Correlation of sulfuric acid-water partial pressures

Fluid Phase Equilibria, 53 (1989) 279-288 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

CORRELATION

279

OF SULFURIC ACID-WATER PARTIAL PRESSURES

Richard W. Wilson and Fred P. Stein Chemical Engineering

Department,

111 Research Drive, Bethlehem,

Lehigh University, Building A,

PA 18015, U.S.A.

ABSTRACT The measured partial pressures of sulfuric acid and water above aqueous solutions of sulfuric acid in the (low) temperature

range 363 K to 443 K were correlated

percent on the average by hypothesizing The temperature kcal.

coefficient

which assumed

constant of the complex

from calorimetric

is 16.2

ideal gases, were as much as an order of

low in predicting sulfuric acid partial pressures.

had been determined

to within 16

solvation of sulfuric acid and water.

of the chemical equilibrium

Previous correlations,

magnitude

vapor-phase

Liquid-phase

and emf measurements,

fugacities,

were taken

which

from the

literature for use in this study.

INTRODUCTION During the study of the condensation gas in air heater focused

passages

on the vapor-phase

particular condensed

rates of sulfuric acid-water

at the back end of coal-fired concentration

interest were the partial pressures acid.

gradients

mixtures from flue

power plants,

of sulfuric

attention

was

acid and water.

Of

of acid and water in equilibrium

with the

In addition, if the equilibrium study could shed any light on the nature of

the types of “sulfuric

acid” species present, the condensation

and diffusion

calculation

would be enlightened. The earliest

works to predict the equilibrium

partial pressures

of sulfuric acid and

water above liquid mixtures of acid and water were by Abel (1946, 1947) and Gmitro and Vermeulen

(1963, 1964). Their work focused on the fugacity of the liquid phase which was

described

in

parameters.

terms

of

pure-component

Later, when vapor-phase

and

concentration-dependent

equilibrium measurements

calorimetric

became available,

shown that their equations,

coupled with the ideal-gas

predictions of the equilibrium

partial pressures of water, but the predicted partial pressures

0378-3812/89/$03.50

assumption,

0 1989 Elsevier Science Publishers B.V.

yielded

it was

reasonable

280

of acid were too small by an order of magnitude. uncertainties

in the pure-component

This disparity was originally

parameters

used for the acid (Verhoff and Banchero,

1972; Ayers -et al, 1980) and the lack of accurate (Banchero

and Verhoff, 1975).

concentration-dependent liquid- concentration

acid partial-pressure

parameters,

the ideal-gas

of the partial pressures of acid. dependence

indicated

of the sulfuric acid-water

assumption

Furthermore,

by the measured

resemble the behavior dictated by the Gmitro and Vermeulen correlation

measurements

In spite of our recent update of the pure-component

calorimetric

severe underestimates

attributed to

still leads to

the temperature

partial pressures equations.

and and

does not

Accordingly

this

partial pressures was launched using the hypothesis

of solvation between acid species and water in the vapor phase.

LIQUID FUGACITIES Gmitro and Vermeulen first principles. component

(1963, 1964) derived the equation

The first five terms

parameters

composition-dependent

determined

on the right-hand from

calorimetric

for liquid fugacities

side of Equation data;

the remaining

terms

+ z;G

f ap

+ lnZi

(1)

A=$[ln(&J+~-1]

(2)

B=;[%+;-298]

(3)

~=;[$-~+f]

(4)

DA&

(5)

E’;

(6) 11

(7)

G =;[f-A]

(8)

H=i[298ln(&)+$$-51

(9)

Pure-Component

are

parameters.

lnff = aiA + bp + ciC + AHYD + ASYE f @

F=$[ln(T)-F+

from

1 are pure-

Parameters

All of the calorimetric

parameters

were reevaluated

using the best and/or most recent

values. For water, the enthalpy of formation

and the absolute entropy of the vapor were taken

from Wagman et al (1968); the corresponding

liquid enthalpy and entropy were taken from

Kelly et al (1960).

Values of the constants for the ideal-gas heat capacity were obtained

by a least-squares

fit of the tabular information

reported by Giguere and Savoie

(1963).

281

The enthalpy

and entropy of the acid were taken from Ayers et al (1980).

measured vapor pressures above a highly-concentrated the enthalpy agreement

and entropy

with values

of vaporization.

calculated

The entropy

in the literature on the enthalpy

and Stafford; 1966).

of vaporization

by Ayers et al is within the range of estimates Vermeulen,

of vaporization

is in close

from the infrared spectra of acid vapors

1971; Gopinath and Rao, 1973, Chackalackal consensus

They utilized

acid solution to regress values for (Stull et al,

Although there is no

of the acid, the value reported

available from other sources (Gmitro and

1963; Wagman et al, 1968; Halstead and Talbot, 1980).

