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Thermodynamic Properties of Aqueous Sulfuric Acid Hannu Sippola*,†,‡ and Pekka Taskinen† †

Department of Materials Science and Engineering, Metallurgical Thermodynamics and Modeling, Aalto University School of Chemical Technology, P.O. Box 16200, FI-00076 Aalto, Finland ‡ FCG Design and Engineering, Osmontie 34, FI-00601 Helsinki, Finland ABSTRACT: Thermodynamic properties of aqueous sulfuric acid were modeled with the Pitzer equation. Both the second dissociation constant K2 for sulfuric acid and the Pitzer parameters were fitted simultaneously. The most accurately considered experimental data including electrochemical cell, osmotic, enthalpy, and vapor pressure data at temperature range (0 to 170) °C were used in the assessment. After variations of the used experimental data and the temperature dependency of the Pitzer parameters, the thermodynamic values for the bisulfate dissociation in aqueous sulfuric acid at 25°C were re-evaluated. The obtained values for the dissociation reaction are (11.00 ± 0.27) and (25.11 ± 0.80) kJ·mol−1 for Gibbs energy and enthalpy change, respectively, yielding to 0.0119 for K2. The obtained thermodynamic values for the cell reactions are in good agreement with CODATA and NBS literature values as well as with other Pitzer based thermodynamic models for aqueous sulfuric acid. The best model selected by using the obtained new thermodynamic data was further tested and compared to the recent Pitzer models with excellent agreement as well as with good extrapolating capabilities with respect to temperature and acid concentration. The total number of fitted terms in Pitzer parameters is eight.

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INTRODUCTION Sulfuric acid is an important chemical for industry widely used in phosphate fertilizer and pigment production, steel pickling, and other hydrometallurgical applications, and the production of organic chemicals, explosives, etc.1 Its thermodynamically related properties have been extensively studied especially at 298.15 K and summarized by Clegg et al.2 The thermodynamic modeling of sulfuric acid is complicated by the incomplete dissociation of sulfuric acid

In general, the local composition models have fewer parameters than Pitzer models, but they are focused on speciation and vapor pressure. The gas phase is assumed ideal in most cases. Available electrochemical data are usually ignored. Thus, these models do not describe so accurately the behavior of sulfuric acid in dilute regions but are more accurate in higher concentrations where the bisulfate ion dominates. A more detailed discussion on thermodynamic models for aqueous sulfuric acid can be found elsewhere.18 In 2012, Sippola19 found out that only four Pitzer parameters with a simple temperature dependency of (a + b/T) is sufficient to present the stoichiometric osmotic and activity coefficients equally well as the more complicated models by Clegg et al.2 and Clegg and Brimblecombe15 in the temperature range (0 to 55) °C up to 6 m sulfuric solution. Several different K2 equations were found to be able to present the studied experimental data equally well. An extension of the temperature range does not change the situation.18 The importance of choosing the best K2 equation for sulfuric acid is a key factor for the further development of model for multicomponent aqueous systems where sulfuric acid is involved. According to the philosophy of CALPHAD method,20,21 the binary systems should be modeled first and critically evaluate the available thermodynamic data before any ternary or higher order

HSO4 − = SO4 2 − + H+K 2 = a(SO4 2 −)a(H+)/a(HSO4 −) (1)

There are several different equations available in the literature for the value of the second dissociation constant of sulfuric acid as a function of temperature. Thermodynamic properties for reaction 1 derived from these equations are listed in Table 1. Pitzer et al.5 have modeled the thermodynamic behavior of aqueous sulfuric acid using the activity coefficient model, named after Pitzer11 himself, from (0 to 55) °C up to 6 m sulfuric acid solution. After that, several other thermodynamic models for aqueous sulfuric acid have been generated with the Pitzer equation (Table 2) or by local composition models (Table 3). The concentration range for Pitzer models is up to 6 mol H2SO4 per 1 kg water, that is, 6 m, except for mole fraction scale models where the weight fraction of sulfuric acid is from 0 to 0.8. As can been seen from Table 2 the total number of excess parameters and fitted terms has increased during years beyond the level of practical usability. © 2014 American Chemical Society

Received: January 2, 2014 Accepted: May 2, 2014 Published: July 3, 2014 2389

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Table 1. Thermodynamic Properties Related to the K2 of Sulfuric Acid ΔH298

temperature range

J·mol−1

authors

year

°C

3

1961 1966 1977 1978 1978 1988 1988 1990 1994 2003

25 to 225 25 to 350 5 to 55 5 to 55 5 to 55 25 to 200 50 to 250 10 to 55 0 to 50 −93 to 200

Lietzke et al. Marshall and Jones4 Pitzer et al.5 Young et al.6 Young et al.6 Matsushima and Okuwaki7 Dickson et al.8 Hovie and Hepler9 Clegg et al.2 Knopf et al.10

ΔS298

ΔCp,298

J·K−1·mol−1

J·K−1·mol−1

K2

−106.95 −92.15 −116.67 −110.91 −112.33 −119.01 −113.92 −116.80 −114.21 −100.06

−209 −239 0 −192 −238 −218 −275 −265 −275 −206

0.01030 0.01029 0.01050 0.01017 0.01068 0.01030 0.01086 0.01036 0.01050 0.01058

−20 546 −16 128 −23 490 −21 693 −22 238 −24 140 −22 756 −23 496 −22 756 −18 555

Table 2. Pitzer Interaction Models for Aqueous Sulfuric Acid author(s) Pitzer et al. Reardon and Beckie12 Sippola13 Holmes and Mesmer14 Clegg et al.2 Clegg and Brimblecombe15 Knopf et al.10 Christov and Moller16 Friese and Ebel17 a

modificationsa

year

5

1977 1987 1992 1992 1994 1995 2003 2004 2010

temperature range (°C)

no. parameters

total no. terms

equation for K2

5 to 55 5 to 55 5 to 55 25 to 200 0 to 55 −70 to 55 −90 to 200 0 to 200 −70 to 55

4 4 4 5 9 10 10 5 11

8 9 8 17 32 40 34 20 66

Pitzer5 Pitzer5 Okuwaki7 Dickson8 Dickson8,b Dickson8,b Knopf10 Dickson8 Dickson8,b

U U UA M A U M

U = unsymmetrical mixing terms; A = Archer extension; M = mole fraction scale. bModified to yield 0.01050 at 25 °C.

Table 3. Local Composition Models for Aqueous Sulfuric Acid author(s)

year

model

temperature

concentration

number of excess parameters and (terms within)

Liu and Grén24,a Bosen and Engels25,a Messnaoui and Bounahmidi26 Bollas et al.27 Que et al.28 Simonin et al.29 Simonin et al.30,b Campos et al.31

1991 1998 2006 2010 2011 2006 2004 2006

Liu−Harvey−Prausnitz NRTL eNRTL eNRTL (refined) eNRTL (symmetric) MSA-NRTL MSA (BIMSA) UNIQUAC

25 °C (0 to 240) °C (25 to 75) °C 25 °C (0 to 500) °C 25 °C 25 °C (0 to 150) °C

(1 to 76) mol·kg−1 w = 0 to 0.96 (1 to 7) mol·kg−1 (0 to 50/65) mol·kg−1 w = 0 to 1 (0.1 to 6.0) mol·kg−1 (0.1 to 27) mol·kg−1 w = 0 to 1

2 10 (17) 4 (6) 10 18 (30) 6 6 7 (15)

a

Complete dissociation of sulfuric acid is assumed. bThe bisulfate ion is considered via equilibrium only. No ion specific parameters are used.

systems is modeled. Choosing the best K2 equation is thus a crucial step in this process. The scope of this article is to generate a practical Pitzer model with reasonable number of parameters and terms to model the thermodynamic properties of the H2SO4−H2O system in a wide temperature range. Theory. In aqueous solutions the chemical potential of the solvent, that is water, is defined as μw = μwo + RT ln(a w )

The practical osmotic coefficient (ϕ) is generally used in aqueous systems instead of the activity of water: ⎛ 1000 ⎞ φ = −⎜ ⎟ln a w ⎝ M w ∑ mi ⎠

(4)

where Mw is the molecular weight of water in g·mol−1. Electrolytes dissociate in aqueous solutions M v +X v − = v+ Mz + + v− Xz −

(2)

(5)

and the chemical potential of the electrolyte is defined to be equal to the sum of chemical potentials of ions:

where the standard state is pure water at the temperature and pressure of the solution. For the solutes the chemical potential is

μ(M v +X v −) ≡ v+μ(Mz +) + v−μ(Xz −)

μi = μio + RT ln(ai) = μio + RT ln(mi) + RT ln(γi) (3)

(6)

This applies also in the case of incomplete dissociation of the electrolyte. Thus, from eqs 3 and 6 follows for any electrolyte:

where mi is the molality and γi is the activity coefficient of the solute. Since the concentration is expressed in molalities, the standard state is hypothetical, 1 m ideally dilute solution at the temperature and pressure of the solution.

μo (M v +X v −) = v+μo (Mz +) + v−μo (Xz −)

(7)

and 2390

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aMX = mMX γMX = (mM γM)v + (mX γX)v−

GE, m = f (I ) + 2 ∑ ∑ mcma [Bca + (∑ mczc)Cca] wwRT c a c

(8)

If the electrolyte dissociates completely, the molalities of ions can be calculated from mM = v+mMX (9) mX = v−mMX

+ +

mMX γMX = (v±m) (γ±)

(11)

v = v+ + v−

(12)

v±v = (v+)v+ (v−)v−

(13)

γ±v = (γM)v+ (γX)v−

(14)

n

2

4

+ RT ln(γH SO )

n

a

+

μo (H 2SO4 ) = 2μo (H+) + μo (SO4 2 −)

(17)

4

+

w , ni , i ≠ M

∑ ma[2BMa + ZCMa] + z M ∑ ∑ mcmaCca 2 zM

c

∑∑ c

+

2 zM

mcma Bca′

∑∑

+

and furthermore

c

mcmc ′Φ′cc ′

+

On the other hand, if the incomplete dissociation of sulfuric acid in eq 1 is considered, the following relationship with the activity of sulfuric acid is obtained:

+

4

+

and furthermore 4

= z X2(f ′(I )/2)

∑ mc[2BcX + ZCcX] + |z X| ∑ ∑ mcmaCca c

(20)

a H2SO4 = K 2m2(1 − α 2)γHγHSO

(24)

n

w , ni , i ≠ X

a H2SO4 = mγH SO = (mHγH) (mSO4 γSO ) = K 2mHγHmHSO4 γHSO 4

ma ma ′Φ′aa ′

ma ma ′ψMaa ′ + 2 ∑ mnλnM

∑∑

⎛ ∂GE, m /RT ⎞ ln γX = ⎜ ⎟ ⎝ ∂nX ⎠T , p , w

2

4

∑∑

where the prime symbol (′) indicates a derivative by ion strength and Z is defined as Z = ∑imi|zi|.

(19)

4

a 2 zM

a