Acids and Bases

Titration Curves

Titration curves are graphical representations of the pH of a solution during a titration. They provide valuable information about the strength of the acid and base involved and the equivalence point of the reaction.

I. Strong Acid - Strong Base Titrations

• Characteristics: These titrations exhibit a rapid pH change near the equivalence point.

• Equivalence Point: The equivalence point in a strong acid-strong base titration is at pH = 7.

• Curve Shape: The curve starts at a low pH (highly acidic), gradually increases as base is added, shows a sharp jump around pH 7, and then levels off at a high pH (highly basic).

• Example: Titration of HCl with NaOH.

  $$ HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l) $$

II. Weak Acid - Strong Base Titrations

• Characteristics: The initial pH is higher than in strong acid titrations, and the pH change near the equivalence point is less drastic. A buffer region exists before the equivalence point.

• Equivalence Point: The equivalence point is at pH > 7 due to the formation of the conjugate base of the weak acid.

• Curve Shape: The curve starts at a higher pH than strong acid titrations, shows a gradual increase, has a buffering region, a smaller pH jump at the equivalence point, and then levels off at a high pH.

• Half-Equivalence Point: Half-Equivalence Point

• Example: Titration of acetic acid ( $ CH_3COOH $ ) with NaOH.

  $$ CH_3COOH(aq) + NaOH(aq) \rightarrow CH_3COONa(aq) + H_2O(l) $$

III. Weak Base - Strong Acid Titrations

• Characteristics: Similar to weak acid-strong base titrations, but the curve is inverted.

• Equivalence Point: The equivalence point is at pH < 7 due to the formation of the conjugate acid of the weak base.

• Curve Shape: The curve starts at a high pH (basic), gradually decreases as acid is added, has a buffering region, a smaller pH jump at the equivalence point, and then levels off at a low pH (acidic).

• Example: Titration of ammonia ( $ NH_3 $ ) with HCl.

  $$ NH_3(aq) + HCl(aq) \rightarrow NH_4Cl(aq) $$

IV. Polyprotic Acid Titrations

• Characteristics: Acids with multiple ionizable protons ( $ H^+ $ ) exhibit multiple equivalence points, one for each proton.

• Curve Shape: The titration curve will have multiple buffer regions and equivalence points. The number of equivalence points corresponds to the number of acidic protons.

• Example: Titration of sulfuric acid ( $ H_2SO_4 $ ) with NaOH.

  $$ H_2SO_4(aq) + NaOH(aq) \rightarrow NaHSO_4(aq) + H_2O(l) $$ $$ NaHSO_4(aq) + NaOH(aq) \rightarrow Na_2SO_4(aq) + H_2O(l) $$

V. Indicators

• Acid-Base Indicators are weak acids or bases that change color depending on the pH of the solution.
• The appropriate indicator should be chosen such that its color change occurs within the rapid pH change region near the equivalence point.
• The pH range where the indicator changes color is called the transition interval.

VI. Determining the Equivalence Point

• Graphical Method: The equivalence point is located at the steepest point on the titration curve. For polyprotic acids, it’s at the midpoint of each steep section.
• First Derivative Plot: The equivalence point corresponds to the maximum of the first derivative of the titration curve.
• Second Derivative Plot: The equivalence point corresponds to the point where the second derivative crosses zero.

VII. Calculations

• Stoichiometry: At the equivalence point, the moles of acid and base are stoichiometrically equivalent.
• Weak Acid/Base Equilibria: Use ICE Tables and $ K_a $ or $ K_b $ values to calculate the pH at various points along the titration curve, especially in the buffer region.
• Henderson-Hasselbalch Equation: $ pH = pK_a + log \frac{[A^-]}{[HA]} $ (for weak acid titrations). This is useful for calculating the pH in the buffer region. $ pOH = pK_b + log \frac{[HB^+]}{[B]} $ (for weak base titrations).

VIII. Important Considerations

• Temperature: Temperature can affect $ K_w $ , $ K_a $ , and $ K_b $ values, which can influence the shape of the titration curve and the pH at the equivalence point.
• Concentration: The concentration of the acid and base affects the steepness of the curve near the equivalence point. More concentrated solutions result in a steeper curve.