Eng. Data 1998, 43, 617−622. (67) Kulmala, M.; Laaksonen, A.; Pirjola, L. Parameterizations for sulfuric acid/water nucleation rates. J. Geophys. Res. 1998, 103, 8301− 8307. (68) Walrafen, G. E.; Yang, W. H.; Chu, Y. C.; Hokmabadi, M. S. Structures of concentrated sulfuric acid determined from density, conductivity, viscosity and Raman spectroscopic data. J. Solution Chem. 2000, 29, 905−936. (69) Vehkamäki, H.; Kulmala, M.; Napari, I.; Lehtinen, K. E. J.; Timmreck, C.; Noppel, M.; Laaksonen, A. An improved parameterization for sulfuric acid-water nucleation rates for tropospheric and stratospheric conditions. J. Geophys. Res. 2002, 107, AAC 3-1. (70) Hyvärinen, A. P.; Raatikainen, T.; Laaksonen, A.; Viisanen, Y.; Lihavainen, H. Surface tensions and densities of H2SO4 + NH3 + water solutions. Geophys. Res. Lett. 2005, 32, L16806. (71) Jaecker-Voirol, A. Etude Physico-Chimique de la Formation des Aerosols: Application aux ″Pluies Acides″ et la Stratosphere; Thesis, Univ. Louis Pasteur, Strasbourg, 1988. (72) Gupta, S. V. Practical Density Measurement and Hydrometry; Series in Measurement Science and Technology; CRC Press, Taylor & Francis Group, 2002; p 154. (73) Ohtake, T. Freezing points of H2SO4 aqueous solutions and formation of stratospheric ice clouds. Tellus, Ser. B 1993, 45, 138−144. (74) Dutrieux, J. F.; Platten, J. K.; Chavepeyer, G.; Bou-Ali, M. M. On the measurement of positive Soret coefficients. J. Phys. Chem. B 2002, 106, 6104−6114. (75) Whalley, E. The Compression of Liquids; Le Neidre, B., Vodar, B., Eds.; In Experimental Thermodynamics; Butterworth: London, 1975; Vol. II, pp 421−500. (76) Cao-Paz, A. M.; Rodríguez-Pardo, L.; Fariña, J.; MarcosAcevedo, J. Resolution in QCM sensors for the viscosity and density of liquids: application to lead acid batteries. Sensors 2012, 12, 10604− 10620. (77) Liu, J.; Li, G. Frequency and Temperature Characteristics of an Ultrasonic Method for Measuring the Specific Gravity of Lead-Acid Battery Electrolyte. Jpn. J. Appl. Phys. 2012, 51, 026601. (78) Zhang, J., Zhang, L., Liu, H., Sun, A., Liu, R.-S., Eds.; Electrochemical Technologies for Energy Storage and Conversion; John Wiley & Sons: Weinheim, Germany, 2011; Vol. II. (79) Vinal, G. W.; Craig, D. N. The viscosity of sulphuric acid solutions used for battery electrolytes. Bur. Stand. J. Res. 1933, 10, 781. (80) Das, A.; Dev, S.; Shangpliang, H.; Nonglait, K. L.; Ismail, K. Electrical conductance and viscosity of concentrated H2SO4/H2O binary systems at low temperatures: correlation with phase transitions. J. Phys. Chem. B 1997, 101, 4166−4170. L


Review and Analysis of Thermophysical Properties of a Sulfuric Acid

Recommend Documents