Lesson on pKa and Weak Acid

Contributors

Faculty

Michael Massiah, Ph.D.
Associate Professor of Chemistry 
Chemistry Department
The George Washington University

Team Members

Richard Graham, Ph.D.
Instructional Designer
Center for Teaching Excellence
The George Washington University

Cristabel Ocasio Ilarraza, M.A.
Instructional Designer
Center for Teaching Excellence
The George Washington University

Eugene Abedejos
Multimedia Producer
Center for Teaching Excellence
The George Washington University

GW-Adobe Science Education Initiative Program Leads

Jason Torres, Ed.D.
Director, Digital Learning
Center for Teaching Excellence
The George Washington University

Sylvain Guiriec, Ph.D.
Physics Innovation Lab
Assistant Professor of Physics
Columbian College of Arts and Sciences, Department of Physics
The George Washington University

Project information

Audience

The intended audience for this lesson is undergraduate chemistry students. 

Learning objectives

• Develop an intuitive understanding of the Hendersen-Hasselbalch equation and the titration curve.
• Calculate the pKa and the buffering capacity of a weak acid.
• Explain the relationship between pH and pKa, including the structure of a weak acid at different levels of pH.

Purpose

The purpose of this activity is to illustrate the concept of pH, pKa, and buffering and recognize the crucial relationship between pH and pKa in determining the buffering capacity of a weak acid.  By conducting experiments and analyzing data, students will gain insights into the behavior of weak acids at different pH levels and how they can act as buffers to resist changes in pH.

Background

The definition we use for an acid is any molecule that donates or releases a proton into aqueous solution. For strong acids, such as hydrochloric acid (HCl), they will completely disassociate in water based on the following equation:

In this case, one can think of the Ka or association constant, as representing the strength of the bond between the acidic proton and the atom it is bonded to in aqueous solution. In the case of HCl, the association constant (Ka) would be small. The negative log of this Ka value is designated as:

For weak acids, the Ka and pKa value would be higher. The higher the pKa value, the stronger the bond between the H⁺ and its attached atom, which in biological system is usually oxygen (O), nitrogen (N), Sulfur (S) and phosphorus (P). The behavior of a weak acid in water is described by the following equation:

Le Chatelier's principal simply states that the direction of a reaction is dependent on the concentration of the reactant(s) (left-side of the equation arrow) and concentration of the reactant(s) (right-side of the arrow). By this concept, if there is more [HA], the reaction will proceed to the right to produce more [A^–] and [H₃O⁺]. Or, if there is less [H⁺], the reaction will also proceed to the right. In contrast, if there is more [H⁺] – indicating the aqueous solution is already acidic – the reaction will proceed to the left and there will be more HA.  The pH of the solution therefore determines the ionic state (HA vs A^–) of the weak acid. Basically, how a weak acid (HA) exists or behaves in aqueous solution depends solely on the pH (concentration of H₃O⁺) of the solution.

Recall this equation:

Like the pKa definition above, it is the negative log of a number. In this case, the concentration of H⁺. (Concentration is designated by the square brackets.)

The Ka and pKa value for any weak acid can be measured by titrating any weak acid with a strong base, in this case, sodium hydroxide (NaOH). The strong base is [^–OH], and it will react with the [H⁺] to form [H₂O]. 

The equation for the titration is as follows:

Notice that on the left side, water is not shown. That is because the concentration of water (55.5M) is very high and any change in its concentration will be negligible compared with the changes in concentrations of HA, and A^–. One can think of the above reaction as the [^–OH] removing the H⁺, and this causing the HA to change to A^– by the amount of [^–OH] added.

Here the disassociation of [HA] to [A^–] can be written as a constant called Ka.

Thus, the pKa is the 

As can be seen, the concentration of [A^–] will be the same as the [^–OH].

Examples of weak acids are acetic acid, phosphoric acid, amino acids, citrate etc. The acidity of weak acid, as described by their pKa values, indicates how easily the molecule will give up its proton in aqueous solution. 

For instance, acetic acid is a mono-protic acid with a pKa value of 4.76. In contrast, lactic acid is another mono-protic acid with a pKa value of 3.5. The lower the pKa value, the more acidic the molecule. Lactic acid is therefore more acidic than acetic acid and will easily lose its proton in aqueous solution where the pH is greater than 3.5. Recall, smaller Ka value means that the bond between the H⁺ and A^– (conjugate base) is weaker and H⁺ wants to leave more. Also note that the pH lower than 3.5 means that there is more H⁺ in solution and on the right-side of the reaction equation. Using Le Chatelier’s principle, we can conclude that both lactic acid and acetic acid will be in their protonated or acidic forms [HA] in solution at pH less than 3.5. In contrast, at pH 4.76, fifty percent of acidic acid is in the [HA] and [A^–] forms, while 10x as much lactic acid will be in the [A^–] state than in the [HA] state. (See below.)

In comparison, the pKa for the [C-H] bond of [CH3-CH3] (ethane) is very large. We know that ethane is not acidic at all and thus the Ka for [C] and [H] will be large.

Titration curve: Calculation of pKa for a weak acid

The pKa values of weak acids that are seen in textbooks are calculated by titration with hydroxide (^–OH). The easier it is to abstract the proton with the ^–OH, the more acidic the proton. Or by adding ^–OH, it will react with and remove the [H⁺] in aqueous solution:

Thus, by decreasing the [H⁺] on the right side of the equation, more HA will change to [A^–] by the same molar or equivalent amount.

