Theoretical Foundation: Henderson-Hasselbalch Equilibrium & Buffer Capacity
A buffer solution resists dramatic changes in hydronium ion concentration (ΔpH) when small quantities of strong acid or base are introduced. The thermodynamic foundation of buffer behavior resides in the chemical equilibrium between a weak Brønsted-Lowry acid (HA) and its conjugate base (A−):
Taking the negative logarithm (−log10) of both sides yields Lawrence Joseph Henderson's classical relationship, later re-formulated by Karl Albert Hasselbalch:
Van Slyke Quantitative Buffer Capacity (β)
While the Henderson-Hasselbalch equation defines equilibrium pH, Donald Van Slyke established the mathematical metric for buffer strength (β), defined as the differential increment of strong base (dB) required to produce a unit change in pH (dpH):
Maximum buffer capacity (βmax = 0.576 × Ctotal) is strictly achieved when pH = pKa, at which point [A−] = [HA]. When target pH deviates by more than ±1.0 pH units from pKa, β drops to less than 33% of maximum capacity, leaving the solution susceptible to sudden pH excursions.
Frequently Asked Questions: Analytical Buffer Formulation
Why must pH be measured and verified at the intended working temperature?
The ionization constant (Ka) of buffer molecules varies with temperature according to the standard enthalpy of dissociation. For amine buffers such as Tris, the temperature coefficient is approximately −0.028 pH/°C. Adjusting a Tris buffer to pH 8.0 at 25°C will yield a pH of approximately 8.4 when placed in a 4°C cold room.
What is the difference between single-component titration and dual-salt weighing?
Dual-salt weighing mixes exact calculated stoichiometric masses of conjugate acid and base (e.g., NaH2PO4 and Na2HPO4), fixing both the final pH and the total ionic strength without adding extra counter-ions. Single-component titration dissolves one form and titrates with concentrated HCl or NaOH, which introduces extraneous counter-ions.
Why does diluting concentrated 10x PBS shift the working pH?
Phosphate dissociation involves multivalent ions whose activity coefficients are strongly sensitive to ionic strength. Diluting from 10x to 1x reduces ionic strength, shifting the apparent pKa upward by 0.2 to 0.4 units. Always verify pH after diluting stock concentrates.