5 Easy Methods to Calculate pKa: Titrimetric,UV, HPLC, NMR And Henderson Equation

pKa is the negative base 10 logarithm of Ka (acid dissociation constant) of a solution.

It plays a unique role in the pharmaceutical development process. Be it chromatographic analysis or titration, or chemical synthesis, everywhere it acts as an important deciding parameter. However, determining the pKa is a complex task. That’s why I decided to share my skill-based knowledge on this topic. In this article, I will discuss 3 simple techniques, titration, UV spectrometer and Nuclear magnetic resonance (NMR) to calculate pKa with case studies and FAQs

pKa

pKa is the negative base 10 logarithm of Ka (acid dissociation constant) of a solution.

pKa = -log₁₀Ka

The pKa of a compound is a measure of the acidity of the compound in solution. pKa is used to compare the strengths of acids; a lower pKa indicates a stronger acid.

Relation between pKa and pH: Henderson equation

The following is the relationship between pH and pKa:

pH = pKa + Log10 ([Salt]/[Acid])

or

pH = pKa + Log10 ([A^–]/[HA])

Where [A^–] is the molar concentration of conjugate base and HA is the molar concentration of acid.

The above equation is also known as the Henderson equation, which is used to calculate the pKa of a molecule.

Note: When the concentration of acid or [Unionised acid] becomes equal concentration to [salt] or [Ionised], then:

pH = pKa

Note: The above equation is used to calculate pKa

How to Calculate pKa?

The following methods are used to determine the pKa:

1. Titrimetric Method
2. Spectroscopic Method
3. HPLC Method
4. Using the Henderson Equation
5. Databases and Literature
6. NMR Method

1. pKa Calculation by Titrimetric Method

In this method, the compound is dissolved in water or a mixture of water and suitable solvent/solvents. The solution is titrated against 0.1N Sodium hydroxide volumetric solution (or any other lower concentration) and pH is measured beyond the endpoint.

pKa = pH at half of the endpoint volume

Steps to Calculate pKa

Use the following steps to determine the pH by the titration method:

1. Prepare the solution: Weigh accurately about 100 mg of the sample. Dissolve the compound in water (or any other appropriate solvent) and measure its concentration
2. Prepare 0.1N NaOH volumetric solution
3. Titrate the solution drop by drop with 0.1N NaOH
4. Note the pH of the solution after each addition of 0.1N NaOH  and the volume of 0.1N NaOH consumed
5. In the beginning, the pH will increase slowly after each addition
6. But there will come a point where the pH of the solution will increase after adding 0.1N NaOH. This is called the equivalence point. Note the volume of 0.1N NaOH consumed along with the pH
7. Plot the graph between pH and 0.1N NaOH volumetric solution
8. Identify the half-equivalence point: Find the volume of 0.1N NaOH consumed at half of the equivalence point and note down the corresponding pH
9. The pH at half the volume of 0.1N NaOH consumed at the equivalence point will be the pKa of the molecule

Note:

• Only use a calibrated pH meter
• The equivalence point, or inflex­ion point, is where the amount of acid equals the amount of base
• At the half-equivalence point, the concentrations of the acid and its conjugate base are equal. The pH at this point corresponds to the pKa of the acid

Case Study: How to calculate pKa of Acetic Acid (CH₃COOH) By Titration Method

Requirements

• 0.1M Acetic acid solution
• 0.1N NaOH Volumetric solution
• pH meter
• Magnetic stirrer
• Magnetic bead

Procedure

• Prepare 0.1M Acetic acid solution in water and transfer 50 ml of it into a 100 ml beaker
• Titrate the above solution with 0.1N NaOH volumetric solution
• Record the pH after every 0.1ml of addition of 0.1N NaOH
• In the beginning, the pH will increase slowly after each addition
• But there will come a point where the pH of the solution will increase after adding 0.1N NaOH. This is called the equivalence point. Note the volume of 0.1N NaOH consumed along with the pH
• Plot the graph between pH and 0.1N NaOH volumetric solution
• Continue to take 4 to 5 more readings.

