Solving Equilibrium Problems Using Tableaux Aquatic Chemistry CEE-367

Find the pH of a solution of HAc Find the pH of a solution of HAc? HAc = Acetic or Ethanoic Acid CH3-COOH! Recipe: [H2O]T = 55.4 M [HAc]T = 10-3 M Reactions (Nrxn = 2) H2O = H+ + OH- Kw HAc = H+ + Ac- Ka Species (Nspecies = 5) H2O, H+, OH-, HAc, Ac- Components Ncomp = Nspecies – Nrxn = 3 choose H2O, H+, HAc (since we expect the pH to be acidic!)

Build the tableau: Need to follow always a consistent method ! How to Define the K ! H+ HAc H2O Log K 1 OH- -1 -14.0 Ac- -4.756 55.4 10-3 {H+} = K {H+} {OH-} = Kw {H+}-1{H2O} {Ac-} = K {H+}-1{HAc}

Mass Balance Equations & Equilibrium Mass Balances TOTH20 = [H2O] +[OH-] = 55.4 M TOTHAc = [HAc] + [Ac-] = 10-3 M TOTH = [H+] – [OH-] – [Ac-] = 0 Solve using the TOTH expression Intuition! Acid in water => pH is Acid The [OH-] should be negligible, then [H+] = [Ac-] Use the equilibrium constant Ka & TOTHAc to solve !

Another Example Sodium Acetate: Na-Ac ! Recipe: Add NaAc to water: [H2O]T = 55.4 M [NaAc]T = 10-3 M Reactions (Nrxn = 2) H2O = H+ + OH- HAc = H+ + Ac- Species (Nspecies = 6) H2O, H+, OH-, HAc, Ac-, Na+ Components Ncomp = Nspecies – Nrxn = 4 choose H2O, H+, Na+, Ac- Select Ac- since we expect the pH to be basic

A new tableau with a different constant ! Ac- Na+ Log K 1 OH- -1 -14.0 HAc 4.756 H2O 55.4 NaAc 10-3 {HAc} = K {H+}{Ac-}

Tableau Method Mass Balances TOTH20 = [H2O] +[OH-] = 55.4 M TOTAc = [HAc] + [Ac-] = 10-3 M TOTNa = [Na+] = 10-3 M TOTH = [H+] – [OH-] + [HAc] = 0 Expect a pH basic => [H+] negligible, then [OH-] = [HAc] Use equilibrium constant &TOTAc to solve!

Sodium Bicarbonate in Water Recipe: Add Na bicarbonate to water [H2O]T = 55.4 M [NaHCO3]T = 10-3 M Reactions (Nrxn = 3) H2O = H+ + OH- H2CO3* = H+ + HCO3- HCO3- = H+ + CO32- Species (Nspecies = 7) H2O, H+, OH-, Na+, H2CO3*, HCO3-, CO32- Components Ncomp = Nspecies – Nrxn = 4 choose H2O, H+, Na+, and HCO3- (likely to be predominant)

The new tableau for this recipe HCO3- Na+ Log K 1 OH- -1 -14 H2CO3* 6.3 CO32- -10.3 H2O 55.4 NaHCO3 10-3

Tableau Method => [H2CO3*]  [CO32-] Mass Balances TOTHCO3 = [H2CO3*] + [HCO3-] + [CO32-]= 10-3 M TOTNa = [Na+] = 10-3 M TOTH = [H+] – [OH-] + [H2CO3*] – [CO32-] = 0 Again: Use TOTH to solve for pH => [H2CO3*]  [CO32-]

How to Solve for H+ in TOTH Make approximations in TOT expressions Based on the predominance of species and how large we think they are compared to the others! The more approximations you make the lower the degree of the polynomial expression that you have to solve for becomes. Solve Numerically or Graphically using a pC-pH diagram Numerically: Carry literal expressions until the last step, your numerical calculation. Use trial and error: write [H+] = f([H+]) and iterate until verified starting from a guessed pH Graphically: demonstration in class And Verify Your Assumptions Check that indeed the species that you have neglected in the TOT expressions are negligible compared to the others! If you do not perform these verifications you cannot expect to receive full credit for your solution – even if it is correct!