# Henderson-Hasselbalch Equation

Overview
• The Henderson-Hasselbach Equation describes the relationship between the pH of a buffer-containing fluid with the relative ratio of the Weak Acid (H-B) and Weak Base (B-) forms of that buffer. Each buffer has a unique ratio of the B- to H-B forms at different pHs (Review: Buffer Basics). For example, a 1:1 ratio of B- to H-B might occur at pH 2.4 for some buffer while for another it might occur at pH 4.5. The relationship between the ratio of B- to H-B forms of a particular buffer at different pHs depends on the unique chemical characteristics of the buffer itself and can be quantitatively described using the Henderson-Hasselbalch Equation.
Henderson-Hasselbalch Equation
• pH = pK + log10([B-]/[H-B])
• Where:
• pH = pH of the buffer-containing solution
• pK = An empirically-determined value unique to each buffer (See below)
• [B-] = Concentration of Weak Base form of the buffer
• [H-B] = Concentration of Weak Acid form of the buffer
pK
• The pK of a particular buffer is the pH of the solution where the ratio between the Weak Base (B-) and Weak Acid (H-B) forms of the buffer are equivalent. As can be seen, when the value of [B-] equals that of [H-B], the log term of the Henderson-Hasselbalch Equation becomes zero, leaving pH = pK. The pK of a buffer must be experimentally determined and cannot be predicted, although it does depend on the unique chemical composition of the buffer.
Features of the Henderson-Hasselbalch Equation
• A key concept to appreciate from the Henderson-Hasselbalch equation is that the pH of a buffer-containing solution is intimately linked to the ratio of the Weak Base (B-) and Weak-Acid (H-B) forms of the buffer. Consequently, externally changing the pH of the solution, say by directly injecting or removing free hydrogen ions, will modify the ratio of B- to H-B forms. Alternatively, externally changing the concentration of the Weak Base form of the buffer, say by directly adding or removing B- from the solution, will change the fluid's pH.
Titration Curves
• Buffers are most capable of resisting changes to the pH of a solution when the pH of that solution equals the unique pK of that buffer. As discussed, when the pH of the fluid equals the buffer's unique pK, the Weak Acid and Weak Base forms of the buffer display equivalent concentration in the fluid. Consequently, there is plenty of the Weak Acid form of the buffer to release free hydrogen ions if H+ is externally removed from the solution and there is also plenty of the Weak Base form of the buffer to absorb free hydrogen ions if H+ is externally added to the solution.
• The relationship between the amount of free hydrogen ions added to a buffered solution compared to the changes in the solution's pH is termed the "Titration Curve" and can be plotted. As can be seen from a buffered solution's titration curve, even large additions of free hydrogen to the solution result in only small changes in the solution's pH when it is close to the pK of the buffering chemical. In contrast, when the pH of the solution is far from the pK of the buffer, even small additions of free hydrogen can radically change the solution's pH.