The constants

in the ideal-gas

squares fit of the tabular information pure-component

calorimetric

heat-capacity

parameters

were obtained

by a least-

are shown in Table 1.

TABLE 1 Pure-Component Component

expression

reported by Stull et al (1971). The values used for the

Property

Calorimetric Parameters Value 10519.

H2S04

Units cal/mol

28.394

cal/mol deg

a=7.97248

cal/mol deg

b=8.7 x 1o-4 c=3.0 x 1o-e

cal/mol deg2 callmol deg3

20168.

cal/mol

32.29

cal/mol deg

a=2.91429

cal/mol deg

b=6.9147 x 1O-2 c=-4.0 x 10-s

cal/mol deg2 cal/mol deg3

J=-6.71464

so3

K=-8.10161 x 104 L=-9643.04 M=l4.74965 N=-9.4577 x 1O-3 Q=2.19062 x 1Os

deg2 deg

1ldeg l/deg2

Cp =a+bT+cT2 InK~=Jln~+~+~+~M+NT+QT2

Composition-Dependent

Parameters

The composition-dependent

parameters

They are too massive to be repeated

here.

appear in the literature as tabulated Giaugue et al (1960) tabulated

values.

values for the

282

liquid activity,

partial

heat-capacity

coefficient

composition

range.

enthalpy

of mixing, partial-molar

Giaugue’s tabulations

Staples (1981) developed

based on an updated and more-complete to acid solutions

containing

data available

equation. a tabulation

for the liquid activity of water

data set. However, Staples limited his tabulation in the data at high concentrations

and range were used in this analysis, but the results are quite similar to

Giaugue’s

because much of the same data were used at the low concentrations. (1979) could not be used for the activities here are beyond the range of applicability

The liquid activities Gibbs-Duhem

analysis

of acid. The

equations encountered

liquid

at the time

less than 0.331 mole fraction because his statistical

showed that there were large uncertainties Staples tabulation

and partial-molar

at 298K over the entire

utilized experimental

and were forced to comply to the Gibbs-Duhem Subsequently,

heat capacity,

for both the acid and water

for the acid were generated

equation.

In order to implement

activity of the acid is required. acid was chosen arbitrarily

Pitzer’s

because the acid concentrations of his correlation. from the water activities

this calculation

a reference

using the

value for the

Giaugue’s value for acid activity at a mole fraction of 0.2

because it was near the middle of the composition

range and

because the activities of water are identical in both the Giaugue and Staples’ tabulations this concentration.

TABLE 2

Giaugue’s

Activities of Sulfuric Acid in Aqueous Mixtures

Mole Fraction Acid

298Rlnili

0.0177 0.0425 0.0833 0.1290 0.1818 0.2381 0.3333

-15418. -13913. -11954. -9994. -8089. -6466. -4559.

tabulation

H2S04

calimol

for all of the other composition-dependent

enthalpy of mixing, partial-molar

heat capacity, and partial-molar

properties

heat-capacity

was used in lieu of other information.

The rather small relative contribution

in calculating

over

experimental

at

A few of these acid activities are shown in Table 2.

the

liquid

fugacities

data is shown in Table 3.

the

range

of conditions

(partial

coefficient)

of these terms

addressed

by the

283

TABLE 3 T=373 K

Relative Contributions

0.311 Mole Fraction Acid

Term

j-f in atm H2O

H2S04

aiA

biB tic

0.0343 0.2625 -0.4165

0.0939 0.0033 -0.0313

AHYD

-27.2124

-14.2918

ASYE

16.2506

14.2899

r!G

2.4667 -0.0103

0.5026 0.0001

9.9779

2.4049

CX;H

lnZi

The largest contributions the majority

to In$

contribution

come from the enthalpy

from the concentration

and entropy of vaporization,

dependent

while

terms comes from the liquid

activity, which values are based on reproducible data.

VAPOR PHASE The postulated chemical reaction scheme for the vapor phase is H,SO, H,SO,

= SO, + Hz0 f Hz0 = H,SO,.H,O

VKO

(10)

TKl

(11)

Where the equilibrium constants are K. ~‘9

(12)

+?.!?-

(13)

PA PW

K. is known independently,

the correlation coefficient

of K,.

depends

but K, is fit to the measured partial pressures.

The success of

on how well the data are fit and the size of the temperature

In the chemical theory of solutions, the vapor fugacity is equated to the

product of the apparent

partial pressure and the apparent fugacity coefficient

(Copeman

and Stein, 1982). For the acid-water system, (14)

pAo+Ao =dt

Assuming

that the actual

species

present

coefficient becomes the ratio of the monomer-acid

behave

ideally,

the apparent

to the apparent-acid

fugacity

partial pressure.

284

PA

TAO=

(15)

*A,

As a result,

the

liquid

fugacity

of acid

(or water)

is equal

to the

monomer

partial

pressure. PA

(‘6)

=3; The

apparent

monomer-acid, at the dilute

acid

partial

pressure

and hydrated-acid acid concentrations

partial

is equal pressures

encountered

to

the

sum

because

of

the

sulfur

trioxide,

the term 5 is essentially

unity

here. (17)

By combining be expressed

the above

equations,

the apparent

in terms of the equilibrium

constants

fugacity-coefficient

of the acid can

and the liquid fugacity

of the water.

(18)

The Equilibrium

Constant,

Kc was determined Bodenstein

and Kataymaya

concentration interpreted

of sulfuric

expression

(1909) acid

in this work

The equilibrium

Gmitro

constant

and Vermeulen

for the reaction

appearing

as the sum

between

by Gmitro

(1963,

1964) fit the data of

sulfur trioxide

in the Bodenstein

of the monomer

Ki reported

for K0 in Equation

and

and

Kataymaya

hydrated-acid

and Vermeulen

and water. data

is, therefore,

The necessary

pressure.

related

12 by

MEASUREMENTS

acid solutions.

claiming

They

corrected

equilibrium

as shown

OF SULFURIC

Haase had

and reported

ACID the acid partial

and Borgman

not been

(1961)

attained

acid partial-pressure

using

17.

(1980)

and 0.90

liquid

transpiration

determined

distinguish

so the reported

by Equation

and Ackers

to 0.566

made

was

cannot

acid hydrate,

1.

the first to measure

equilibrium

et al (1980) 0.484

were vapor

experiments

in Table

pressures

disqualified

the earlier

in the Othmer-Cotrell measurements

above

still.

in the range

liquid acid mole fraction.

range

measurements

were

Soon thereafter,

the problem

Halstead

composition

(1959)

that thermal

of 0.256 to 0.418 Later,

for K, are shown

and Rehse

data

to the

(19)

constants

PARTIAL-PRESSURE Haase

The

set was

partial

1 +Kl.?-w)

ql=q)(l

sulfuric

& independently.

among

from

an

sulfur

measured

techniques, assay trioxide,

data are measurements

acid partial

mole-fraction

of

acid,

where the

sulfuric

pressures

respectively.

the composition

condensed acid monomer,

of the apparent

in the These

vapors.

of the The

and sulfuric

acid partial

pressure,

285

RESULTS The partial-pressure

data were regressed in order to determine the constants in

In (K1) = -17.28 + F

where K, is defined by Equation 13. The data of Haase and Rehse (1959) were not included in the regressed because

of the disqualification

liquid acid mole fractions observation

by Haase and Borgman

greater

data set

(1961) and all measurements

than 0.331 were excluded

in view of Staples

at

(1981)

that the liquid activities were not reliable at higher concentrations.

Figure

1 shows the equilibrium

constants

determined

using each measured

acid

partial pressure and the fit of Equation 20.

6.0

Fit

0.0 2.2

I

I

I

I

I

2.3

2.4

2.5

2.6

2.7

: 8

l/T (DegK X 1000)

Figure 1 Equilibrium Constant for H,S0,+H20=H,S0,:H20

Fioure 2 shows the comoarison

between

the measured

acid oartial oressures

and

286

those

calculated

Equations

using liquid fugacities

10 and 11. The correlation

and the vapor-phase

reactions

is good to within an average

postulated

in

absolute error of 16

percent.

-4.0

XAI A X=0.28

x=0x.25 -6.0

-8.0 E

I

Temperature

Figure 2

Comparison

Degrees

Celsius

of Measured and Calculated Acid Partial Pressures

DISCUSSION This correlation entropy

of vaporization

was found to be relatively

insensitive to the values of enthalpy

of the acid used in the liquid fugacity equation.

and

Different values

altered the intercept of Figure 1, leaving the slope relatively unchanged. The temperature

coefficient of Equation 20 gives a heat of formation of 16.2 kcal/mol,

which is in the range of values expected solvation

of sulfuric acid and water.

for the formation

The reasonableness

of two hydrogen

of the fit of the data shown in

Figure 2 and the value of the inferred heat of formation from the temperature Figure 1 demonstrate

that the postulate of a sulfuric acid-water

vapor

sulfuric

over aqueous

evidence

of this solvation

acid solutions

reaction

is not denied.

in the vapor phase.

bonds in the coefficient of

hydrate in the equilibrium But, there

is independent

Sievert and Castleman

(1988)

287

found

substantial

quantities

of

sulfuric

acid-water

clusters

in

measurements

of the products of the reaction between sulfur trioxide

Jaecker-Voirol

et al (1987)

used nucleation

theory

mass

spectroscopic

and water at 353K.

to demonstrate

that vapor-phase

hydration of sulfuric acid is expected under equilibrium conditions. Previous correlations pressures

using the ideal-gas assumption

of water within about ten percent.

resulted in a slight improvement

Although

had predicted

measured

partial

not shown here, this correlation

for the water partial pressures.

