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International

(Palmrose) definition

Total SO2 % od wood 17.5 17.5

Free SO2 % od wood 10.5 14.0

of total SO2 60 80

Combined SO2 % od wood 7.0 3.5

MgO % od wood 2.2

Liquor-to-wood ratio 3.5

Actual SO2 concentration

Total SO2 mol L–1 0.78

Free SO2 mol L–1 0.47

Bound SO2 (HSO3

–) mol L–1 0.31

a) Denoted also as true free and true combined SO2; this definition

may be used to convert both definitions into each other: % True

free SO2 = (% Free SO2 – % Comb. SO2)

% True Comb. SO2 = 2* % Comb. SO2.

396 4 Chemical Pulping Processes

The concentrations of the sulfur(IV) species in the aqueous cooking liquor are

defined through the following equilibria:

SO2 H2O _ H2SO3 SO2 _ H2O _ __H HSO_3 _159_

It has been shown that the major part of the sulfur dioxide in an aqueous solution

is not hydrated to sulfurous acid [6]. The hydrated and non-hydrated form of

the free SO2 are combined to express the first equilibrium constant Ka,1:

Ka_1 _

H _ _ HSO_3 __SO2 __H2SO3 _ _160_

The dissociation constant Ka,1 of combined SO2 decreases clearly with increasing

temperature, as seen in Tab. 4.53.

Tab. 4.53 Temperature-dependence of the first equilibrium

constant of free SO2 (according to [6]).

Temperature

[ °C]

pKa,1

25 1.8

70 2.3

100 2.6

110 2.8

120 3.0

130 3.1

140 3.3

150 3.5

Hydrogen sulfite ions are also in equilibrium with monosulfite ions and protons

according to the following expression:

HSO_3 _ H SO2_ 3 _161_

Hydrogen sulfite is a weak acid, and its equilibrium constant derived from

Eq. (159), and denoted as second equilibrium constant, Ka,2, is expressed as:

Ka_2 _

_H _ SO2_ 3 HSO_3 _ _ _162_

4.3 Sulfite Chemical Pulping 397

The pKa,2 can be approached by a value of about 7.0 at 25 °C. The change in ionization

of the hydrogen sulfite ion with temperature is unknown, and is assumed to

be insignificant. Consequently, pKa,2 is kept constant in the temperature range

prevailing in acid sulfite cooking.

The concentrations of the active cooking chemicals in a pure aqueous acid sulfite

cooking liquor, [H+], [HSO3

– ]and [SO3

2–], can be calculated by the following

simple equations:

The total SO2 concentration at any time and any pH is calculated as:

SO2_tot _ Ctot _ SO2 _ H2O _ HSO_3 SO2_ 3 _163_

The concentrations of [SO2.H2O], [HSO3

– ]and [SO3

2–]can be calculated accordingly:

SO2 _ H2O _ _Ctot _ HSO_3 SO2_ _ 3_ _164_

HSO_3 _ Ctot __SO2 _ H2O SO2_ _ 3_ _165_

SO2_ 3 _ Ctot _ SO2 _ H2O _ HSO_3 _ _ _166_

The pH-dependent concentrations of sulfur(IV) species can be calculated by using

the equilibrium equations:

Ka_1 _ Ctot _ HSO_3 SO2_ 3 _ _ _ __ H _ _ HSO_3 _167_

The hydrogen sulfite ion concentration can be calculated by rearranging Eq. (167):

HSO_3 _

Ka_1 _ Ctot _ SO2_ _ 3_ _Ka_1 _H _ _168_

A similar procedure can be applied to calculate the monosulfite ion concentration:

Ka_2 _ Ctot __SO2 _ H2O SO2_ _ _ 3____H _ SO2_ 3 _169_

SO2_ 3_

Ka_2 __Ctot __SO2 _ H2O _

_Ka_2 _H _ _170_

The course of pH as a function of the concentrations of the sulfur(IV) species in a

pure sulfite cooking liquor can be calculated by considering the equilibrium conditions

for the titration of a weak two-basic acid with strong alkali according to the

following expression:

398 4 Chemical Pulping Processes

__A_ _OH_ __H _AH _171_

Assuming the total concentration of the sum of the conjugated bases [A– ]and the

acid [AH]to be Ctot (in mol L–1), the acid–base equilibria can be calculated as:

_H _

Ka_1 _ Ctot

_Ka_1 _H _

Ka_2 _ Ctot

_Ka_2 _H _

10_14

_H _ C* _172_

where C* is the molar amount of the titrator base NaOH.

