Current timeTotal duration Google Classroom Facebook Twitter. Video transcript we've already talked about how to write an equilibrium expression so if we have some generic acid H a that donates a proton to h2o h2o becomes h3o plus and H turns into the conjugate base which is a minus and so here's our equilibrium expression and the ionization constant ka for a weak acid we already talked about the fact that it's going to be less than 1 so here we have three weak acids so hydrofluoric acid acetic acid and methanol and over here are the KA values so you can see that hydrofluoric acid has the largest KA value so even though they're all considered to be weak acids all right 3.
Ka and acid strength. Using a pKa table. Up Next. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products.
List of Partners vendors. Share Flipboard Email. Anne Marie Helmenstine, Ph. Chemistry Expert. Helmenstine holds a Ph. She has taught science courses at the high school, college, and graduate levels. Facebook Facebook Twitter Twitter. Updated January 30, The lower the pKa, the stronger the acid and the greater the ability to donate a proton in aqueous solution. The Henderson-Hasselbalch equation relates pKa and pH.
However, it is only an approximation and should not be used for concentrated solutions or for extremely low pH acids or high pH bases. Depending on the sample and matrix under investigation, the choice of technique can be a difficult one, even for the case of monovalent ions, to which this paper is limited to. For multivalent components, matters are more complicated as the pK a differences are smaller.
This is because all methods, except perhaps for nuclear magnetic resonance NMR , require curve fitting in addition to the normal calculation procedure for the respective technique. Investigating both acidic and basic pK a of amphoteric compounds also requires curve fitting in a much broader range. For such compounds, especially peptides and proteins, the isoelectric point is often relevant for identification purposes but beyond the scope of this paper.
Figure 5 displays an overview of the first time these techniques where used for this purpose. Timeline of the first notion of the various techniques to determine pK a dissociation constant, acid strength.
The simplicity and low cost of potentiometric titration has made it one of the most commonly used methods for pK a determination. In a potentiometric titration, a known volume of reagent is added stepwise to a solution of analyte. The change in potential E upon reaction is consequently measured with the use of two electrodes, an indicator, and a reference electrode. These are often integrated in what is now commonly called a combined pH electrode.
Plotting the potential versus volume subsequently gives rise to a sigmoid curve, where the inflection point gives the potential at equilibrium.
With the use of standards with known pH, this potential can be linearly converted into a pH, equaling pK a. Increasing understanding of electrochemical processes in the late 19th century gave rise to the first potentiometer.
The first description of the use of a setup to determine equilibrium constants was made by Denham in It was not long until the cumbersome hydrogen electrode was replaced by the familiar glass electrode. Completely automated and self-adjusting pH-measuring equipment by Keeler is known from as early as Because temperature influences not only the measurement but also the pK a itself, it is of vital importance to conduct the titration at constant temperature.
A good review about the various errors of the electrode itself is given by Gardiner 19 while Benett 20 discusses the various ways to determine pK a from the measured potential. Another practical complication is the pK a -measurement of substances with a low water-solubility. One example is extrapolation of measurements in solvent mixtures.
A precise determination of the pH from the titration slope has also been difficult in the earlier period of its use. However, over the years various software programs have become available to minimize most of the previous mentioned errors. Potentiometric titration requires a relatively large amount of sample compared with separation methods such as high performance liquid chromatography HPLC and capillary electrophoresis CE.
Completely automated potentiometric pH meters for a wide range of applications and with complicated calibration software are widely available. Because of this and the simplicity and relatively low costs associated with the potentiometric pH-meter, it will probably remain in use in the foreseeable future. This of course only holds for those analytes that are available in sufficient quantity and purity. The determination of acid dissociation constants by conductometry relies on the assumption that strong electrolytes are completely dissociated at all concentrations, while weak electrolytes only attain complete dissociation at infinite dilution.
A measurement of the conductivity of a sample yields a value that is the sum of the independent contributions of all ions present in the solution:. It can also be seen from Figure 6 , however, that this linear extrapolation does not hold for weak acids or bases.
This is because for these electrolytes, the assumption that all ions are independent of their counter ions does not hold as these species are not fully dissociated.
