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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
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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 characteristics of the solution • Lewis & Randall (1921) • I = ½ S zi2mi • 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 fromg±KCl • Then other gusing 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*106ro1/2(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 Setchenoweqn (Lewis & Randall, 1961) Log gi = KiI, where Ki = 0.02 ~ 0.23 Table 4.5 on p.144.