1. Ch. 5. ACTIVITY COEFFICENTS OF DISSOLVED SPECIES 5-1. Introduction 5-1. Introduction What is activity of a dissolved species? What is activity of a dissolved species? Effective concentration Effective concentration Equivalent to the concentration acting in effect Equivalent to the concentration acting in effect Why do we need activity (or have activity)? Why do we need activity (or have activity)? Interactions among the dissolved matter Interactions among the dissolved matter Interference among the dissolved matter Interference among the dissolved matter  causes partial influences on the solution properties  causes partial influences on the solution properties Where can we observe the activity effect? Where can we observe the activity effect? Boiling point increase, freezing point decrease Boiling point increase, freezing point decrease Conductivity Conductivity Others Others

2. 5-2. Activity Coefficient & Ionic Strength 5-2. Activity Coefficient & Ionic Strength Activity coefficient: A function of the ionic strength of the solution Activity coefficient: A function of the ionic strength of the solution a i =  i m i a i =  i m i Ionic strength: A measure of the ionic characteristics of the solution Ionic strength: A measure of the ionic characteristics of the solution Lewis & Randall (1921) Lewis & Randall (1921) I = ½  z i 2 m i I = ½  z i 2 m i Examples Examples Mono-monovalent salts: KCl  I=m KCl Mono-monovalent salts: KCl  I=m KCl Mono-divalent salts: K 2 SO 4  I=3m K2SO4 Mono-divalent salts: K 2 SO 4  I=3m K2SO4 Di-divalent salts: CaSO 4  I = 4m CaSO4 Di-divalent salts: CaSO 4  I = 4m CaSO4

3. Approximate estimation of I from TDS Approximate estimation of I from TDS Eqn (4.4) to (4.6) on p.124 Eqn (4.4) to (4.6) on p.124 Approximate estimation of I from SpC Approximate estimation of I from SpC Eqn (4.7) to (4.9) on p.124 Eqn (4.7) to (4.9) on p.124 Otherwise? Otherwise? Should be calculated from the chemical composition Should be calculated from the chemical composition

4. 5-3. Mean Ion-Activity Coefficients 5-3. Mean Ion-Activity Coefficients The coefficients measured for a solutions which is due to the net effect of both cations and anions The coefficients measured for a solutions which is due to the net effect of both cations and anions  ± =[  n+  n- ] 1/n, n = (n+ + n-)  ± =[  n+  n- ] 1/n, n = (n+ + n-) Fig. 4.1 on p.125 Fig. 4.1 on p.125 McInnes convention (McInnes 1919) McInnes convention (McInnes 1919)  ±KCl =  K =  Cl  ±KCl =  K =  Cl Obtain  K and  Cl from  ±KCl Obtain  K and  Cl from  ±KCl Then other  using the above relation Then other  using the above relation Example 4.1 on p.127 Example 4.1 on p.127

5. 5-4. Theoretical Calculation of the Activity Coefficients 5-4. Theoretical Calculation of the Activity Coefficients Debye-Hückel limiting law (DHLL) Debye-Hückel limiting law (DHLL) When I <0.001: eqn (4.30) on p.129 When I <0.001: eqn (4.30) on p.129 Extended Debye-Hückel equation (EDHE) Extended Debye-Hückel equation (EDHE) When I<0.1: eqn (4.28) on p.128 When I<0.1: eqn (4.28) on p.128 A=1.824928*10 6  o 1/2 (  T) -3/2, 0.5092 (at 25C) A=1.824928*10 6  o 1/2 (  T) -3/2, 0.5092 (at 25C) B=50.3(  T) -1/2, 0.3283 (at 25C) B=50.3(  T) -1/2, 0.3283 (at 25C) Table 4.1 for effective ionic radii on p.130 Table 4.1 for effective ionic radii on p.130 Fig. 4.3 on p.132 Fig. 4.3 on p.132 Other equations for higher I Other equations for higher I Davies et al.; eqn (4.31) on p.132 Davies et al.; eqn (4.31) on p.132 Trusdell & Jones (1974) Trusdell & Jones (1974) Bronsted-Guggenheim-Scatchard specific ion interaction theory (SIT) equaton: eqn (4.32) p.133 Bronsted-Guggenheim-Scatchard specific ion interaction theory (SIT) equaton: eqn (4.32) p.133 Fig. 4.4. p.135. Fig. 4.4. p.135. Pitzer model; eqn (4.49) p.138 Pitzer model; eqn (4.49) p.138

6. 5-5. Limitation of Debye-Huckel Theory 5-5. Limitation of Debye-Huckel Theory All interactions are not purely ionic All interactions are not purely ionic Ions are not point charges Ions are not point charges Ion size varies with I Ion size varies with I Ions do interact w/ other ions and even with the same species Ions do interact w/ other ions and even with the same species

7. 5-6. Activity Coefficients of Molecular Species 5-6. Activity Coefficients of Molecular Species In most cases, approximately  =1 In most cases, approximately  =1 Generally follow Setchenow eqn (Lewis & Randall, 1961) Generally follow Setchenow eqn (Lewis & Randall, 1961) Log  i = K i I, where K i = 0.02 ~ 0.23 Log  i = K i I, where K i = 0.02 ~ 0.23 Table 4.5 on p.144. Table 4.5 on p.144.