Result discussion

• Equivalent point: In this case, the Equivalent point is 25 ml of 0.1N NaOH
• Half Equivalent point: In this case, it is 12.5 ml of 0.1N NaOH
• The corresponding pH at half the equivalence point is about 4.76, and hence the pKa of acetic acid will be 4.76

Table: 0.1N NaOH vs PH

Expert Tips

• At the half-equivalence point, the concentration of the acid is equal to the concentration of its conjugate base.
• According to the Henderson-Hasselbalch equation, when the concentrations of the acid and its conjugate base are equal, the pH of the solution equals the pKa of the acid.
• Therefore, the pH at the half-equivalence point is the pKa of the acid.

2. pKa Determination by UV-Visible Spectroscopic Method

The pKa can be determined from spectroscopic data, especially if the compound has a chromophore. When the pH changes, the position of the absorption peak may shift due to ionisation, and this shift can be used to determine the pKa by plotting absorbance vs. pH.

Case Study: How to calculate pKa for Phenol (C₆H₅OH) by UV Method

Phenol is a weak acid and it ionize in basic conditions to form phenoxide ion (C₆H₅O⁻).

C₆H₅OH = NaOH ⇌C₆H₅O⁻ + H₂O

Phenol (C₆H₅OH) absorbs UV light at different wavelengths than its conjugate base phenoxide (C₆H₅O⁻). This gives a chance to monitor the changes in absorbance as the pH is varied.

Procedure:

The following 5-step procedure plays a vital role in determining the pKa by UV method:

1. Prepare a stock solution of phenol:
   • Prepare 100mcg/ml of Phenol solution in water (or any other appropriate solvent).
2. Prepare a 10mcg/ml solution of phenol in four different buffer solutions at pH 3, 4, 5, 6 7, 8 9, 10, 11 (from stock solution):
   • The range should cover the pH where the ionisation of phenol is expected to occur.
3. Measure the UV-Vis spectra:
   • Use a UV-Vis spectrophotometer to measure the absorbance of each solution over the range of wavelengths where phenol and phenoxide are known to absorb (typically 200–400 nm).
   • Record the absorbance at the wavelength corresponding to the peak absorbance of phenol and phenoxide. Phenol typically absorbs around 270 nm, while the phenoxide ion absorbs around 280 nm.
4. Plot the absorbance vs. pH:
   • For each pH, note the absorbance at the specific wavelength for both phenol and phenoxide (if different wavelengths are observed for each form). Plot the absorbance at each wavelength against the pH of the solution.
5. Determine the pKa:
   • The pH buffer at which the Phenol gives the same absorbance at both wavelengths ( 270nm and 280 nm) is taken as the pKa of phenol

Result: pKa of phenol is approximately 9.95

3. pKa Determination By HPLC Method

High-performance liquid Chromatography (HPLC) has become a useful technique for measuring the pKa values of compounds having low solubility in water due to its precision, accuracy and Reliability. It determines the pH at which a molecule exists in a 50/50 mixture of protonated and deprotonated forms.

The pKa of a compound can be determined by measuring its chromatographic behaviour under different pH conditions. The retention time of the analyte in an HPLC system is affected by its ionisation state. A compound’s retention time will change as a function of pH because:

1. At lower pH, the compound will be more protonated.
2. At higher pH, the compound will be more deprotonated.

By plotting the retention time of the analyte against the pH of the mobile phase, you can determine the pH at which the compound undergoes a transition between its protonated and deprotonated forms (i.e., the pKa).

Case Study: How to determine the pKa of the following Compound A by the HPLC method

Experimental Setup:

1. HPLC System:
   • Column: C18 reversed-phase column (250 mm x 4.6 mm, 5 µm particle size) or equivalent column
   • Mobile phase: A mixture of water (adjusted with acids or bases) and acetonitrile (ACN)
   • Detector: UV-VIS detector at 254 nm
2. pH Range:
   • The pH of the mobile phase was varied from 2.5 to 9.0. This range was chosen to cover the expected pKa values of the compound.
3. Sample Preparation:
   • A standard solution of Compound X (10 µM) was prepared in the mobile phase.
4. Chromatographic Conditions:
   • Flow rate: 1.0 mL/min
   • Column temperature: 25°C
   • Injection volume: 20 µL

