Ch. 5. ACTIVITY COEFFICENTS OF DISSOLVED SPECIES

5-1. Introduction What is activity of a dissolved species?

Effective concentration Equivalent to the concentration acting in effect

Why do we need activity (or have activity)? Interactions among the dissolved matter Interference among the dissolved matter causes partial influences on the solution properties

Where can we observe the activity effect? Boiling point increase, freezing point decrease Conductivity Others

5-2. Activity Coefficient & Ionic Strength

Activity coefficient: A function of the ionic strength of the solution ai = gimi

Ionic strength: A measure of the ionic characteris-tics of the solution Lewis & Randall (1921) I = ½ S zi

2mi

Examples Mono-monovalent salts: KCl I=mKCl

Mono-divalent salts: K2SO4 I=3mK2SO4

Di-divalent salts: CaSO4 I = 4mCaSO4

Approximate estimation of I from TDS Eqn (4.4) to (4.6) on p.124

Approximate estimation of I from SpC Eqn (4.7) to (4.9) on p.124

Otherwise? Should be calculated from the chemical composition

5-3. Mean Ion-Activity Coefficients

The coefficients measured for a solutions which is due to the net effect of both cations and anions g± =[gn+ gn-]1/n , n = (n+ + n-)

Fig. 4.1 on p.125 McInnes convention (McInnes 1919)

g±KCl = gK = gCl

Obtain gK and gCl from g±KCl

Then other g using the above relation

Example 4.1 on p.127

5-4. Theoretical Calculation of the Activity Coefficients

Debye-Hückel limiting law (DHLL) When I <0.001: eqn (4.30) on p.129

Extended Debye-Hückel equation (EDHE) When I<0.1: eqn (4.28) on p.128 A=1.824928*106ro

1/2(eT)-3/2, 0.5092 (at 25C) B=50.3(eT)-1/2, 0.3283 (at 25C) Table 4.1 for effective ionic radii on p.130 Fig. 4.3 on p.132

Other equations for higher I Davies et al.; eqn (4.31) on p.132 Trusdell & Jones (1974) Bronsted-Guggenheim-Scatchard specific ion interaction theory (SIT)

equaton: eqn (4.32) p.133 Fig. 4.4. p.135. Pitzer model; eqn (4.49) p.138

5-5. Limitation of Debye-Huckel Theory

All interactions are not purely ionic Ions are not point charges Ion size varies with I Ions do interact w/ other ions and even with the

same species

5-6. Activity Coefficients of Molecular Species

In most cases, approximately g=1 Generally follow Setchenow eqn (Lewis & Ran-

dall, 1961) Log gi = KiI, where Ki = 0.02 ~ 0.23 Table 4.5 on p.144.