Most chemical systems are governed by equilibria Chemical Equilibrium such that if: aA + bB cC + dD, then & Activity c d (ac) (ad ) K = a b where ax = γx[X], γx is the activity coefficient (aa) (ab)
In dilute solutions, γx →1, if we assume γx =1, [C]c[D]d K = [A]a[B]b
Equilibrium constants may be written for dissociations, associations, reactions, or distributions. Equilibrium Constant
aA + bB cC + dD
[C]c[D]d K = [A]a[B]b
• 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 ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) constant allows us to make some predictions about the system.
Important items to regarding K expressions Equilibrium and Thermodynamics 1. All solute concentrations should be in mol/L (M). • Gibbs free energy: 2. All gas concentrations should be in atmospheres. 3. By convention, all K’s are calculated relative to 1 M G o -RT ln K solutions or 1 atm gas, so the resulting constants are = o dimensionless. K = e−∆G / RT 4. Concentrations of pure solids, pure liquids and solvents are omitted from the equilibrium constant expression. • If K >1 ‰ Go<0 ‰ Spontaneous Equilibrium constant expressions are • If K<1 ‰ Go ‰ NOT Spontaneous thermodynamic relations.
1 Using equilibria to characterize Reaction Quotient (Q) systems The equilibrium constant expression with non- equilibrium concentrations plugged in. Solubility: solubility product (Ksp) Complexation: formation constants (Kn), • If Q>K, the reaction must proceed to the left cumulative formation constants (n) • If Q
Solubility Solubility - Separation by
The solubility product (Ksp) describes the concentrations of precipitation species present when ions are in equilibrium with undissolved salt. It is possible to quantitatively separate two or more species based on their solubility. 2+ 2- Ability to do so is related to the magnitudes of the Ksp for each Example: CaCO3 = Ca + CO3 ion. 2+ 2- 2+ 2- -9 K= [Ca ][CO3 ]/[CaCO3]= [Ca ][CO3 ] = Ksp = 6.0 x 10 Example: What is the concentration of calcium in a saturated solution Is it possible to precipitate 99% of 0.010M Ce3+ by adding 2- 2+ of calcium carbonate? oxalate (C2O4 ) without precipitate 0.010M Ca -8 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 Kw = [H 3O ][OH ] = [H ][OH ] =10
2 Acid and Base Strength Solubility – Common Ion Effects Based on percent dissociation in solution A salt will be less soluble if one of its constituent ions is already present in the solution. • Strong acids/bases dissociate essentially completely in water
• Weak acids/bases only partially dissociate, results in Example: What is the solubility of ferric hydroxide equilibrium concentrations of both the acid and its -38 conjugate base in pH 8.0 buffered aqueous solution (Ksp=4x10 ) Ka - + Ka - HA +H2O A +H3O H A A + H +
Kb + - B + H2O BH +OH
Weak Acid/Base Equilibria Diprotic acids/Dibasic bases Polyprotic acids/Polybasic bases • Weak Acid: acid dissociation constant (Ka) + − Ka [H ][HA ] A- +H O+ − + − + HA +H2O 3 [A ][H O ] [A ][H ] + - Ka1 = 3 H A H + HA Ka = = 2 [H 2 A] Ka - + H A A + H [HA] [HA] - + 2- + 2− HA H + A [H ][A ] Ka = • Weak Base, hydrolysis reaction: base hydrolysis 2 [HA− ] constant (Kb) Ka1, Ka2 … [BH + ][OH − ] Kb + - + - -3 B + H2O BH +OH Kb = H PO H + H PO Ka1 = 7.11 x 10 [B] 3 4 2 4 - + 2- -8 H2PO4 H + HPO4 Ka2 = 6.32 x 10 • Relationship between Ka and Kb for conjugate HPO 2- H+ + PO 3- Ka3 = 7.1 x 10-13 acid/base pairs: 4 4
+ − + − −14 Kw = Ka × Kb = [H 3O ][OH ] = [H ][OH ] =10
Complex Formation Activity Formation of coordinate bonds between Lewis Acids/Bases
+ K1 + If aA + bB cC + dD, then Ag (aq ) + NH 3 (aq) Ag ( NH 3 ) (aq )
+ K2 + Ag ( NH 3 ) (aq ) + NH 3 (aq) Ag ( NH 3 ) 2 (aq ) c d c d (ac ) (ad ) (γ c[C]) (γ d [D]) + + K = = [Ag(NH 3 ) ] [Ag(NH 3 )2 ] a b a b (aa ) (ab ) (γ a[A]) (γ b[B]) K1 = + K 2 = + [Ag ][NH 3 ] [Ag(NH 3 ) ][NH 3 ] where ax is the activity of x Formation constants (Kf) are the equilibrium constants for complex ion a = γ [X], γ is the activity coefficient formation. The overall, or cumulative, formation constants are x x x denoted i + Kf + If γ x →1, ax → [X ] Ag (aq) + 2NH3 (aq) Ag(NH3 )2 (aq) + c d c d c d (ac ) (ad ) (γ c[C]) (γ d [D]) [C] [D] [Ag(NH 3 )2 ] K = = = K f = + 2 = β 2 = K1 ⋅ K 2 a b a b a b (aa ) (ab ) (γ a[A]) (γ b[B]) [A] [B] [Ag ][NH 3 ]
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 = (c1 z1 +c2 z2 +...) = ƒci zi i solution to interact with one another. 2 2 where c is concentration and z is charge of each ion 0.51z 2 µ log r = − α µ 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 0.51z 2 µ • Increased ionic conc. ‰ log r = − α µ • 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 : 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.
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