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

2. 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!)

3. 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}

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 !
Ac-
Na+
Log K 1
OH- -1
-14.0
HAc
4.756
H2O
55.4
NaAc
10-3
{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
HCO3-
Na+
Log K 1
OH- -1
-14
H2CO3*
6.3
CO32-
-10.3
H2O
55.4
NaHCO3
10-3

10. 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-]

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!