SYMBOLS Constants in ideal-gas heat capacity; See Table 1 Activity at 298 K ideal-gas heat capacity Partial molar liquid heat capacity Liquid-phase

fugacity

Heat of Vaporization

Ko,Ko,K1

Equilibrium constants defined by Equations 12,i 9,and 13, respectively

E! Pi0 R

Partial molar enthalpy Partial pressure Apparant partial pressure Gas Constant

Assy

Entropy of vaporization

Pj'

Temperature coefficient of ??ki Apparant fugacity coefficient Subscripts Acid or Water A

H2S04

s

so3

W

H2O

MS

H,SO,:H,O

Superscript Liquid REFERENCES Abel,

E., 1946.

The vapor

phase

above the system

sulfuric

acid-water.

Journal

of

Physical Chemistry, 50:260-282. Abel, E., 1947.

On the experimental

bases for the calculation

pressure above the sulfuric acid-water system.

of the sulfuric acid vapor

J. Phys. Chem., 908-914.

288

Ayers, G.P., Gillett, R.W., and Gras, J.L., 1980. On the vapor pressure of sulfuric acid. Geophysical Research Letters, 7:433-436. Banchero, J.T., and Verhoff, F.H., 1975. Evaluation and interpretation of the vapour pressure data for sulfuric acid aqueous solutions with application to flue gas dewpoints. Journal of the Institute of Fuel, 76-80. Bodenstein, M., and Kataymaya, M., 1909. Die dissoziation von hydratischer schwefelsaure und von Stockstofff diozyd. Zietschrift fur Electrochemie, 15:244. Chackalackal, S.M., and Stafford, F.E., 1966. Infrared spectra of the vapours above sulfuric and deuteriosulphuric acids. JACS, 88:723. Copeman, T.W., and Stein, F.P., 1982. On the derivation and application of solution thermodynamics for reactive components. Fluid Phase Equilibria, 9:149-165. Giaugue, W.F., Hornung, W., Kunzler, J.E., and Rubin, T.R., 1960. The thermodynamic properties of sulfuric acid solutions and hydrates from 15 to 300 K. JACS, 82:62. Giguere, P.A., and Savoie, R., 1963. Normal vibrational frequencies of H2SO4 and D2SO4. JACS, 85:287-289. Gmitro, J.l., and Vermeulen, T., 1963. Vapor-liquid equilibria for aqueous sulfuric acid. UCRL-10886. Gmitro, J.l., and Vermeulen, T., 1964. Vapor-liquid equilibria for aqueous sulfuric acid. AIChE Journal, 10:740. Gopinath, C.R., and Rao, K.S.R., 1973. Thermodynamic properties of some molecules of XO2Y2 and XO3 YZ types. Current Science, 42:164. Haase, R., and Rehse, M., 1959. Ermittlung der taupunkte yon rauchgasen ausdem verdampfungsgleichgewicht des systems wasser-schwefelsaure. Mitteilungen Der VGB, 82:367-371. Haase, R., and Borgmann, H.W., 1961. sauertaupunkten, Korrosion, 15:47.

Prazisionmessungen

zur ermittlung yon

Halstead, W.D., and Talbot, J.R.W., 1980. The sulfuric acid dewpoint in power station flue gases. Journal of the Institute of Fuel, 142-145. Jaecker-Voirol, A., Mirabel, P., and Reiss, H., 1987. Hydrates in supersaturated binary sulfuric acid-water vapor: a reexamination. J. Phys. Chem., 87:4849-4852. Pytkowicz, R.M., ed. "Activity Coefficients in Electrolyte Solutions," Vol. 1, chapter 7 oy K.S. Pitzer "Theory: Ion Interaction Approach," CRC Press, Inc.,1979. Sieved, R.H., and Castleman, A.W., Jr., 1984. Reaction of SO3 with water clusters and the formation of H2SO4. J. Phys. Chem., 88:3329-3333. Staples, B., 1981. Activity and osmotic coefficients of aqueous sulfuric acid at 298.15K. Journal of Physical Chemical Reference Data, 10:779-797. Stull, D.R., 1971. JANF Thermochemical Tables 2rid Edition. U.S. National Bureau of Standards, NSR DS-NBS 47. Verhoff, R.H., and Banchero, J.T., 1972. A note on the equilibrium partial pressures of vapors above sulfuric acid solutions. AIChE Journal, 18:1267-1268.