In the example of a titration curve shown, acetic acid is being titrated with hydroxide. The structures of acidic acid and its conjugate base are shown below:

Figure 1 pKa and Weak Acid plotting sample

• By simply adding a known concentration of acetic acid (100 mM or 0.1M), it will immediately but partially disassociate to a small amount of its conjugate base. The amount of acetate (its conjugate base) and acetic acid is defined by its Ka or pKa value. (Note: The solution will become acidic as there will be more [H+] in solution. This is the reason why adding some vinegar in water taste bitter.)
• The initial pH of the solution can be calculated using the ICE equation performed in general chemistry. 

For simplicity, the acetic acid solution with the same concentration of hydroxide will be titrated. In this case, the molar equivalence of hydroxide to acetic acid is used. In a laboratory, one would use a burette containing 100 mM of NaOH. There will be a pH meter measuring the pH of the solution in the beaker as small amounts of the hydroxide is slowly added to the beaker. 

Figure 2 pKa and Weak Acid plotting sample

Interactive titration curve plotting  

The titration curve demonstrates that as hydroxide is added the pH increases. And rather quickly. Interact with the chart by moving the cursor on the line to see how increasing the concentration of [–OH] a small amount results in a larger increase of the pH value of the solution.

The relationship between pH and the amount of [HA] and [A^–] present is represented by the Henderson-Hasselbalch equation:

Note: As [^–OH] increases, [A^–] increases and correspondingly [HA] decreases.

In our example, if 10 mM of OH is added, then there will be 10mM of [A^–] and 90mM of [HA]. What is missing in this equation now is the value of pKa. While we do not know at present the value of pKa, using the titration experiment as example, it is something we are trying to determine. The change in pH is directly impacted by this pKa value. For acetic acid, the pKa is 4.76 and by plugging in the values, the pH can be determined. Move the cursor on the line to roughly where [OH] is 1/10 the molar equivalent point and identify the corresponding pH.

After the initial rapid rise in pH, notice on the curve that by adding more [–OH] the pH now changes by much smaller increments. The curve appears to flatten. In actuality, it is taking a considerable amount of [–OH] before the pH begins to rise rapidly again.

In our example the shape of the curve looks like a side-ways ‘S’ that’s a bit stretched out. After the flattened portion of the curve, the value of pH will increase and continue to increase because now base or ^–OH is being added and so the solution is becoming more alkaline. 

The flattened portion of the graph indicates that with added [^–OH] the pH is not changing much. The solution is being buffered. This is an important property of weak acids. They can also buffer aqueous solution from changes in [^–OH] or [H⁺], but only for a specific range. That range is ±1 pH unit from the pKa value. In the case of acetic acid, it has a buffering capacity between 3.76 and 5.76. The closer the pH of the solution is to the pKa value, the better the buffering capacity of the weak acid.

General assignment

Lesson activity 1: Understanding the titration plot

In this activity, the learner will have the opportunity to plot the titration curve for various acids by applying the principles of the Henderson-Hasselbalch equation. To accomplish this task, we will utilize the interactive chart provided above.

Steps for plotting the titration curve

1. On the same plot of pH vs [OH], draw the titration curves for lactic acid (pKa 3.75) and acetic acids as best as possible using concepts of the Henderson-Hasselbalch equation.
   1. Lactic acid: On the titration graph identify on the curve where there is 10x more conjugate base than acid.
   2. Acetic acid: On the titration graph add the curve for ammonium ion (NH4+), which has a pKa of 10.5.
2. Draw the structure of the predominate form of acetic acid at pH 7.0.

Lesson activity 2: Determining the pKa value

In this laboratory the learner will plot the curve of change in [-OH] versus pH and the result will be the flattened ‘S’ shape plot. To do this the interactive chart above should be used. Note the center region of the flattened or buffered zone in the curve. It is important to keep in mind that in this area the concentration of [-OH] is half the concentration of [HA].

Some important notes in plotting the curve

• The log of [A^–] / [HA] when both [A^–] = [HA] = 1 is zero. Thus, the pH is equal to the pKa. So, where the molar equivalent of [OH] is ½ that of [HA], the corresponding pH value will be the pKa value of the weak acid, which for acetic acid is 4.76.
• The buffered region corresponds to ±1 pH unit from 4.76. That is, the pH stops increasing rapidly between 3.76 and 5.76. Therefore, acetic acid can serve as a buffer in aqueous solution if we want to maintain a pH of the solution between 3.76 and 5.76. This is an important property of weak acid. 

Discussion activity: Rapid fluctuation of pH

Instructions: 

For either an in-person or online learning experience, discussion can help learners to draw meaningful connections to the content being learned and the real-world. For either in-person or online use the following topic and lines of exploration to add additional meaning to their learning.

In biological systems if the pH were to rapidly fluctuate, then biological processes will be disrupted. This is significant because a pH of less than 6.8 can be fatal in humans. Yet, human cells can buffer changes in pH and maintain a level of 7.4. The result is that consuming highly acidic drinks such as Coca-Cola, Pepsi or orange juice does not cause us harm.

Lines of exploration with learners

• Causes of rapid pH fluctuation.
• That which enables the cell buffering that protects them.
• Types of consumables we should be cautious about ingesting.

Defined success 

The intended outcome of this chemistry experiment was to equip learners with a comprehensive understanding of titration curves for various acids through the application of the Henderson-Hasselbalch equation. Through this experiment learners are expected to gain a good understanding of accurate plotting techniques for titration curves. This experiment also applied mathematical formulas related to titration graphs by referencing both Henderson-Hasselbalch equation and Le Chatelier's principles. Similarly, this experiment has laid out a good foundation to understanding pKa values and how they relate to the strength of weak acids. Learners are expected to be better prepared to tackle more complex chemical analyses and have a deeper appreciation for the fundamental principles underlying acid-base chemistry.

Additional resources

Design References

Henderson-Hasselbalch equation