Though the limiting conductance of a weak electrolyte cannot be directly extrapolated, their value can still be obtained quite readily.
Even for weak electrolytes, the Kolhrausch law 23 of the independent migration of ions holds. This law can be stated as meaning that at infinite dilution, each ion makes a specific contribution to the conductivity regardless of the ions associated with it.
Expressing the limiting conductance of a salt in terms of ionic contributions is useful as it allows the calculation of the limiting conductance of a weak electrolyte. In order to do this, the limiting conductance of other relevant salts of a strong electrolyte is extrapolated. For a weak acid formic acid relevant plots are shown in Figure 6. One would obtain the ionic contributions for the limiting conductance of the acid from the salt of its conjugate base and from hydrochloric acid, subtracting the value for sodium chloride to eliminate the ionic contributions of the sodium and chlorine counter ions in the reference compounds.
This yields the sum shown in Equation 8 :. Equation 9 yields the dissociation constant for a given analytical concentration c and a series of measurements would yield the dissociation constant as a function of ionic strength. It is worth noting that this determination does not require knowledge of the pH of the solution, making it easily applicable to non-aqueous systems where such a measurement of pH would be impracticable.
It also means that the method, unlike many others which express their measured quantity as a function of pH, is not constrained by the precision of the pH electrode. This requires working with pure compounds. Foundational work that enabled the development of the conductometric method was undertaken by Friedrich Kohlrausch.
Among the key ideas he developed was the use of alternating current to prevent electrolysis during conductivity measurements. His work examining a variety of electrolyte solutions led to the law of independent migration of ions that is ascribed to him. Building on this early work, and further contributions by Ostwald and Arrhenius, the method reached maturity during the late s, and the accuracy of the method approached that of modern methods. Work on the conductometric method came to a virtual standstill after the outbreak of World War II, and further research was practically abandoned after the end of the war.
Renewed activity would not come until the s, when two new conductance equations were published. These equations enabled the study of asymmetrical electrolytes, and even mixtures of electrolytes. Since then, it has been remarked that the spectacular interest for the method that existed during its early period has waned with time, leaving the subject a somewhat unfashionable topic of research. With the developments made over its history, however, the method has achieved a high degree of precision.
In voltammetry, a changing potential is applied over a sample solution and the resulting current is measured. When the potential reaches the reduction potential of the analyte this will give rise to an increase in current, followed by a decrease due to depletion of the molecule. In the case of cyclic voltammetry, for example, this will lead to results much like those shown in Figure 7.
Example of a cyclic voltammetric curve. The upper line represents an increase in potential, the lower line the following decrease. A typical voltammetry setup usually consists of 3 electrodes: reference, working, and auxiliary electrode. The working and auxiliary electrodes act as the anode and cathode, respectively, while the reference electrode acts as a fixed point to measure the applied voltage. Modern-day voltammetric methods can be extremely sensitive; with specific techniques it is possible to accurately measure very low concentrations.
The earliest use of voltammetry was the use of a dripping mercury electrode in by Jaroslav Heyrovsky to develop the first polarograph. When the pK a of a substance is being determined voltammetrically, one could in principle measure the electrochemical response of the molecule itself. The shift of the peaks of the reference upon addition of the acid is then used to determine the pK a value.
Additionally, its concentration should be in the same order as that of the analyte to give optimal sensitivity. More recently, advanced techniques have been developed such as those measuring the surface pK a of self-assembled monolayers. The reason for this is the need for an electro-active molecule which is soluble in a conductive solvent. Also, it is often necessary to recalibrate the apparatus when different samples are used.
On the other hand, voltammetry has some advantages. It is of particular use in measurements of pK a values in less polar solvents, something which is often difficult to do accurately with the use of techniques such as potentiometric titration.
Another advantage over other techniques is that it is able to conduct a quantitative measurement of different oxidation states. All calorimetric methods work by the same principle: a physical or chemical process takes place in a sample and the amount of heat evolved is measured.
Here, a regular acid-base titration is carried out inside the calorimeter while the energy needed to keep the temperature constant is measured. It is also one of the oldest analytical techniques. The first recorded model was made by Lavoisier and Laplace in In recent years, the ITC-method has been used to measure the dissociation constants of peptides and the influence of binding on the specific ionizable groups. Here the reagent for the ionizable groups is added in equivalent amounts and at once.
