Acid-Base Titration Notes

Acid-Base Titrations

A titration is a method of quantitative analysis based on a reaction of known stoichiometry.
It involves determining the volume of a solution needed to react exactly with a known amount of another substance (acid or base).

Titration Defined: A process to find the volume of a solution containing an amount of acid (or base) that reacts exactly with a known amount of base (or acid).
Example Reaction: Determining the mass of oxalic acid (H2C2O_4) in an impure sample by titration with a strong base.
- Reaction: H2C2O4(aq) + 2OH^-(aq) \rightarrow C2O4^{2-}(aq) + 2H2O(l)

Procedure:
- Accurately measure the mass of the impure oxalic acid sample.
- Dissolve the sample in water.
- Add small increments of a sodium hydroxide (NaOH) solution of known concentration.
Equivalence Point: The point at which the amount of added NaOH solution is just enough to react with all the oxalic acid present.
- H2C2O4(aq) + 2OH^-(aq) \rightarrow C2O4^{2-}(aq) + 2H2O(l)

Definition: Occurs when acid or base has been titrated with an equivalent amount of the corresponding species.
Strong Acid and Base Titration:
- Results in a neutral solution at a pH of 7.0.
Other Combinations:
- The pH at equivalence is not always 7.
- Strong acid + weak base: pH < 7.
- Strong base + weak acid: pH > 7.
Importance of Titration:
- One of the most important ways of determining the concentration of acid or base in a solution.

Initial State:
- Solution is 0.1 M HCl, so pH = 1.
As NaOH is Added:
- The amount of HCl decreases.
- The remaining HCl is in an ever-increasing volume.
- The pH slowly increases.
Just Before Equivalence Point:
- The solution is still quite acidic (e.g., at 49 mL, pH = 3).
Equivalence Point:
- The midpoint of the vertical section of the titration curve.
- The pH rises very rapidly around this point (e.g., 8 pH units between 49 and 50 mL).

pH at Equivalence Point:
- pH = 7.0 in titration of a strong acid with a strong base.
pH Before Equivalence Point:
- Calculated from the amount of unreacted acid.
Immediately After Equivalence Point:
- Addition of a small amount of base causes a dramatic increase in pH.
- Essentially adding a strong base to water.
After More Base Added:
- The rate of increase decreases.
Reason for Rapid Change at Equivalence Point:
- At the equivalence point, the pH is neutral.
- Adding a relatively concentrated base increases the base concentration by orders of magnitude, causing sharp increases in pH.
- After a few drops, the curve levels out because the ion concentration is only doubling or adding to the existing magnitude instead of changing the order of magnitude.

Initial pH:
- Found from the acid concentration and the acid pK_a.
At the Equivalence Point:
- Acetic acid and NaOH have been consumed.
- The pH is controlled by the acetate ion (conjugate base).
At Half Equivalence Point:
- Half of the acid has been neutralized.
- [CH3COOH] = [CH3COO^-] (CH_3COO^-Na^+ 100% dissociates).
- pH = pK_a.
- pK_a of the acid can be determined.
Slow pH Change (0-90 mL):
- The solution is buffered (buffer region).
Above Equivalence Point:
- pH rises sharply.
- pH > 7 at the equivalence point for a weak acid with a strong base.
- The pH can be calculated using K_b of the conjugate base.
- Ka = \frac{[H3O^+][conjugate \ base]}{[acid]}
Kb = \frac{Kw}{K_a}

Initial pH:
- Comes from the acid concentration and pK_{a1}.
First Rise (around 100 mL):
- The first H has been titrated.
- HC2O4^- controls the pH (conjugate base).
Second Rise:
- When the 2nd H is titrated, the pH rises more sharply.
- C2O4^{2-} controls the pH (conjugate base).
- C2O4^{2-} + H2O \rightarrow HC2O_4^- + OH^-
- K_b = 1.6 \times 10^{-10}
- pH = 8.5 (K{a1} = 5.9 \times 10^{-2}, K{a2} = 5.9 \times 10^{-5}).

If K{a1} >> K{a2}, the most acidic proton is removed from nearly all molecules before the second one is removed.
Prior to the first equivalence point, the solution is a buffer solution, and when the volume of NaOH solution is exactly half that needed to reach the first equivalence point, pH = pK_{a1}.
Between the first and second equivalence points, the solution is a buffer solution, and when the volume added is midway between the first and second equivalence points, pH = pK_{a2}.

Initial pH:
- A function of the base concentration and its pKa (or pKb).
At the Half Equivalence Point:
- Half of the NH3 has been converted to NH4^+Cl^-.
- [NH4^+] = [NH4^+Cl^-].
- pH = pK_a.
As More HCl Is Added:
- The pH falls slowly due to the buffer effect.
At the Equivalence Point:
- pH of the solution is due to the weakly acidic NH_4^+(aq) ions, and the pH is about 5.
As More HCl Is Added:
- NH4^+Cl^- is formed, and the pH falls due to the dissociation of NH4^+.
- Ka = \frac{[H3O^+][conjugate \ base]}{[acid]}

Importance of pH Maintenance:
- Maintaining pH in cellular fluids of living organisms is vital because enzyme activity is influenced by pH.
Protection Against pH Changes:
- The main protection against harmful pH changes in cells is provided by buffers.
pH Range:
- In most cells, the pH is maintained between 6.9 and 7.4 through the action of phosphate (H2PO4^-/HPO4^{2-}) and carbonate (H2CO3/HCO3^-) buffers.
Effect of CO2:
- Just as increasing CO2(g) in the atmosphere causes acidification of seawater, increased CO2(g) concentration in the lungs can affect blood pH.