Buffers

Buffers

When an Arrhenius acid (HA) is added to water, it dissociates into its conjugate base (A^–) and a hydrogen cation (H⁺).

HA + H₂O → H⁺_(aq) + A^–_(aq)

The amount of hydrogen ions present in the solution determines the acidity of the solution, where more hydrogen ions indicate a lower or more acidic pH. Similarly, when a strong Arrhenius base (BOH) is added to water, it dissociates into its conjugate acid (B⁺) and a hydroxide ion (OH^–).

BOH + H₂O → B⁺_(aq) + OH^–_(aq)

Generally, the addition of strong acids or bases to a solution changes the pH dramatically because the acid or base reacts with the water molecules in solution, increasing the concentration of either hydrogen ions or hydroxide ions. However, this change in pH can be mitigated using a buffer. Buffers are solutions that work towards maintaining a constant pH in a system, regardless of the addition of strong acids or bases.

Most often, the components of a buffer are the conjugate acid-base pair of a weak acid or weak base. For this reason, strong acids or bases that dissociate completely in water make very poor buffers and weak acids or bases that partially dissociate make better buffers. When the buffer is present, the strong acid or base does not react with the water molecules present in solution and instead reacts with the weak acid/conjugate base. This results in little to no change in the pH of the solution.

The Common Ion Effect

A buffer works through a phenomenon called the common ion effect. The common ion effect occurs when a given ion is added to a mixture at equilibrium that already contains the given ion. When this happens, the equilibrium shifts away from forming more of that ion.

For example, acetic acid (CH₃COOH) dissociates slightly in water, forming the acetate ion (CH₃COO^–) and hydrogen ion.

CH₃COOH_(aq) H₂O ⇔ H⁺_(aq) + CH₃COO^–_(aq)

If more of the acetate ion is added from soluble sodium acetate, the equilibrium position shifts to the left to form more non-dissociated acetic acid, and the concentration of hydrogen ions decreases. Here, the common ion — acetate — suppresses the dissociation of acetic acid.

A buffer must contain high concentrations of both the acidic (HA) and basic (A^–) components to buffer a solution. If the amount of hydrogen or hydroxide ions added to the buffer is small, they cause a small amount of one buffer component to convert into the other. As long as the concentration of added ions is much smaller than the concentrations of HA and A^– already present in the buffer, then the added ions will have little effect on pH since they are consumed by one of the buffer components. When the concentration of hydrogen or hydroxide exceeds the concentrations of the acid and its conjugate base, the buffering effect is lost, and the pH will change.

Henderson-Hasselbalch Equation

The dissociation constant, K_a, of a weak acid is calculated using the concentrations of the non-dissociated acid HA, and the concentrations of the hydrogen ions and the conjugate base, A^–.

Higher K_a values represent stronger acids, while smaller K_a values represent weaker acids. To determine the concentration of hydrogen ions, the equation is rearranged. In this form, it is clear that the ratio of acid species to base species is important in determining the concentration of hydrogen ions, and by extension, pH.

Taking the negative common logarithm of both sides results in the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation enables the calculation of buffer pH directly, without having to calculate the concentration of hydrogen ions first.

For example, it can be used to determine the pH of a 1 L buffer after adding 0.02 moles of a strong base. The strong base dissociates completely, so the concentration of hydroxyl ions added is 0.02 M. This will decrease the concentration of the acid by 0.02. Assuming that the original concentration of the acid (HA) and base (A^–) components are each 0.5 M, the new concentration of base increases by 0.02 M to 0.52 M, while the concentration of acid decreases by 0.02 M to 0.48 M. Knowing the pK_a of the acid component of the buffer, we can substitute these new component concentrations into the Henderson-Hasselbalch equation to determine the pH.

This is useful in determining buffer capacity, or how much strong acid or strong base can be added to a buffer without significantly affecting the pH.

Buffer Capacity

Buffer capacity is the measure of a buffer’s ability to resist pH change. This ability depends on the concentration of the buffer components, meaning the acid and its conjugate base. A higher buffer concentration has a greater buffer capacity. This means that a greater amount of hydrogen ions, or a stronger acid, would have to be added to disrupt the equilibrium and change the pH of the buffer.

Buffer capacity is also affected by the relative concentrations of the buffer components. The buffer is more effective when the concentrations of the components are similar. If the buffer component ratio is similar, then the component concentration ratio doesn’t change significantly when acid or base is added; large amounts of acid or base must be added to offset the ratio and change the pH.

The pH of the buffer differs from its buffer capacity. The pH range is the range at which the buffer is effective. Typically, buffers have a usable range within 1 pH unit of the pK_a of the acid component of the buffer.

References

1. Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012). Chemistry and Chemical Reactivity. Belmont, CA: Brooks/Cole, Cengage Learning.
2. Silberberg, M.S. (2009). Chemistry: The Molecular Nature of Matter and Change. Boston, MA: McGraw Hill.