Procedure:

1. Prepare Mobile Phases with varying pH:
   • Prepare a series of mobile phases with different pH values by adjusting the pH using either Phosphoric acid or sodium hydroxide (NaOH).
2. Inject Samples:
   • Inject the same sample of Compound under different pH conditions and record the retention times.
3. Plot Retention Time vs. pH:
   • As the pH changes, monitor the retention time of Compound A. The retention time will change as the compound goes from a more protonated form (at low pH) to a more deprotonated form (at high pH).
4. Identify pKa:
   • The inflexion point on the retention time vs. pH plot corresponds to the pKa of the compound. The inflexion point is the pH at which the rate of change in retention time is maximal, indicating a transition from protonated to deprotonated forms.

Results Interpretation:

After performing the HPLC analysis interpret the result such as:

• At pH 2.5, the retention time of Compound A was 8.5 minutes.
• At pH 4.0, the retention time decreased to 7.0 minutes.
• At pH 5.5, the retention time continued to decrease to 5.5 minutes.
• At pH 7.0, the retention time was 4.0 minutes.
• At pH 9.0, the retention time remained at 3.5 minutes.

The plot of retention time vs. pH showed a significant drop in retention time around pH 5.0, suggesting a change in the ionisation state of the compound.

Interpretation:

• The pKa of Compound A is approximately 5.0, based on the inflection point where the retention time decreased significantly.
• Below pH 5.0, Compound A is primarily protonated (as COOH), which results in stronger interactions with the stationary phase and longer retention times.
• Above pH 5.0, Compound A becomes deprotonated (as COO-), which interacts less strongly with the stationary phase, leading to shorter retention times.

Advantages of pKa Determination by HPLC:

1. High Sensitivity, Accuracy and Reliability: HPLC can detect even trace amounts of a compound, providing accurate pKa values for very low-concentration samples.
2. No Need for Complex Buffers: pKa determination by HPLC does not require complex buffer systems, making it simpler than traditional methods like potentiometric titration.
3. High Throughput: Multiple samples can be analysed quickly by adjusting the pH of the mobile phase, enabling rapid screening of compounds.
4. No Need for Large Sample Volumes: Only small amounts of sample are required, making it suitable for limited quantities.

4. pKa Calculation Using Henderson’s Equation

Case study: Calculate the pKa value of acetic acid when Ka of acetic acid is 1.8 x 10^-5

Here Ka of acetic acid is 1.8 x 10^-5. Hence from equation-2 pKa of acetic acid will be

pKa = -log₁₀(1.8 x 10^-5 ) or pKa =-{log₁₀(1.8) +-log₁₀(10^-5 )} or pKa = -{0.255 – 5) =4.775

5. pKa Using Databases and Literature

Sometimes, the pKa of a compound can be found in published literature or chemical databases. Many common compounds have well-established pKa values that can be directly referenced. Databases like the CRC Handbook of Chemistry and Physics or specialized databases like PubChem or ChemSpider can be useful.

Typical compounds and their pKa

^. New Advancement: pKa Determination by NMR

NMR (Nuclear Magnetic Resonance) spectroscopy can provide information about the protonation state of a molecule, allowing for the determination of pKa. Changes in the chemical shifts of specific protons can indicate the pKa, especially if the proton environment changes significantly upon protonation/deprotonation.

Case Study: Determination of pKa of Acetic acid by NMR method

Determining the pKa of a compound by NMR spectroscopy is a useful method for studying the acid-base properties of a substance in solution. The general approach relies on observing the shift in the NMR chemical shifts of protons (or carbons) as a function of pH, which allows the determination of the pKa values of acidic or basic functional groups.

Procedure:

The following are step-by-step procedures for how to determine the pKa of a weak acid using proton NMR:

1. Prepare the Solution:
   • Prepare a series of solutions of the acetic acid in a solvent (commonly D2O or a mix of D2O and water).
   • Vary the pH of the solutions by adding small amounts of a strong acid (HCl) or strong base (NaOH), and take measurements at different pH values. Usually, a buffer solution is used to control the pH.
2. Acquire NMR Spectra at Different pH Values:
   • For each pH value, record a 1H NMR spectrum (proton NMR). It’s essential to measure the spectrum across a broad range of pH values (e.g., from pH 2 to pH 12).
3. Identify the Relevant Proton Signals:
   • Identify the proton signals that correspond to the protonated and deprotonated forms of the molecule. In the case of acetic acid, you would observe a signal from the carboxylic acid proton (–COOH) at lower pH and a different signal from the carboxylate anion (–COO⁻) at a higher pH.
   • As the pH changes, these proton signals will shift because of changes in the electronic environment of the molecule.
4. Monitor the Chemical Shift Changes:
   • Measure the chemical shift of the relevant proton(s) (usually the proton on the functional group like –COOH or –NH₂).
   • As the pH increases (the solution becomes more basic), the carboxylic acid proton will deprotonate, causing the NMR signal of the carboxyl proton (–COOH) to disappear and a new signal from the deprotonated carboxylate (–COO⁻) group to appear.
   • Track the changes in chemical shifts and relative intensities of the peaks over the pH range.
5. Plot the Chemical Shift vs. pH:
   • Plot the chemical shift of the proton signal of interest (usually the proton on the functional group) as a function of pH.
   • The data will typically form a sigmoidal curve that shows two distinct regions:
     • One where the proton is mostly in the protonated form (at low pH).
     • One where the proton is mostly deprotonated (at high pH).
6. Calculate the pKa:
   • The pKa corresponds to the pH at which the concentration of the protonated and deprotonated species is equal. This is where the curve is steepest.
   • The pKa can be determined from the pH at which the chemical shift of the proton is halfway between the values for the protonated and deprotonated species.

NMR Data Interpretation:

• At low pH (e.g., pH 2–4), you might observe a signal at 12.0 ppm for the –COOH proton.
• As you increase the pH, the protonated –COOH form will deprotonate, and you will see a shift in the signal to a new resonance, often around 2.0–3.0 ppm for the –COO⁻ group.
• The pKa value is approximately at the pH where these two signals are equally intense or where the chemical shift shows a noticeable midpoint transition.

Key Considerations:

• Resolution: The NMR should have good resolution, especially if you are observing subtle changes in chemical shifts.
• Temperature: Conducting the experiment at a constant temperature (usually room temperature) helps to minimise any temperature effects on the pKa.
• Buffer Choice: Choose an appropriate buffer range that covers the expected pKa of the compound.

Notes:

• Multi-proton Systems: If the compound has multiple acidic or basic sites (e.g., carboxylic acid and amine), you can analyze the pKa values of each functional group separately by monitoring their respective NMR signals.
• Other NMR Techniques: For more complex compounds, 2D NMR (such as COSY, NOESY, or HSQC) might be employed to better resolve overlapping signals or to examine the proton-proton interactions at different pH values.

Applications of pH and pKa

The following are some important applications of pKa;

• pKa are very helpful in HPLC method development
• pKa defines whether a molecule is a strong acid or weak acidic
• pKa is very helpful in drug development. For example, pKa influences the solubility, oral absorption, distribution, and pharmacokinetics of a drug
• pKa helps in determining the ionisation state of a drug at different physiological pH levels

Conclusion

Titration, UV-Vis spectroscopy, NMR, HPLC and Handerson equation methods are the effective methods for determining the pKa of weak acids and bases. The above case studies demonstrate how these methods provide an accurate and reliable means of measuring pKa, which is essential for pharmaceutical and chemical applications. Out of the above methods, the titration method and UV spectroscopic methods are widely used in pharmaceutical industries. I hope this article will clear all your doubts related to pKa, and now you can easily find out pKa for your research work using these simple techniques.

Related

• Relative Response Factor (RRF) in Pharmaceutical Analysis

FAQs: Top interview questions on pKa

References:

• Importance of pKa
• pKa Value – Definition, Calculation and Conversion
• usp31nf26s1_c1160, General Chapters – uspbpep.com