A buffer solution is a mixture engineered to stabilize the acidity or alkalinity of a liquid, resisting significant shifts in pH when small quantities of a strong acid or strong base are introduced. This property is important in biological systems, such as the human bloodstream, where pH must be tightly regulated to maintain proper function. Understanding how a buffer achieves this stability requires examining the specific chemical components and the equations that govern their behavior.
Identifying the Buffer Components
The fundamental requirement for creating a buffer is the presence of a weak conjugate acid-base pair, meaning the solution must contain a weak acid (HA) and its corresponding conjugate base (A-), or a weak base and its conjugate acid.
When the weak acid HA is dissolved in water, an equilibrium is established where the acid partially dissociates into its conjugate base and hydrogen ions (H+). This equilibrium is expressed by the acid dissociation constant, \(K_a\). The mathematical expression for this constant is \(K_a = \frac{[H+][A-]}{[HA]}\), where the square brackets denote the molar concentrations of the species at equilibrium.
The presence of both the weak acid (HA) and a significant concentration of the conjugate base (A-), usually added as a soluble salt, provides the buffering capacity. This pool of both the acid and the base component is necessary to counteract any added external acid or base.
Writing the Chemical Action Equations
The stability of a buffer is demonstrated by the specific chemical reactions that occur when a strong acid or strong base is added. These reactions are stoichiometric and proceed essentially to completion, consuming the added strong species. The buffer components act as neutralizing agents.
When a strong acid is added, it releases hydrogen ions (H+). The conjugate base (A-) immediately reacts with these added H+ ions to form more of the weak acid (HA). This reaction is represented as \(H^+ + A^- \rightarrow HA\). Since the H+ ions are converted into the weak acid HA, the overall concentration of free H+ remains nearly constant, and the pH changes only slightly.
Conversely, if a strong base is introduced, it releases hydroxide ions (OH-). The weak acid component (HA) neutralizes the added strong base by donating a proton to the hydroxide ion to form water (\(H_2O\)) and the conjugate base (A-). The equation for this process is \(HA + OH^- \rightarrow A^- + H_2O\). The added OH- ions are consumed, preventing a drastic increase in pH.
From Equilibrium to the Henderson-Hasselbalch Equation
The chemical action of a buffer shifts the concentrations of the weak acid (HA) and its conjugate base (A-), which determines the new equilibrium pH. To simplify this calculation, the initial equilibrium expression, \(K_a = \frac{[H+][A-]}{[HA]}\), is rearranged. Isolating the hydrogen ion concentration yields \([H^+] = K_a \frac{[HA]}{[A-]}\).
To make this expression practical for pH calculations, which use a logarithmic scale, the negative logarithm of both sides is taken. This transformation results in the equation: \(-\log[H^+] = -\log(K_a) – \log(\frac{[HA]}{[A-]})\). By definition, \(-\log[H^+]\) is pH, and \(-\log(K_a)\) is \(pK_a\).
Substituting these definitions provides the simplified form: \(pH = pK_a – \log(\frac{[HA]}{[A-]})\). Applying the rule of logarithms to flip the concentration ratio results in the Henderson-Hasselbalch equation: \(pH = pK_a + \log(\frac{[A-]}{[HA]})\). This formula relates the buffer’s pH, the intrinsic acidity (\(pK_a\)), and the ratio of the conjugate base concentration to the weak acid concentration.
Applying the Equation to Solve Problems
The Henderson-Hasselbalch equation is a powerful tool used to quickly estimate the pH of a buffer solution when the concentrations of the acid and base components are known. The equation is accurate when the concentrations of both the weak acid and its conjugate base are high compared to the \(K_a\) value. The \(pK_a\) value, a characteristic of the specific weak acid, must be determined first by taking the negative logarithm of the acid’s published \(K_a\).
For example, consider an acetic acid/sodium acetate buffer, where acetic acid (HA) has a \(K_a\) of \(1.8 \times 10^{-5}\). The \(pK_a\) is calculated as \(-\log(1.8 \times 10^{-5})\), which is approximately \(4.74\). If a buffer is prepared with an acetic acid concentration of \(0.15\) M and a sodium acetate (A-) concentration of \(0.25\) M, these values are substituted into the formula.
The calculation is \(pH = 4.74 + \log(\frac{0.25}{0.15})\). The ratio of the concentrations is \(1.67\), and \(\log(1.67)\) is approximately \(0.22\). Adding this to the \(pK_a\) yields a final pH of \(4.74 + 0.22\), or \(4.96\). This application of the Henderson-Hasselbalch equation allows for the prediction of a buffer’s pH.