# 3.2 Buffer Solutions and their Applications A buffer solution is a solution whose pH does not change significantly when a small amount of acid or base is added to it. Such a solution maintains a constant pH over time. ## Types of Buffer Solutions Buffer solutions can be broadly classified into two types based on their pH: 1. **Acidic Buffers:** * Formed by mixing a **weak acid** and a salt of that weak acid with a strong base. * These solutions have a pH less than 7. * *Example:* Acetic acid ($\mathrm{CH_3COOH}$) and Sodium Acetate ($\mathrm{CH_3COONa}$). 2. **Basic Buffers:** * Formed by mixing a **weak base** and a salt of that weak base with a strong acid. * These solutions have a pH greater than 7. * *Example:* Ammonium hydroxide ($\mathrm{NH_4OH}$) and Ammonium chloride ($\mathrm{NH_4Cl}$). ## Buffer Action Let's consider a typical acidic buffer solution containing acetic acid ($\mathrm{CH_3COOH}$) and sodium acetate ($\mathrm{CH_3COONa}$). The principle of buffer action relies on the **common ion effect**. * **Components and Equilibria:** * Acetic acid is a weak electrolyte and dissociates partially: $$ \mathrm{CH_3COOH}_{(\mathrm{aq})} + \mathrm{H_2O}_{(\mathrm{l})} \rightleftharpoons \mathrm{CH_3COO^{-}}_{(\mathrm{aq})} + \mathrm{H_3O^{+}}_{(\mathrm{aq})} $$ * Sodium acetate is a strong electrolyte and dissociates completely: $$ \mathrm{CH_3COONa}_{(\mathrm{s})} \longrightarrow \mathrm{CH_3COO^{-}}_{(\mathrm{aq})} + \mathrm{Na^{+}}_{(\mathrm{aq})} $$ * The common ion $\mathrm{CH_3COO^-}$ from the salt suppresses the dissociation of the weak acid, shifting its equilibrium to the left. * **Action Upon Addition of Acid (e.g., HCl):** When a small amount of a strong acid ($\mathrm{HCl}$) is added, it introduces $\mathrm{H^+}$ ions into the solution: $$ \mathrm{HCl}_{(\mathrm{aq})} \longrightarrow \mathrm{H^{+}}_{(\mathrm{aq})} + \mathrm{Cl^{-}}_{(\mathrm{aq})} $$ The added $\mathrm{H^+}$ ions are consumed by the acetate ions ($\mathrm{CH_3COO^-}$) present in abundance from the salt, forming undissociated weak acetic acid: $$ \mathrm{CH_3COO^{-}}_{(\mathrm{aq})} + \mathrm{H^{+}}_{(\mathrm{aq})} \rightleftharpoons \mathrm{CH_3COOH}_{(\mathrm{aq})} $$ This reaction effectively neutralizes the added acid, preventing a significant change in pH. * **Action Upon Addition of Base (e.g., NaOH):** When a small amount of a strong base ($\mathrm{NaOH}$) is added, it introduces $\mathrm{OH^-}$ ions into the solution: $$ \mathrm{NaOH}_{(\mathrm{aq})} \longrightarrow \mathrm{Na^{+}}_{(\mathrm{aq})} + \mathrm{OH^{-}}_{(\mathrm{aq})} $$ The added $\mathrm{OH^-}$ ions are neutralized by the $\mathrm{H^+}$ ions produced by the weak acid, forming water. To replenish the consumed $\mathrm{H^+}$ ions, the weak acetic acid dissociates further: $$ \mathrm{H^{+}}_{(\mathrm{aq})} + \mathrm{OH^{-}}_{(\mathrm{aq})} \rightleftharpoons \mathrm{H_2O}_{(\mathrm{l})} $$ The overall reaction where the weak acid neutralizes the added base is: $$ \mathrm{CH_3COOH}_{(\mathrm{aq})} + \mathrm{OH^{-}}_{(\mathrm{aq})} \rightleftharpoons \mathrm{CH_3COO^{-}}_{(\mathrm{aq})} + \mathrm{H_2O}_{(\mathrm{l})} $$ This reaction consumes the added base, preventing a significant change in pH. ## Calculation of pH of Buffer Solution The pH of a buffer solution can be calculated by assuming that the concentration of the conjugate base is predominantly supplied by the strong electrolyte (salt), and the original concentration of the weak acid (or base) can be approximated as its equilibrium concentration. This approach is the basis of the **Henderson-Hasselbalch equation**. For a weak acid/conjugate base buffer: $$ K_a = \frac{[\text{Conjugate Base}][\mathrm{H^+}]}{[\text{Weak Acid}]} $$ Which can be rearranged to: $$ [\mathrm{H^+}] = K_a \frac{[\text{Weak Acid}]}{[\text{Conjugate Base}]} $$ And then $\mathrm{pH} = -\log[\mathrm{H^+}]$. ## Worked Examples ### Example 3.2: pH Calculation of an Acetic Acid-Sodium Acetate Buffer **(a) Calculate the pH of an acetic acid-sodium acetate buffer solution containing 1.0 moles of each component.** 1. **Given Values:** * $[\mathrm{CH_3CO_2H}] = 1.0\,\mathrm{M}$ (concentration of weak acid) * $[\mathrm{CH_3COO^-}] = 1.0\,\mathrm{M}$ (concentration of conjugate base, from salt) * $K_a$ for acetic acid = $1.8 \times 10^{-5}$ 2. **Apply the Formula (Acid Dissociation Constant):** The dissociation of acetic acid is: $$ \mathrm{CH_3CO_2H} \rightleftharpoons \mathrm{CH_3COO^-} + \mathrm{H^+} $$ The equilibrium constant expression is: $$ K_a = \frac{[\mathrm{CH_3COO^-}][\mathrm{H^+}]}{[\mathrm{CH_3CO_2H}]} $$ 3. **Show Calculation:** Substitute the given values: $$ 1.8 \times 10^{-5} = \frac{[1.0\,\mathrm{M}][\mathrm{H^+}]}{[1.0\,\mathrm{M}]} $$ Therefore, $[\mathrm{H^+}] = 1.8 \times 10^{-5}\,\mathrm{M}$. Calculate pH: $$ \mathrm{pH} = -\log[\mathrm{H^+}] $$ $$ \mathrm{pH} = -\log(1.8 \times 10^{-5}) $$ $$ \mathrm{pH} = 4.745 $$ *The pH of the initial buffer solution is 4.745.* **(b) What will be the pH of this solution after the addition of 0.01 mole of hydrochloric acid to $1\,\mathrm{dm}^3$ of the solution? Assume that the volume of the solution remains unchanged with the addition of hydrochloric acid.** 1. **Given Values:** * Initial moles of $\mathrm{CH_3COOH}$ = 1.0 mole * Initial moles of $\mathrm{CH_3COO^-}$ = 1.0 mole * Moles of $\mathrm{HCl}$ added = 0.01 mole * Volume of solution = $1\,\mathrm{dm}^3$ (or 1 L) * $K_a$ for acetic acid = $1.8 \times 10^{-5}$ 2. **Impact of HCl Addition:** $\mathrm{HCl}$ is a strong acid and dissociates completely, producing 0.01 mole of $\mathrm{H^+}$ ions: $$ \mathrm{HCl}_{(\mathrm{aq})} \longrightarrow \mathrm{H^{+}}_{(\mathrm{aq})} + \mathrm{Cl^{-}}_{(\mathrm{aq})} $$ These $\mathrm{H^+}$ ions react with the conjugate base ($\mathrm{CH_3COO^-}$) present in the buffer: $$ \mathrm{CH_3COO^{-}}_{(\mathrm{aq})} + \mathrm{H^{+}}_{(\mathrm{aq})} \longrightarrow \mathrm{CH_3CO_2H}_{(\mathrm{aq})} $$ Each 0.01 mole of $\mathrm{H^+}$ will consume 0.01 mole of $\mathrm{CH_3COO^-}$ and produce 0.01 mole of $\mathrm{CH_3CO_2H}$. 