As an example, the course of pH of a pure aqueous sulfite solution with a total

SO2 concentration of 50 g L–1 (0.78 mol L–1) is calculated as a function of the free

SO2 concentration (Fig. 4.151). In the first case, the titration curve is calculated

according to Eq. (172), using sodium hydroxide as a titrator base. In the second

approach, the titration curve is calculated by means of ASPEN-PLUS simulation

software, using magnesium hydroxide as a titrator base. ASPEN-PLUS uses a

high-performance electrolyte module based on the NRTL model (nonrandom,

two-liquid) to calculate the thermodynamic properties of aqueous electrolyte systems

[9]. The model provides an accurate description of the nonideality of concentrated

aqueous solutions.

The titration curve estimated by means of Eq. (172) agrees well with that calculated

by ASPEN-PLUS in the pH range 1 to 4.5, until any of the free SO2 is quantitatively

converted to hydrogen sulfite ions. The course of pH beyond this point

1.0 0.5 0.0 -0.5 -1.0

0

2

4

6

8

10

Titrator base, NaOH: 25 .C 140 .C

Titrator base, Mg(OH)

2

25 .C

pH-value

Free SO

2

, mol/l

Fig. 4.151 Course of pH as a function of the

free SO2 concentration assuming an initial

total SO2 concentration of 0.78 mol L–1 at 25 °C

and 140 °C. Two calculation modes: (a) titration

curve calculated according to Eq. (170), using

NaOH as titrator base; (b) titration curve simulated

by means of ASPEN-PLUS using

Mg(OH)2 as titrator base.

4.3 Sulfite Chemical Pulping 399

develops differently for the two bases. The addition of Mg(OH)2 causes a rather

even slope of pH until the equilibrium is shifted to monosulfite ions, while the

addition of NaOH raises the pH more steeply.

The concentrations of ionic species of a sulfite cooking liquor are given as a

function of the liquor composition (e.g., the molar content of free SO2 and active

base) in Tab. 4.54.

Tab. 4.54 Concentrations of ionic species of sulfite cooking

liquor with increasing amount of active base concentration;

initial free S02 concentration 0.78 mol L–1; [H+]calculation

according to Eq. (172), [HSO3

– ]according to Eq. (168), [SO3

2– ]

according to Eq. (170) and [SO2-H2O]according to Eq. (164).

Free SO2

[moI L–1]

Base

[moI L–1]

[H+]

[moI L–1]

pH-Value [SO2.H2O]

[moI L–1]

[HSO3

]

[moI L–1]

[SO3

2– ]

[moI L–1]

[H+]*[HSO3

]

0.78 0.00 1.04·10–1 0.98 6.77·10–1 1.04·10–1 1.00·10–7 1.07·10–2

0.58 0.20 3.65·10–2 1.44 5.44·10–1 2.37·10–1 6.48·10–7 8.63·10–3

0.39 0.39 1.47·10–2 1.83 3.76·10–1 4.05·10–1 2.76·10–6 5.96·10–3

0.28 0.50 8.49·10–3 2.07 2.72·10–1 5.09·10–1 5.99·10–6 4.32·10–3

0.08 0.70 1.79·10–3 2.75 7.92·10–2 7.02·10–1 3.92·10–5 1.26·10–3

0.00 0.78 3.94·10–5 4.40 1.93·10–3 7.77·10–1 1.97·10–3 3.06·10–5

–0.02 0.80 3.97·10–6 5.40 1.91·10–4 7.62·10–1 1.92·10–2 3.02·10–6

–0.22 1.00 2.57·10–7 6.59 9.10·10–6 5.62·10–1 2.19·10–1 1.44·10–7

–0.42 1.20 8.64·10–8 7.06 1.97·10–6 3.62·10–1 4.19·10–1 3.13·10–8

–0.62 1.40 2.62·10–8 7.58 2.67·10–7 1.62·10–1 6.19·10–1 4.24·10–9

–0.74 1.52 5.68·10–9 8.25 1.51·10–8 4.20·10–2 7.39·10–1 2.39·10–10

–0.78 1.56 3.58·10–11 10.45 3.04·10–13 2.79·10–4 7.81·10–1 1.00·10–14

The relative concentrations of sulfur dioxide, hydrogen sulfite, and sulfite are

determined by the pH of the aqueous solution. Figure 4.152 shows that sulfur

dioxide is present predominantly as SO2.H2O and hydrogen sulfite ions at pH 1–

2, typical for acid sulfite cooking. With increasing pH, the proportion of hydrogen

sulfite ion increases significantly, and in the pH range characteristic for magnefite

cooking (3–5), sulfur dioxide is present almost exclusively in the form of hydrogen

sulfite ions. Above this pH level, the sulfite ions start to become the dominating

ionic species in the sulfite cooking liquor.