The resulting heat released upon reaction is measured in buffer solutions with different pH values Fig. By plotting the minima or maxima versus pH, a sigmoid curve is obtained from which the pK a can be determined from the inflection point. Curves created after a typical direct measurement of pK a with the use of calorimetry.
The amplitude of the minimum at different pH values is proportional to the degree of dissociation. Before NMR was used to determine acid dissociation constants, the technique was already applied to determine the site of deprotonation of an acid, or the site of protonation of a base.
In , Grunwald et al 48 used NMR to determine the pK a of mono-, di- and trimethyl-amine, thus determining the chemical shift of the triplet from the protons in the CH 3 group s as a function of pH. A linear correlation was found between the chemical shift and the acid-base ratio. Experiments could be carried out in water by using a reference measurement.
A sigmoid curve is obtained from which the pK a was calculated. Pioneering work was performed by Lee et al, 49 who determined the pK a values of a wide range of functional groups with good concurrence towards existing literature. Based on his work, further knowledge of the pH-chemical shift relation was described and published. Because the equilibrium is pH dependent, the chemical shift will also change with the pH level.
For this situation, the pK a can be written as Equation 10 :. This yields a familiar sigmoid curve where the pK a is located at the inflection point. Instead of performing a continuous titration, a known amount of a strong acid or base is added to different samples constant volume titration , from which the pH is consequently calculated. This however neglects the influences of the target molecule on the pH and the risk of a systematic error is added.
The main advantage of the NMR technique is that it is possible to measure mixtures, even when impurities are present, because mole fractions are observed instead of the total acid concentration, in contrast to potentiometric titrations. When observing the chemical shift of one characteristic group, no other groups are involved, so even the pK a values of diprotic acids with pK a values close together can be observed separately, provided that the chemical shifts do not overlap. With this characterization method, even more complex molecules, such as enzymes can be fully characterized.
So, the pK a of individual acid sites on complex molecules can be determined, making this a promising technique for further development. This was discovered by Rabenstein and Sayer in who determined microscopic dissociation constants for polyprotic acids by means of curve fitting.
The main errors for the NMR method are found to be caused by imprecision of the chemical shift and the pH level, which is calculated and not measured. Because an internal reference can interfere with the acid-base equilibrium, an external reference is recommended, either with an extra measurement or a second co-axial sample tube. Control of temperature in NMR is often not a problem, but when performing NMR the fact that energy dissipation can occur must be taken to account; locally, at the vibrating nucleus of interest the temperature can rise.
Glaser et al presented the first fully-automated NMR apparatus for measuring the pK a. With this automation and stronger magnets, the NMR technique is a promising technique to measure multiple enzymes at specific de- protonation sites within a reasonable time frame.
For less complex acids and bases with only one protonation site, however, this technique is rather expensive. In electrophoresis, charged species are separated under the influence of an electric field, migrating with a velocity proportional to their size-to-charge ratio.
The ratio of the linear velocity v i and field strength E is defined as the electrophoretic mobility m i :. The relation with previously discussed conductometric methods and electrophoretic ones is important: in the latter we measure individual mobilities m i Equation 11 whereas in the former we measure the sum of mobilities of all ions together Equation 7.
They are interrelated on the basis of individual ions using the Faraday constant F:. The use of electrophoresis for the determination of the pK a value depends on the differing mobilities of the protonated and deprotonated forms of the analyte. When the degree of dissociation for acids is expressed in terms of mobility, one obtains the relation shown in Equation 13 :. Here, m eff is the effective mobility, m d is the mobility of the fully dissociated species, and m 0 the mobility of the non-dissociated species which equals zero.
For bases, a similar equation is derived. A sigmoid curve is obtained by plotting m eff vs. Model equations can be derived for weak acids and bases with any number of ionizable centers by rewriting Equation These models for species with up to three ionizable centers were summarized in a review article by Poole.
