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:

SO 2 H 2 O _ H 2 SO 3 SO 2 _ H 2 O _ __ 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 __ SO 2 __ H 2 SO 3 _ _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 SO 2_ 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 _ SO 2_ 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:

SO 2_ tot _ Ctot _ SO 2 _ H 2 O _ HSO _3 SO 2_ 3 _163_

The concentrations of [SO2.H2O], [HSO3

– ]and [SO3

2–]can be calculated accordingly:

SO 2 _ H 2 O _ _ Ctot _ HSO _3 SO 2_ _ 3_ _164_

HSO _3 _ Ctot __ SO 2 _ H 2 OSO 2_ _ 3_ _165_

SO 2_ 3 _ Ctot _ SO 2 _ H 2 O _ HSO _3 _ _ _166_

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

the equilibrium equations:

Ka _1 _ Ctot _ HSO _3 SO 2_ 3 _ _ _ __ H _ _ HSO _3 _167_

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

HSO _3 _

Ka _1 _ Ctot _ SO 2_ _ 3_ _ Ka _1 _ H _ _168_

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

Ka _2 _ Ctot __ SO 2 _ H 2 O SO 2_ _ _ 3____ H _ SO 2_ 3 _169_

SO 2_ 3_

Ka _2 __ Ctot __ SO 2 _ H 2 O _

_ 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

Titrator base, NaOH: 25.C 140.C

Titrator base, Mg(OH)

25.C

pH-value

Free SO

, 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).

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