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Solving Equilibrium Problems Using Tableaux

Solving Equilibrium Problems Using Tableaux. Aquatic Chemistry CEE-367. Find the pH of a solution of HAc? HAc = Acetic or Ethanoic Acid CH 3 -COOH!. Recipe: [H 2 O] T = 55.4 M [HAc] T = 10 -3 M Reactions ( N rxn = 2) H 2 O = H + + OH - K w HAc = H + + Ac - K a

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Solving Equilibrium Problems Using Tableaux

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  1. Solving Equilibrium Problems Using Tableaux Aquatic Chemistry CEE-367

  2. 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!)

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

  4. 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 !

  5. 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

  6. A new tableau with a different constant ! {HAc} = K {H+}{Ac-}

  7. 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!

  8. 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)

  9. The new tableau for this recipe

  10. Tableau Method • 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 • TOTH = [H+] – [OH-] + [H2CO3*] – [CO32-] = 0 => [H2CO3*]  [CO32-]

  11. 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!

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