3. **Calculate New Moles/Concentrations:** * Moles of $\mathrm{CH_3CO_2H}$ after $\mathrm{HCl}$ addition: $$ (1.0 + 0.01)\,\mathrm{mole} = 1.01\,\mathrm{mole} $$ * Moles of $\mathrm{CH_3COO^-}$ after $\mathrm{HCl}$ addition: $$ (1.0 - 0.01)\,\mathrm{mole} = 0.99\,\mathrm{mole} $$ Since the volume is $1\,\mathrm{dm}^3$, these values also represent the new concentrations: * $[\mathrm{CH_3CO_2H}] = 1.01\,\mathrm{M}$ * $[\mathrm{CH_3COO^-}] = 0.99\,\mathrm{M}$ 4. **Show Calculation for New pH:** Rearrange the $K_a$ expression to solve for $[\mathrm{H^+}]$: $$ [\mathrm{H^+}] = K_a \frac{[\mathrm{CH_3CO_2H}]}{[\mathrm{CH_3COO^-}]} $$ Substitute the new concentrations: $$ [\mathrm{H^+}] = \frac{(1.8 \times 10^{-5}) \times (1.01\,\mathrm{M})}{0.99\,\mathrm{M}} $$ $$ [\mathrm{H^+}] = 1.836 \times 10^{-5}\,\mathrm{M} $$ Calculate pH: $$ \mathrm{pH} = -\log[\mathrm{H^+}] $$ $$ \mathrm{pH} = -\log(1.836 \times 10^{-5}) $$ $$ \mathrm{pH} = 4.736 $$ *The pH after adding HCl is 4.736.* ## Applications of Buffer Solutions Buffers are vital in maintaining stable pH environments across various fields. ### The Buffer System in Blood Plasma * The **bicarbonate buffer system** is crucial for maintaining blood pH within a narrow range of 7.35-7.45. Deviation outside 6.8-7.8 can be fatal. * **Formation of Carbonic Acid:** Carbon dioxide reacts with water to form carbonic acid. This reaction is catalyzed by carbonic anhydrase in red blood cells. $$ \mathrm{CO}_{2(\mathrm{g})} + \mathrm{H_2O}_{(\mathrm{l})} \rightleftharpoons \mathrm{H_2CO}_{3(\mathrm{aq})} $$ * **Decomposition of Carbonic Acid:** Carbonic acid then dissociates into bicarbonate ions and hydrogen ions. $$ \mathrm{H_2CO}_{3(\mathrm{aq})} \rightleftharpoons \mathrm{HCO}_{3(\mathrm{aq})}^{-} + \mathrm{H^{+}}_{(\mathrm{aq})} $$ * **Neutralization of Acids:** If blood becomes too acidic (excess $\mathrm{H^+}$ ions), bicarbonate acts as a base to neutralize them: $$ \mathrm{HCO}_{3(\mathrm{aq})}^{-} + \mathrm{H^{+}}_{(\mathrm{aq})} \rightleftharpoons \mathrm{H_2CO}_{3(\mathrm{aq})} $$ * **Neutralization of Bases:** If blood becomes too basic (excess $\mathrm{OH^-}$ ions), carbonic acid donates $\mathrm{H^+}$ ions to neutralize the base: $$ \mathrm{OH^{-}}_{(\mathrm{aq})} + \mathrm{H_2CO}_{3(\mathrm{aq})} \rightleftharpoons \mathrm{HCO}_{3(\mathrm{aq})}^{-} + \mathrm{H_2O}_{(\mathrm{l})} $$ ### Household Cleaning Products * **Detergents:** Contain buffers to maintain a stable pH, ensuring effective cleaning without damaging surfaces or irritating skin. ### Personal Care Products * **Shampoos and Soaps:** Buffers are used to maintain pH, preventing skin irritation and ensuring product gentleness. ### Swimming Pools * **Water Treatment:** Buffers help maintain a stable pH level, preventing corrosion of pool equipment and ensuring comfort for swimmers. ### Food and Beverage Industry * **Food Preservation:** Used to control acidity, preserve flavors, and maintain the stability of food products. * **Beverage Production:** Help control pH in beverages for consistent taste and to prevent spoilage. ### Photography * **Developer Solutions:** Buffers maintain a stable pH for controlled and consistent development of film or prints.