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Experiment # 9: The Henderson-Hasselbalch Equation
A buffer is commonly defined as a solution that resists changes in pH when a small amount of acid or base is added or when the solution is diluted with pure solvent. This property is extremely useful in maintaining the pH of a chemical system at an optimum value to appropriately influence the reaction kinetics or equilibrium processes. A buffer solution actually is a mixture of a weak acid and its conjugate base or a mixture of a weak base and its conjugate acid. The conjugate forms are commonly referred to as “salts”.
For a typical weak acid, the dissociation equilibrium is represented as:
Acid l H+^ + Base; Ka = [H+^ ] [Base]
[Acid]
according to the Bronsted-Lowry concept. If a pure weak acid is dissolved in a pure solvent the
concentrations of H+^ and conjugate Base will be equal, neglecting autoprotolysis of the solvent.
Rearranging the dissociation constant equation and solving for [H+^ ] gives: [H +^ ]
= [Ka (Acid)] 1/2^. If other factors governing conjugate base concentration are present in the system (either as added salt of the weak acid or as added base to partially neutralize the acid), the
concentrations of H+^ and conjugate Base will no longer be the same. Under these conditions, the
equation for [H+^ ] becomes:
[H+^ ] = Ka [Acid]/[Base] = K [Acid]/[Base].
Taking negative logarithms of both sides of the above equation gives:
-log ([H
]) = -log (Ka ) – log ([Acid]/[Salt]) or pH = pKa – log ([Acid]/[Salt]).
Upon inversion of the argument the last log term becomes positive, as:
pH = pKa + log ([Salt]/[Acid]).
This form of the ionization or dissociation constant expression is called the Henderson-Hasselbalch equation. This equation is very useful in calculating the pH of a solution containing a weak acid and its conjugate base (or salt). A comparable equation is obtained for a buffer solution consisting of a mixture of a weak base and its salt, namely:
pOH = pKb + log ([Salt]/[Base]).
Solutions of a weak acid and its salt (conjugate base) may be obtained by mixing an excess of weak acid with some strong base to produce the salt by partial neutralization. A similar mixture can be obtained by mixing an excess of salt with a strong acid to produce the weak acid component. Most often, however, a weak acid-conjugate base buffer is prepared by a direct mixing of the weak acid with
its salt. This third method allows an accurate control of the concentrations of both the weak acid and conjugate base species.
The buffering mechanism of a mixture of a weak acid and its salt can be explained as follows. The buffer pH is governed by the logarithm of the ratio of the salt and acid concentrations, as: pH =
constant + log ([Salt]/[Acid]), where the constant is the pKa of the particular weak acid used in the buffer. If the buffer solution is diluted with pure solvent, the common volume of the salt and acid components is increased, but the amounts of each are unchanged. Consequently, the ratio remains constant, and the solution pH does not change. (In actuality, the pH increases slightly due to an increase in the activity coefficient of the salt resulting from the decrease in ionic strength. But for practical purposes, the pH does not change significantly)
If a small amount of a strong acid is added to the buffer, the strong acid will combine with an equivalent amount of the conjugate base, converting it to the weak acid form. Thus, [Salt] decreases and [Acid] increases, but the logarithm of the overall ratio does not change significantly. A comparable affect is seen if a small amount of strong base is added to the buffer; the [Salt] increases slightly as the [Acid] decreases accordingly, but the logarithm of the ratio changes only slightly.
The amount of acid or base that can be added without causing a large change in pH is governed by the buffering capacity of the solution. This property is determined by the relative concentrations of acid and salt. The higher their concentrations, the more acid or base the solution can accommodate before the relative acid/salt ratio is changed. The buffering capacity is also controlled by the ratio of acid to salt. The capacity is at a maximum when the ratio is unity, that is, when the pH = pKa. In general, the
buffering capacity is satisfactory over a pH range of pKa ± 1.
A buffer solution of a given pH can be prepared by choosing a weak acid (or a weak base) and its conjugate salt that has a pKa value near the pH (or pOH) that is desired. There are a number of such weak acids and bases, and any pH region can be buffered by a proper choice of components. The salt does not react with water (or other solvent) to ionize as an acid or base due to the presence of the acid or base in the mixture. The presence of appreciable amounts of acid will suppress the ionization of the salt to the acid form (and similarly for a weak base/salt buffer system).
In this experiment, the dissociation constant, Ka , of a weak acid will be determined by a technique based on the Henderson-Hasselbalch relationship. Specifically, standard solutions (equimolar) of a weak acid and its conjugate base (or salt) will be mixed in a standard series. For this system, it may be considered that negligible reaction occurs, since transferring a proton between the species in a conjugate acid-base pair changes nothing, and the relative concentrations of the conjugate pair species in the mixture will be the same as that in the proportionate volumes of standard solutions.
Plots of measured mixture pH versus various functions of the conjugate pair concentrations will be made in order to demonstrate the usefulness of the Henderson-Hasselbalch equation in determining the
acid strength (i.e., Ka ) of the weak acid in the buffer. The functions of conjugate pair concentrations to be examined with respect to mixture pH include: volumes of acid (or salt), ratio of volumes of salt and acid, and logarithm of the ratio of volumes of salt and acid.
Interpretations of the resulting plots should show that the Henderson-Hasselbalch equation gives an accurate description of the variation of pH in mixtures of conjugate pairs or buffers. If such a plot of pH versus log ratio salt/acid results in a straight line, the intercept should measure the acid dissociation
On the third page, make a single plot of pH (ordinate) versus log ratio salt/acid (abscissa), using appropriate large scales. Since the log of ratio values will range from negative to positive numbers, set the ordinate origin in the center of the long side of the papers and place negative log values on the left side and positive log terms on the right side. Select a pH scale such that the experimental data points cover the full graph page.
Table I
Sample # mL acid mL salt Salt/acid ratio Log ratio pH 1 10.00 0. 2 8.00 2. 3 7.50 2. 4 7.00 3. 5 6.50 3. 6 6.00 4. 7 5.50 4. 8 4.50 5. 9 4.00 6. 10 3.50 6. 11 3.00 7. 12 2.50 7. 13 2.00 8. 14 0.00 10.
Draw the best straight line through the data points, assuming that the Henderson-Hasselbalch equation is valid: pH = pK (^) a + log ([salt]/[acid]). Determine the value of the pH at the intersection of the data
point line through the ordinate axis; this value of pH equals the pKa of the weak acid. Write the value
on the graph beside the point of intersection, and label it as pKa.
Look up the literature value for the pKa of acetic acid, and record this as the “literature” value on the
first page of the report, citing the source. Record the experimental value of pKa for acetic acid, labeling it “Henderson-Hasselbalch” value.