400 4 Chemical Pulping Processes

0 2 4 6 8 10

0

20

40

60

80

100

SO

2

.H

2

O HSO

3

- SO

3

2-

mol percentage

pH-value

Fig. 4.152 Relative molar percentage of SO2·H2O, hydrogen

sulfite and sulfite ions as a function of the pH at 25 °C. Data

based on information in Tab. 4.54.

Due to the decrease in the acid dissociation constant of hydrated sulfur dioxide,

Ka,1, with increasing temperature, the pH level of the acid sulfite cooking liquor is

shifted to higher values at cooking temperature (Fig. 4.151, Tab. 4.51). This must

be considered in acid calcium sulfite pulping by increasing the proportion of the

free sulfur dioxide concentration to avoid the formation of insoluble calcium sulfite.

The ionic product, [H+].[HSO3

– ], is said to be proportional to the rate of delignification

in the course of sulfite pulping [6]. According to Tab. 4.54, this ionic product

increases exponentially with decreasing pH, which is equal to an increase in

the free SO2 concentration. This result corresponds well with industrial experience.

Increasing the proportion of free SO2 in the cooking acid continuously

reduces the cooking time at given process conditions.

Moreover, the presence of free SO2 largely determines the vapor pressure of the

cooking acid at the prevailing temperature. Figure 4.153 illustrates the development

of the partial pressure of SO2 of a cooking acid with a total SO2 concentration

of 0.78 mol L–1 containing two different amounts of free SO2, 0.39 mol L–1

(50% of total) and 0.23 mol L–1 (30% of total), respectively, at varying temperature

levels.

The inter-relation of partial SO2 pressure, and free and total SO2 is exemplified

in Fig. 4.154 for two temperatures, 100 °C and 140 °C, the latter being typical for

the cooking phase.

4.3 Sulfite Chemical Pulping 401

0 50 100 150

0

2

4

6

0.78 mol/l ΣSO

2

/l; 0.39 mol/l free SO

2

0.78 mol/l ΣSO

2

/l; 0.23 mol/l free SO

2

partial pressure of SO

2

[bar]

Temperature [. C]

Fig. 4.153 Development of partial pressure of

SO2 of a cooking acid comprising two different

proportions of free SO2, 50% and 30% of total

SO2 concentration (0.78 mol L–1), as a function

of temperature. The equilibrium conditions

were simulated by means of ASPEN-PLUS [10]

based on the pioneering studies of Hagfeldt et

al. [11].

0,1 0,3 0,5 0,7

1

4

7

10

pH value

pSO2: 100 °C 140 °C

partial pressure of SO2 [bar]

Free SO2 [mol/l]

1

2

3

4

Total SO2: 0.78 mol/l

pH: 100 °C 140 °C

Fig. 4.154 Development of partial pressure of

SO2 and pH of the three-component system

magnesium oxide-sulfur dioxide-water as a

function of free SO2 concentration for two different

temperatures, 100 °C and 140 °C,

respectively, while keeping the total SO2 concentration

constant at 0.78 mol L–1. The equilibrium

conditions were simulated by means of

ASPEN-PLUS [10]based on the pioneering studies

of Hagfeldt et al. [11].

402 4 Chemical Pulping Processes

The total pressure of sulfite cooking acids containing large quantities of free

SO2 is largely determined by the partial pressures of SO2, water and, in the case of

hardwood pulping, also by considerable amounts of volatile carbonic acids (e.g.,

acetic acid, furfural, etc.) and carbon dioxide. Digester pressures are usually limited

to 8–10 bar, which means that gas must be released through the relief pressure

valve during the entire cooking phase. New cooking digesters are designed to

operate at higher pressures (>12 bar), which is an effective measure to further

reduce cooking time.

4.3.3