Biochemistry I Fall Term, 2000

Lecture 3: Acid-Base Equilibria & Buffers

Assigned reading in Campbell: Chapter 2.3-2.6.

Take a Review Quiz on these concepts:
http://www.bio.cmu.edu/courses/03231/MCQF00/MCQLec03.htm

2.3 Acids and Bases

• Acid: can donate protons
• Base: can accept protons

Example:

The compound M-O-H is an acid if it looses its proton, but it is a base if it releases an OH^- group. Whether a compound is an acid or a base depends on the relative strength of the M-O bond versus the O-H bond. The strength of the acid increases with the electronegativity of M. The higher the electronegativity the more electrons are drawn from the OH group. This electron density stablilizes the M-O bond.

For example, the alkali earth metals (Li, Na, K) all have electronegativities of one or less. Thus the M-O bond is more ionic in nature and LiOH, NaOH, KOH are very basic. In general, most hydroxides of metals are basic.

When M is a non-metal (e.g. C, S, N, Cl), the compound is usually acidic. The more electron-withdrawing M (and its ligands) are, the stronger the acid. Fluorine has the highest electronegativity, 4. Consider the following three compounds:

Ethanol is a very weak acid, acetic acid somewhat stronger, and trichloracetic acid is very strong. A quantitative measure of the strength of an acid is given by the acid dissociation constant, K_a.

Equilibrium Constant:

The acid dissociation constant, K_a, is the equilibrium constant for a dissociation reaction. Consider first a simple reaction and its equilibrium features:

Kinetics gives the following rate equations:

At equilibrium there is no change in the concentration of A or B; therefore:

At equilibrium the reaction has not stopped. Rather, the rates of the forward reaction (k₁[A]) and the reverse reaction (k₂[B]) are equal, thus:

At equilibrium, the fraction of A (f_a) and B (f_b) are given by:

Some simple intuitive conclusions can be drawn from the above equations:

If K_eq>>1 then f_b=1 and f_a=1/K_eq

If K_eq<< 1 then f_b=K_eq and f_a=1

A separate page, Ratios & Fractions in the Henderson-Hasselbalch Equation, relates the above principles to the specific case of problem solving using the Henderson-Hasselbalch Equation.

2.4 Self-Dissociation of Water

The equilibrium constant for the ionization of water is:

Since the concentration of water is very high (55.5 M) and practically constant, we can incorporate it into the equilibrium constant to give:

This is the ion product constant for water.
In pure water [H⁺] = [OH^-] = 10^-7 M because water has no net charge.

Definition of pX: pX = - log[X]

A specific example is: pApples = -log[Apples], or more important:

pH = -log[H⁺]

Acid Base Equilibrium

The equilibrium for ionization (dissociation) of an acid is given by:

as above, assuming that the concentration of water is constant:

Which gives rise to the Henderson-Hasselbalch equation:

When the pH = pK_a, there are equal amounts of [A^-] and [HA] in solution. When the pH is lower than the pK_a, the [HA] > [A^-]. When the pH is higher than the pK_a, then [HA] < [A^-]. This is a simple example of the application of Le Chatelier's principle:

If we add acid (to decrease the pH), the system will respond by increasing the amount of [HA] to reduce the concentration of the added acid and return the system to its initial pH

The acidity constant, K_a, is a property of the acid. For example:

2.5 Titration Curves

• See the pH titration animation at:
  http://www.bio.cmu.edu/courses/03231/MCQF00/pHAnim/pHSim2.html
• In-class demo of the pH Titration Example for Problem Set #1. at:
  http://www.bio.cmu.edu/courses/03231/DryLabF00/pH/pHCalc.htm

2.6 Buffers

A pH buffer is an acid which resists changes in the solution pH. Buffers play an important role in cellular processes because they maintain the pH at an optimal level for biological processes. All acids are good buffers at pH values near (within one pH unit of) their pK_a. Strong acids (such as HCl) are poor buffers while weaker acids (such as acetic acid) are good buffers in the pH ranges found in biological environments. Conversely, weaker acids (such as imidazole, pK_a = 6.04) are good buffers in this range The reason for this is that strong acids are completely dissociated in this pH range while weak acids are not. For example, consider a 10 mM solution (1L) of HCl or acetic acid at pH 4.7. At this pH all of the HCl is ionized and exists as H⁺ and Cl^-. In contrast, only about 50% of the acetic acid is ionized. If we added 1 mmole of a strong acid (i.e. HCl) to each solution the pH changes would be as follows:

• In the case of the HCl, all of the added acid would remain as H⁺; thus, the H⁺ concentration would increase from 10^-5 M to 10^-3 M, or the pH would drop to 3.

• In the case of the acetic acid solution, most of the added acid would simply protonate the acetate ions, reducing their concentration from 5 mM to 4 mM. The resultant pH of the solution is:

The buffering capacity of a weak acid decreases as the dissociation becomes more complete. For example, acetate is a poor buffer at pH3 or at pH7 (see Figure 2.8).

The actual pH of a solution of a weak acid can be calculated from the known concentration of the weak acid. For example, if C^o moles of a weak acid are dissolved in water and x moles of protons are released from the acid then the concentration of the various species is:

From the definition of the acidity constant:

We can solve for x under any conditions using the quadratic equation. However, this equation can be simplified if the concentration of the released protons is small compared to the concentration of the weak acid (i.e. C^o >> x), giving:

Polyprotic Acids

• Many compounds can release more than one proton in the pH range of 0-12. Examples are phosphate (pK_a = 2.15, 6.82, 12.38), carbonate, and dicarboxylic acids.
• If the pK_as are separated by 2 or more pH units (i.e. phosphoric acid) each ionization can be treated separately.
• Depending on the structure of the polyprotic acid the pK_a for each ionization can vary widely. Consider the following:

Zwitterionic Compounds

Zwitterionic compounds can bear both a negative and a positive charge. Amino acids are examples of zwitterions:

1. Titration curves show 2 ionizations.
2. pK_a1 = 2.3.
3. pK_a2 = 9.8.
4. At pH << pK_a1, the charge is +1.
5. At pH = 1/2(pK_a1 + pK_a2), the amino acid has no net charge.
6. At pH >> pK_a2, the charge is -1.

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