Title: Lesson 7: K a /pK a and K b /pK b Learning Objectives: – Understand the concepts of K a and K b – Understand the concepts of pK a and pK b

Main Menu Refresh  Which values are correct for a mol dm –3 solution of NaOH(aq) at 298 K? (K w = 1.0×10 –14 mol 2 dm –6 at 298 K) A. [H + ] = 1.0×10 –12 mol dm –3 and pH = B. [OH – ] = 1.0×10 –12 mol dm –3 and pH = C. [H + ] = 1.0×10 –12 mol dm –3 and pOH = D. [OH – ] = 1.0×10 –12 mol dm –3 and pOH = 12.00

Main Menu Dissociation constants express the strength of weak acids and bases  Weak acids and bases do not dissociate fully.  This means that we cannot deduce the concentrations of ions in their solutions from the initial concentrations, as ion concentration will depend on the extent of dissociation that has occurred.  The dissociation reactions of weak acids and weak bases can be represented as equilibrium expressions, each with their own equilibrium constant.  E.g. Generic weak acid HA dissociating in water:  Therefore: Given that concentration of water is considered constant, we can combine with K c  K a is known as the acid dissociation constant. It will have a fixed value for a particular acid at a specified temperature. K a tells us the equilibrium position  direct measure of strength of the acid. E.g. Higher K a  More dissociation  Stronger acid

Main Menu Base dissociation constant  Dissociation/Ionisation of generic weak base B:  Therefore: Given that concentration of water is considered constant, we can combine with K c  K b is known as the base dissociation constant. It will have a fixed value for a particular base at a specified temperature. K b tells us the equilibrium position  direct measure of strength of the base. E.g. Higher K b  More dissociation  Stronger base

Main Menu

Solutions

Main Menu Calculations involving K a and K b These values allow us to:  Compare the strength of weak acids and bases  Calculate ion concentrations at equilibrium  Calculate pH and pOH These calculations are similar to the ‘ICE’ calculations you did in chapter 7:  Given concentrations are the INITIAL concentrations (before dissociation)  pH or pOH refers to the concentration of H + ions (or OH - ions) at EQUILIBRIUM  Concentration values substituted into the expressions for K a and K b must be EQUILBIUM values  If dissociation is very small (very low value for Ka or Kb), use these approximations:

Main Menu 1 Calculation of K a and K b from pH and initial concentration

Main Menu

2 Calculation of [H + ] and pH, [OH - ] and pOH from K a and K b

Main Menu

Solutions

Main Menu

Weak Acids: K a and pK a  Weak acids dissociate to form an equilibrium  HA(aq)  H + (aq) + A - (aq)  This has the equilibrium constant (aka acid dissociation constant), K a  The values for K a are often very small (negative exponents), so we use ‘pK a ’ to make them easier to handle: pK a = -log 10 (K a ) K a = 10 -pKa

Main Menu K a and pK a in action  In order of decreasing acid strength:  Smaller K a  weaker acid  Smaller pK a  stronger acid AcidKaKa pK a Hydronium ion, H 3 O Oxalic acid, HO 2 CCO 2 H5.9x Hydrofluoric, HF7.2x Methanoic, CHOOH1.77x Ethanoic, CH 3 COOH1.76x Phenol, C 6 H 5 OH1.6x

Main Menu Weak Bases: K b and pK b  Weak bases dissociate to form an equilibrium  BOH(aq)  B + (aq) + OH - (aq)  This has the equilibrium constant (aka base dissociation constant), K b  The values for K b are often very small (negative exponents), so we use ‘pK b ’ to make them easier to handle: pK b = -log 10 (K b ) K b = 10 -pKb

Main Menu K b and pK b in action  In order of decreasing base strength:  Smaller K b  weaker base  Smaller pK b  stronger base Things about pK a and pK b to consider:  They are positive with no units  A change of one unit of pK a or pK b represents a 10 fold change in the value of K a or K b (scale is logarithmic base 10)  pK a and pK b must be quoted at specified temperatures (K a and K b are temperature dependent) BaseKbKb pK b Diethylamine1.3x Ethylamine5.6x Methylamine4.4x Ammonia1.8x Data on pK a and pK b is found in Table 21 in the data booklet

Main Menu Relationship between K a and K b, pK a and pK b for a conjugate pair  Consider the K a and K b expressions for the conjugate acid-base pair HA and A -  This relationship is true for any conjugate acid-base pair in aqueous solution.  From the value of K a we can calculate K b for its conjugate base.  Stronger acids have weaker conjugate bases and vice versa.

Main Menu Inverse relationship between the strengths of acids and their conjugate bases

Main Menu

Solutions

Main Menu

Measuring K a /pK a and K b /pK b  pK a and pK b can be determined experimentally  At the point of half neutralisation:  pH = pK a  pOH = pK b  This is a convenient artefact of the mathematics  Follow the instructions herethe instructions here

Main Menu Key Points  For a weak acid:  AND pK a = -log 10 (K a )  For a weak base:  AND pK b = -log 10 (K b )  At the point of half-neutralisation:  pK a = pH AND pK b = pOH