Buffer Solutions
A buffer solution is a special aqueous system that resists significant changes in pH when small amounts of strong acid or strong base are added to it. This resistance to pH change is vital in many biological, chemical, and industrial contexts. Human blood, for example, is maintained at a remarkably constant pH of approximately 7.35–7.45 by a carbonate–bicarbonate buffer system; deviations of even 0.2 pH units can be life-threatening. Buffer solutions achieve this stability through a dynamic equilibrium between a weak acid and its conjugate base (acidic buffer) or a weak base and its conjugate acid (basic buffer). Acidic buffers are prepared by mixing a weak acid (such as acetic acid, CH₃COOH) with a soluble salt of that acid containing its conjugate base (such as sodium acetate, CH₃COONa). When a small amount of strong acid (H⁺) is added, the conjugate base neutralises it: CH₃COO⁻ + H⁺ → CH₃COOH. When a small amount of strong base (OH⁻) is added, the weak acid neutralises it: CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O. In both cases, the equilibrium shifts, but because both the acid and its conjugate base are present in significant concentrations, the pH changes only minimally. Basic buffers work analogously using a weak base (e.g. ammonia, NH₃) and its conjugate acid (e.g. ammonium chloride, NH₄Cl). The quantitative description of buffer behaviour is given by the Henderson–Hasselbalch equation, which relates the pH of a buffer to the pKₐ of the weak acid and the ratio of the concentrations of its conjugate base to the weak acid. Buffer capacity — the ability of a buffer to resist pH change — depends on both the total concentration of the buffer components and how close the ratio [A⁻]/[HA] is to 1:1, which occurs when pH = pKₐ. Understanding these principles allows chemists and biologists to design buffer systems for specific pH requirements.
- The Weak Acid Equilibrium
- Adding a Strong Acid to an Acidic Buffer
- Adding a Strong Base to an Acidic Buffer
- Basic Buffers (Ammonia–Ammonium System)
- Buffer Capacity
The Weak Acid Equilibrium
A weak acid HA partially dissociates in water: \ce{HA(aq) <=> H+(aq) + A-(aq)}. The acid dissociation constant is Ka = [H⁺][A⁻]/[HA]. Because HA is weak, only a small fraction dissociates, leaving a large reservoir of both HA and A⁻ in solution.
Adding a Strong Acid to an Acidic Buffer
When H⁺ ions are introduced (e.g. from HCl), the conjugate base A⁻ reacts immediately: \ce{A-(aq) + H+(aq) -> HA(aq)}. The added H⁺ is consumed, converting A⁻ into HA. Because [A⁻] and [HA] are both large, their ratio changes only slightly, so the pH barely shifts. For example, if [A⁻] = 0.10 mol/L and [HA] = 0.10 mol/L, adding a small amount of acid might change the ratio from 1.00 to 0.95, producing a negligible pH drop.
Adding a Strong Base to an Acidic Buffer
When OH⁻ ions are introduced (e.g. from NaOH), the weak acid neutralises them: \ce{HA(aq) + OH-(aq) -> A-(aq) + H2O(l)}. The OH⁻ is consumed and HA is converted to A⁻. Again, large reservoirs of both components ensure the [A⁻]/[HA] ratio changes only slightly, keeping the pH relatively stable.
Basic Buffers (Ammonia–Ammonium System)
Basic buffers use a weak base B and its conjugate acid BH⁺. The ammonia buffer is a common example: \ce{NH3(aq) + H2O(l) <=> NH4+(aq) + OH-(aq)}, with Kb = 1.8 × 10⁻⁵ at 25 °C. Added acid reacts with NH₃: \ce{NH3 + H+ -> NH4+}; added base reacts with NH₄⁺: \ce{NH4+ + OH- -> NH3 + H2O}. The Henderson–Hasselbalch equation can be applied using the pKₐ of the conjugate acid NH₄⁺ (pKₐ = 9.25 at 25 °C).
Buffer Capacity
Buffer capacity (β) is defined as the moles of strong acid or base required to change the pH of 1 litre of buffer by 1 unit. Mathematically, β = dCb/dpH, where Cb is the concentration of added base. Buffer capacity is maximum when pH = pKₐ (i.e. [HA] = [A⁻]) and increases with the total buffer concentration. A buffer is generally effective within ±1 pH unit of its pKₐ. For example, an acetic acid/acetate buffer (pKₐ = 4.76) is effective between pH 3.76 and 5.76.
The Key Equation
- \mathrm{pH} — pH of the buffer (dimensionless): The negative base-10 logarithm of the hydrogen ion concentration; measures acidity.
- \mathrm{p}K_a — Acid dissociation constant (log form) (dimensionless): Equals −log₁₀(Ka); a lower pKa means a stronger weak acid.
- [\ce{A-}] — Concentration of conjugate base (mol L⁻¹): Molar concentration of the deprotonated form of the weak acid (the anion from the salt).
- [\ce{HA}] — Concentration of weak acid (mol L⁻¹): Molar concentration of the undissociated weak acid in the buffer solution.
Worked Example
Problem. A buffer is prepared by dissolving 0.200 mol of sodium acetate (CH₃COONa) and 0.150 mol of acetic acid (CH₃COOH) in enough water to make 1.00 L of solution. The pKa of acetic acid is 4.76. (a) Calculate the pH of the buffer. (b) Calculate the pH after adding 0.020 mol of NaOH to 1.00 L of this buffer.
Answer. pH of buffer = 4.89; pH after adding NaOH = 4.99 (change of only 0.10 pH units)
Origins · 1 minLawrence Joseph Henderson and how this was discovered
Lawrence Henderson was a biochemist and physiologist at Harvard University who derived the fundamental equation describing the pH of buffer solutions in 1908. Working to understand the acid–base balance of blood, he showed that the ratio of bicarbonate to carbonic acid governed blood pH. His equation was later cast in its familiar logarithmic form by the Danish chemist Karl Albert Hasselbalch in 1917, giving us the Henderson–Hasselbalch equation used worldwide in chemistry, biochemistry, and medicine. Henderson also introduced the broader concept of the 'fitness of the environment,' exploring why water and carbonate chemistry are uniquely suited to support life. Henderson was so influential at Harvard that he ran an interdisciplinary 'Pareto circle' seminar bringing together sociologists, physiologists, and economists — an unusually broad intellectual reach for a chemist!
Related Concepts
- Weak Acids and Bases — Buffer solutions are built from weak acid–conjugate base pairs; understanding partial dissociation and Ka is essential before studying buffers.
- pH and Hydrogen Ion Concentration — The Henderson–Hasselbalch equation directly calculates pH; a solid grasp of the pH scale and its logarithmic nature is a prerequisite.
- Salt Hydrolysis — The salt component of a buffer (e.g. sodium acetate) undergoes hydrolysis; understanding why salt solutions are not neutral explains the role of the conjugate base in a buffer.
- Le Chatelier's Principle — The mechanism by which a buffer resists pH change is a direct application of Le Chatelier's principle — the equilibrium shifts to counteract the added stress.
- Acid–Base Titrations — The buffer region in a titration curve (around the half-equivalence point) is a real-world demonstration of buffer action and connects directly to pKa determination.