Lecture 10 Proton Balance, Graphical Solutions & Ionization Fractions for Multiprotic SystemsProton balance equation (mass balance on H+)Graphical solutions for multiprotic systemsPlot species concentration (pC) versus Master Variable (pH)Diprotic [H+]: pH = pH[OH-]: pOH = pKW - pH[H2B] = BT*a0[HB-] = BT*a1[B2-] = BT*a2

Start with System DefinitionSystem: ClosedComponents: HA & H2OSpecies: HA, A-, H2O, OH-, H+Equilibria:H2O = H+ + OH-Kw = [H+][OH-] = 10-14HA = H+ + A-KA = [H+][A-]/[HA] = 10-6Mass Balance: AT = [HA] + [A-] = 10-3 MCharge Balance: [A-] + [OH-] = [H+]

Summary of steps Plot line for [H+]: pH = pHPlot line for [OH-]: pOH = pKW -pHPlot AT: horizontal line at pC = pAT

Plot system point: pH = pKA on pAT line

Plot ATATSystempoint

Lines for the acid speciesAcid species [HA]: Combine mass balance and mass action to get

In log form

At low pH (pH > pKA)

pH dependence of pHAHA

Lines for the acid speciesConjugate base [A-]: Combine mass balance and mass action to get

In log form

At low pH (pH > pKA)

Including dependence of [A-] with pH

Complete systemIntercept ~ 0.3 log below AT

System with 10-3 M Benzoic Acid

System with 10-3 M Benzoic Acid

What is the equilibrium pH for a solution comprised of AT M of the salt of the conjugate base, NaA?System: ClosedComponents: Na+, HA & H2OSpecies: HA, A-, H2O, OH-, H+Equilibria:H2O = H+ + OH-Kw = [H+][OH-] = 10-14HA = H+ + A-KA = [H+][A-]/[HA] = 10-pKaMass Balance: AT = [HA] + [A-]NaT = [Na+] = ATCharge Balance: [A-] + [OH-] = [H+] + [Na+]Proton Balance equation: [HA] + [H+] = [OH-]

Monoprotic Weak Acid - NaAcetate (salt of the conjugate base)

What is the equilibrium pH for a solution comprised of AT M of the salt of the conjugate base, NaA?System: ClosedComponents: Na+, HA & H2OSpecies: HA, A-, H2O, OH-, H+Equilibria:H2O = H+ + OH-Kw = [H+][OH-] = 10-14HA = H+ + A-KA = [H+][A-]/[HA] = 10-pKaMass Balance: AT = [HA] + [A-]NaT = [Na+] = ATCharge Balance: [A-] + [OH-] = [H+] + [Na+]Proton Balance equation: [HA] + [H+] = [OH-]

Monoprotic Weak Acid - NaAcetate (salt of the conjugate base)

Monoprotic Weak Acid - NaCN (salt of the conjugate base)

What is the equilibrium pH for a solution comprised of BT M of a generic acid diprotic acid H2B?System: ClosedComponents: H2B & H2OSpecies: H2B, HB-,B2- H2O, OH-, H+Equilibria:H2O = H+ + OH-Kw = [H+][OH-] = 10-14H2B = H+ + HB-KA1 = [H+][HB-]/[H2B] = 10-pKa1HB- = H+ + B2-KA2 = [H+][B2-]/[HB-] = 10-pKa2Mass Balance: BT = [H2B] + [HB-] +[B2-]Charge Balance ( = PBC): 2[B2-] + [HB-] + [OH-] = [H+]

Diprotic Acid - Carbonate systemSystempointsCT

What is the equilibrium pH for a solution comprised of BT M of the salt of the conjugate base of H2B?System: ClosedComponents: Na+, H2B & H2OSpecies: H2B, HB-,B2- H2O, OH-, H+Equilibria:H2O = H+ + OH-Kw = [H+][OH-] = 10-14H2B = H+ + HB-KA1 = [H+][HB-]/[H2B] = 10-pKa1HB- = H+ + B2-KA2 = [H+][B2-]/[HB-] = 10-pKa2Mass Balance: BT = [H2B] + [HB-] +[B2-]= 10-3 MNaT = [Na+] = BTCharge Balance: 2[B2-] + [HB-] + [OH-] = [H+] + [Na+]Proton Balance: [H2B] + [H+] = [B2-] + [OH-]

Diprotic Acid - NaHCO3 (salt of the conjugate base of H2B)

What is the equilibrium pH for a solution comprised of BT M of the salt of the conjugate base of HB-?System: ClosedComponents: Na+, HB- & H2OSpecies: H2B, HB-,B2- H2O, OH-, H+Equilibria:H2O = H+ + OH-Kw = [H+][OH-] = 10-14H2B = H+ + HB-KA1 = [H+][HB-]/[H2B] = 10-pKa1HB- = H+ + B2-KA2 = [H+][B2-]/[HB-] = 10-pKa2Mass Balance: BT = [H2B] + [HB-] +[B2-]= 10-3 MNaT = [Na+] = 2BTCharge Balance: 2[B2-] + [HB-] + [OH-] = [H+] + [Na+]Proton Balance: 2[H2B] + [HB-] + [H+] = [OH-]

Diprotic Acid - NaHCO3 (salt of the conjugate base of HB-)