Equilibrium Constant Chapters 6 and 8 aA + bB cC + dD Chemical Equilibrium DC ][][ dc & Activity K = [][ BA ]ba
• If K is very large, that the equilibrium lies far to the right (or towards products). If K is small, the reaction lies towards reactants. • Knowledge of reaction stoichiometry and the equilibrium constant allows us to make some predictions about the system.
EquilibriumEquilibrium constants constants may may be be written written for for dissociations, dissociations, associations, associations, reactions, reactions, oror distributions. distributions. Important items to regarding K expressions 1. All solute concentrations should be in mol/L (M). 2. All gas concentrations should be in atmospheres. 3. By convention, all K’s are calculated relative to 1 M solutions or 1 atm gas, so the resulting constants are dimensionless. 4. Concentrations of pure solids, pure liquids and solvents are omitted from the equilibrium constant expression.
©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) Equilibrium constant expressions are thermodynamic relations.
Equilibrium and Thermodynamics Reaction Quotient (Q)
• Gibbs free energy: The equilibrium constant expression with non- equilibrium concentrations plugged in. G o = -RT ln K
o • If Q>K, the reaction must proceed to the left ∆− / RTG = eK • If Q
1 Using equilibria to characterize Solubility
systems The solubility product (Ksp) describes the concentrations of species present when ions are in equilibrium with undissolved salt.
Solubility: solubility product (Ksp) 2+ 2- Example: CaCO3 = Ca + CO3 2+ 2- 2+ 2- -9 Complexation: formation constants (Kn), K= [Ca ][CO3 ]/[CaCO3]= [Ca ][CO3 ] = Ksp = 6.0 x 10 cumulative formation constants (n) (Ch.12) Acids and Bases: acid dissociation constant What is the concentration of calcium in a saturated solution of calcium carbonate? (Ka), base hydrolysis constant (Kb) This presence of carbonate results in a common ion effect. What should happen?
Solubility - Separation by Solubility – Common Ion Effects precipitation It is possible to quantitatively separate two or more species A salt will be less soluble is one of its constituent based on their solubility. ions is already present in the solution. Ability to do so is related to the magnitudes of the Ksp for each ion.
Example: Is it possible to precipitate 99% of 0.010M Ce3+ by adding 2- 2+ Example: What is the solubility of ferric hydroxide oxalate (C2O4 ) without precipitate 0.010M Ca -8 in pH 8.0 buffered aqueous solution CaC2O4 Ksp = 1.3 x 10 -29 Ce2(C2O4)3 Ksp = 3.0 x 10
Acids and Bases pH - H O OH +H + • Definitions: Lewis – Electrons (acid: electron pair acceptor); 2 BrØnsted-Lowry (acid: proton donor) P-function: pX = - log10[X] • Conjugate Acid-Base Pairs: related by the gain or loss of one proton (ex. Acetic acid & acetate ion). pH = -log [H+] • Neutralization Reactions: reactions of acid and base to form salts and water pH > 7 is basic, pH<7 is acidic • Solvent Autoprotolysis or self-ionization: water is the most common, in which it acts both an acid and a base: pOH=-log[OH-] 2H O H O ++O H - 2 3 pH + pOH = pKw = 14.00 at 25oC - OH +H + H 2O + - o Autoprotolysis constant (equilibrium constants) Ex. Concentration of H and OH in pure water at 25 C -7 + − + − −14 ANS: 1.0x10 M = 3 = OHHOHOHKw =10]][[]][[
2 Acid and Base Strength Weak Acid/Base Equilibria
Based on percent dissociation in solution • Weak Acid: acid dissociation constant (Ka) Ka - + − + − + HA +H2O A +H3O [A ][H O ] [A ][H ] Ka = 3 = Ka - • Strong acids/bases dissociate essentially completely HA A + H + HA][ HA][ in water (Table 6-2, p.108) • Weak Base, hydrolysis reaction: base hydrolysis constant (Kb) [BH + ][OH − ] Kb + - • Weak acids/bases only partially dissociate, results in B + H2O BH +OH Kb = equilibrium concentrations of both the acid and its B][ conjugate base • Relationship between Ka and Kb for conjugate Ka - + Ka - + HA +H2O A +H3O HA A + H acid/base pairs:
