Buffers and Acid-Base Titrations | General Chemistry 3

Neutralization reactions:

Neutralization reactions occur when an acid reacts with a base to form water and a salt. These reactions are typically exothermic and proceed to completion when a strong acid and strong base are involved. The general equation of a neutralization reaction is:

Acid + Base → Salt + Water
 

The neutralization of hydrochloric acid with sodium hydroxide is:

HCl (aq) + NaOH (aq) → NaCl (aq) + H₂O (l)

Types of neutralization reactions:

• Strong acid - strong base neutralization: Both the acid and base are fully dissociated in solution, resulting in a complete reaction.
• Weak acid - strong base neutralization: The weak acid partially dissociates, while the strong base fully dissociates. The reaction results in the formation of water and the conjugate base of the weak acid.
• Strong acid - weak base neutralization: The strong acid fully dissociates, while the weak base partially dissociates. The reaction results in the formation of water and the conjugate acid of the weak base.
• Weak acid - weak base neutralization: Both the acid and base partially dissociate, and the reaction may not proceed fully to completion. The final pH depends on the relative strengths of the acid and base.
   

• Neutralization of acetic acid (CH₃CO₂H), a weak acid, with NaOH, a strong base:
  CH₃CO₂H (aq) + HO^- (aq) $\rightleftharpoons$ H₂O (l) + CH₃CO₂^- (aq)
• Neutralization of HCN, a weak acid, with aqueous ammonia (NH₃), a weak base:
  HCN (aq) + NH₃ (aq) $\rightleftharpoons$ NH₄⁺ (aq) + CN^- (aq) 

The common-ion effect:

The common-ion effect occurs when a common ion is added to a solution containing a weak acid (or weak base). The presence of the common ion increases its concentration, causing the equilibrium to shift towards the non-ionized form of the weak acid or base, thereby reducing its dissociation. This phenomenon is a direct application of Le Châtelier's Principle.
 

In a solution of acetic acid (CH₃COOH) and sodium acetate (CH₃COONa), both substances share the common ion, acetate (CH₃COO⁻).

Dissociation reaction of acetic acid: CH₃COOH (aq) + H₂O (l) ↔ CH₃COO⁻ (aq) + H₃O⁺ (aq)

When sodium acetate is added to the solution, it increases the concentration of acetate ions. According to Le Châtelier's principle, the equilibrium shifts to the left, reducing the ionization of acetic acid. This results in a lower concentration of hydronium ions and thus a higher pH than if the common ion were not present.

Calculating pH with the common-ion effect:

The common-ion effect influences the pH calculation in solutions containing a weak acid or base. For example, in a solution where both a weak acid and its conjugate base are present, the additional conjugate base suppresses the ionization of the weak acid, leading to a higher pH than expected for the acid alone.
 

Application in buffers:

The common-ion effect is critical in buffer solutions, where both the weak acid and its conjugate base are present in significant amounts. This allows the buffer to resist changes in pH by mitigating the effects of added acids or bases through the common-ion effect.

Buffer solutions:

Buffer solutions are aqueous solutions that resist significant changes in pH when small amounts of an acid or base are added. Buffers are crucial in maintaining stable pH levels in various chemical, biological, and industrial systems. They are typically composed of a weak acid and its conjugate base, or a weak base and its conjugate acid.
 

• Acetic acid (CH₃COOH) and its conjugate base, sodium acetate (CH₃COONa), form a buffer that maintains a pH around 4.75.
• Ammonia (NH₃) and its conjugate acid, ammonium chloride (NH₄Cl), form a buffer that stabilizes pH around 9.25.

Henderson-Hasselbalch equation:

The pH of a buffer solution can be estimated using the Henderson-Hasselbalch equation:
 

Conditions for applying the Henderson-Hasselbalch equation:

• K_a should be in the range of approximately 10^-4 M to 10^-11 M.
• The ratio $\frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}$ must be between 0.1 and 10. Therefore, the pH of a buffer cannot be more than one pH unit from the pK_a of the weak acid. This defines the buffer rnage as pH = pK_a $\pm$ 1.
• The concentrations of [A^-] and [HA] should be in the range of 10^-3 M to 1 M.

The equation applies to acidic buffers, and a similar form applies to basic buffers using the base dissociation constant K_b​.

Buffer capacity:

Buffer capacity refers to the amount of acid or base that can be added to a buffer solution before the pH changes significantly. Buffers have a higher capacity when both the weak acid and its conjugate base (or the weak base and its conjugate acid) are present in nearly equal and substantial concentrations. The larger the concentration of the buffer components, the higher the buffer capacity.

Acid-base indicators:

Acid-base indicators are substances that change color depending on the pH of the solution. These indicators are typically weak acids or bases, and they exhibit different colors in their protonated and deprotonated forms. They are used to signal the endpoint of titrations by undergoing a visible color change within a specific pH range, which is determined by the acid dissociation constant (pK_a​) of the indicator.
 

Mechanism of acid-base indicators:

The equilibrium for an acid-base indicator (HIn) in solution is:

HIn (aq) $\rightleftharpoons$ H⁺ (aq) + In^- (aq)

• In acidic conditions, the equilibrium shifts to the left, favoring the protonated form (HIn), which exhibits a particular color.
• In basic conditions, the equilibrium shifts to the right, favoring the deprotonated form (In⁻), which exhibits a different color.

Thus, the color change is dependent on the pH of the solution relative to the pK_a​ of the indicator. The pH range in which the indicator changes color is typically close to the pK_a​ value of the indicator.

Bromthymol blue (pK_a = 7.3) changes from yellow to blue around pH = 7.3

• Yellow color: Indicates an excess of acid in the solution (pH < 7.3).
• Blue color: Indicates an excess of base in the solution (pH > 7.3).

pH Indicators in titrations:

In titrations, indicators are used to signal the endpoint, the point at which a stoichiometrically equivalent amount of acid and base has reacted. At the equivalence point, the moles of acid and base satisfy the relationship:
 

Titration of a strong acid with a strong base (or vice versa): pH changes abruptly at the equivalence point
Titration curve for the titration of a 0.100M HCl (aq) solution with a 0.100M NaOH (aq) solution:
 

Titration of a weak acid with a strong base (or vice versa): pH = pKa at the Midpoint
Titration curve for the titration of a 0.100M CH₃COOH (aq) solution with a 0.100M NaOH (aq) solution: