Exact Treatment of AcidBase Equilibria

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Exact Treatment of Acid-Base Equilibria
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Exact Treatment of Acid-Base Equilibria
Previously Assumed H3O, OH- resulted
entirely from ionization of acid or base
Ignored the autoionization of water
For very dilute solutions and/or very weak acids
or bases cannot approximate initial H3O
initial OH- 0
Exact Treatment of a weak acid (HA) and its salt
(NaA) 5 species HA, A-, Na, H3O, and OH-
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Exact Treatment of Acid-Base Equilibria
Conservation of A-material ca
cb HA A-
Balance of charge Na H3O A-
OH-
Step 1 Solve for A- using the balance of
charge equation
Step 2 Substitute A- in to conservation
equation Solve for HA
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Exact Treatment of Acid-Base Equilibria
Step 3 Solve for Ka
Step 4 Use Kw to eliminate OH-
OH- Kw/H3O
Step 5 Fun with Algebra!!!
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Exact Treatment of Acid-Base Equilibria
Step 5 Fun with Algebra!!!
Multiply both sides by H3O
Collect terms of H3O
Solve cube root with calculator
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Exact Treatment of Acid-Base EquilibriaSimplify
with Approximations
Approximation 1 Assume for an acidic buffer
H3O gtgt OH-
Approximation 2 Assume for a basic buffer
H3O ltlt OH-
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Exact Treatment of Amphoteric Equilibria
What happens when NaHCO3 is dissolved in water?
What is the pH?
HCO3-(aq) H2O(l) H3O(aq)
CO32-(aq)
HCO3-(aq) H2O(l) H2CO3(aq)
OH-(aq)
Six species Na, H2CO3, HCO3-, CO32-, OH-,
and H3O
Conservation of carbonate material HCO3-0
HCO3- CO32- H2CO3
Balance of charge Na H3O
HCO3- 2 CO32- OH-
Na HCO3-0
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Exact Treatment of Amphoteric EquilibriaApproxim
ation
Na HCO3-0
Na H3O HCO3- 2 CO32- OH-
1
2
HCO3-0 HCO3- CO32- H2CO3
Subtract 2 from 1
HCO3-0 H3O HCO3- 2 CO32- OH-
- ( )
HCO3-0 HCO3- CO32- H2CO3
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Exact Treatment of Amphoteric EquilibriaApproxim
ation
Multiply both sides by Ka1H3O
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Exact Treatment of Amphoteric EquilibriaApproxim
ation
Collect the terms of H3O2
Both Ka2 and Kb2 are very small Assume
HCO3- HCO3-0
In many cases HCO3-0 gtgt
Ka1 Ka2HCO3-0 gtgt Kw
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Exact Treatment of Amphoteric EquilibriaApproxim
ation
What is the pH of a solution that is 0.100 M in
NaHCO3? Ka1 4.3 x 10-7 Ka2 4.8 x 10-11
Check assumptions Is HCO3-0 gtgt Ka1? Is
Ka2HCO3-0 gtgt Kw?