+ − + − −14 Kb + - = × = 3 = OHHOHOHKbKaKw =10]][[]][[ B + H2O BH +OH
Diprotic acids/Dibasic bases Complex Formation Polyprotic acids/Polybasic bases Formation of coordinate bonds between Lewis Acids/Bases + − K1 [H ][HA ] + + aqAg )( + NH 3 (aq) 3 a qNHAg )()( + - Ka1 = H A H + HA + K2 + 2 2 AH ][ 3 aqNHAg )()( + NH 3 (aq) 23 aqNHAg )()( - + 2- + 2− HA H + A [H ][A ] + Ka + 2 = − Ag NH 3 ])([ NHAg ])([ HA ][ K = K = 23 1 + NHAg ]][[ 2 + NHNHAg ]][)([ Ka1, Ka2 … 3 3 3 + - -3 H3PO4 H + H2PO4 Ka1 = 7.11 x 10 Formation constants (Kf) are the equilibrium constants for complex ion formation. The overall, or cumulative, formation constants are H PO - H+ + HPO 2- Ka2 = 6.32 x 10-8 2 4 4 denoted i 2- + 3- -13 + Kf + HPO4 H + PO4 Ka3 = 7.1 x 10 aqAg + NH3 (aq)2)( 23 aqNHAg )()( +
([ NHAg 23 ]) K f = + 2 β 2 ⋅== KK 21 NHAg 3 ]][[
Equilibrium Constant (Activity) Equilibrium Constant (Activity) If aA + bB cC + dD, then Most chemical systems are governed by equilibria such that if: c d c d aa dc )()( γγ dc [D][C] )()( aA + bB cC + dD, then K = ba = ba aa ba )()( γγ ba [B][A] )()( c d )( (aa dc ) where ax theis ofactivity x K = ba where = [X], γγ xxax theis activity tcoefficien aa ba )()( = [X], γγ xxax theis activity tcoefficien dc dc aa dc )()( c )( γγ d[D][C] )( ,1 assume weif ,1 solutions, diluteIn diluteIn solutions, γx → ,1 weif assume γx = ,1 K = a b = ba aa ba )()( γγ ba [B][A] )()( DC ][][ dc K = If γ ,1 →→ Xaxx ][ BA ][][ ba
3 Activity Coefficient Ionic Strength • Related to the size of the hydrated species • Calculate using the extended Debye-Hückel equation, 1 2 2 1 2 which relates activity coefficients to the ability of ions in µ ( 1 zc 1 zc 22 ...) =++= ƒc zii i solution to interact with one another. 2 2 where c is concentration and z is charge of each ion 51.0 z 2 µ log r −= µα Ex. What is the ionic strength of a 0.010 M Na2SO4? 1+ ½*{(0.020*1)+(0.010*(-2)2)}=0.030 M 305 If add 0.020 M KBr? z = charge of the ion ½*{(0.020*1) + (0.020*1) + (0.020*1) + (0.010*4)}=0.050 M = effective diameter "hydrated" of the ion in nanometers = ionic strength of the solution
Ionic Strength and Ionic Atmospheres Hydrated Radius
• Ions with small ionic radii and large charge tend to more strongly bind to solvent molecules (Ion-dipole interactions).
• The result of this binding is a larger hydrated radius, causing diminished interaction The greater the ionic strength of a solution, the higher the charge in the with other ions. ionic atmosphere. Each ion-plus-atmosphere contains less net charge and there is less attraction between any particular cation and anion.
Ionic Strength, Ion Charge, and Ion Size effect pH Revisited 51.0 z 2 µ • Increased ionic conc. ‰ log r −= µα • Concentration is replaced with activity decreased activity coefficient 1+ 305 + • Increased ion charge (±) ‰ pH = -log aH+ = -log [H ]γH+ increased departure of activity coefficient from unity (Multiply charged ions are generally more likely to interact with other ions than Examples (P.147): singly charged.) • Calculate the pH of pure water using activity coefficients • Smaller hydrated radius ‰ correctly. increased importance of activity effects • Calculate the pH of water containing 0.10 M KCl at 25oC.
4 Example
• Calculate the solubility of Ag2CrO4 2- (expressed as moles of CrO4 per liter) in
(a) 0.050 M KClO4 (b) 0.005 0 M AgNO3
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