Curve fitted to data for electrophoretic mobility of 2-aminopyridine as a function of pH, data from Poole et al. The shape of these curves depends only upon m d and the position depends only upon pK a , therefore this regression directly yields the pK a value s of interest.
The method has a number of key advantages in comparison to more traditional alternatives. This allows for the processing of poorly soluble species without much difficulty. Since electrophoresis is a separation technique, impure samples can be readily processed and as the molecules are measured directly, exact knowledge of sample concentrations is not required.
In addition, commercially available equipment is capable of automatic operation without requiring modification, allowing large numbers of measurements to be conducted at speed. This makes the method quite suitable for screening applications. The relationship between the electrophoretic mobility of an acid or base and the pH of the background electrolyte was already considered when Consden and Martin 56 published their paper on ionophoresis in , which discussed the separation of two analytes based on a difference in their pK a values.
This relation was explicitly applied to the estimation of acid dissociation constants by Waldron in the s 57 and by Kiso et al in the s 58 using a paper strip as a supporting medium. However, despite the known advantage of requiring only minute amounts of sample, both methods were found to be impractical in application. Improvements over the next decades would eventually lead to the introduction of the fused silica capillaries.
By the end of the s, isotachophoresis was considered a viable method for the determination of dissociation constants. While the method showed reduced precision in comparison to potentiometric or conductometric methods, this was offset by its faster measurement times and lower sample requirements.
To avoid the complexities and limitations of isotachophoresis, it was proposed that the simpler method of capillary zone electrophoresis be used specifically for the determination of mobilities and pK a values. The potential sensitivity of the method had already been demonstrated 61 and further refinements of the technique would be made over the next few years.
A general methodology for the determination of pK a values by CE was proposed in , and further refined by the addition of terms concerning the rate of electroosmotic flow and a method of handling potential discontinuities between buffer electrolytes.
Developments over the next decade would include further examinations of the pK a equations, comparing different regression techniques, and better experimental methods. The first observation that the time of elution can be changed by adjusting the pH level was made by Singhal. Plotting k vs. The similarity of Equations 13 and 14 are immediately obvious. A solid theory was formulated by Foley 73 , 74 where the pH dependence of the capacity factor follows the dissociation curve. Again, some recommendations and optimizations were formulated to improve selectivity, retention, and efficiency.
Of course, the addition of organic modifiers decreases all k values but hugely complicates matters if we desire aqueous pK a values. The first investigation into the division of a substance between two immiscible solvents was carried out by Berthelot and Jungleisch in They came to the important conclusion that the ratio of the concentration was a constant, e.
Following up on this research, Nernst concluded in that the partition coefficient P was only a constant if a single substance was considered. Later insight further revealed that for ionizable components, the partition coefficient depended on the pH of the aqueous phase. In the limiting case where the ionization is completely suppressed by pH for bases, for example, at high pH a distribution coefficient D can be defined mathematically for bases :.
Several derivations for pK a from P and D are found in literature, 76 , 77 but all of them result in roughly the same expression for bases as they combine Equations 1 , 15 , and 16 :. There are two main techniques used to determine log P.
In some specific cases, the technique used to determine pK a by P is largely unaffected by the choice of solvent. The use of partition coefficients to determine pK a is not used extensively.
Partition coefficients are however still very much in use in drug development as they give information about the uptake of a certain drug in various parts of the body. A particularly illuminating example of this follows. In some surgeries, the body temperature and blood pH values deviate from normal values.
This naturally affects the log P value and drug efficacy. Thurlkill et al 81 reported an additional aspect for the case of Fentanyl, a local anesthetic. It was found that its pK a significantly depends on temperature, which might lead to further complications in drug administration, in other words a temperature and blood gas dependent bioavailability. In , Krebs 82 described the relationship between pH, pK a , and the solubility of sparingly soluble weak acids and bases, where a derivation of the Henderson-Hasselbalch equation was used to describe the behavior.
A drawback of this method at that time was the solubility of the non-ionized analyte had to be known, which was not often the case. This theory was further expanded by Zimmerman et al 83 who made mathematical derivations by which it was possible so determine the solubility of the neutral analyte and the pK a. By these means, the solubility of the neutral compound was no longer required and the use of solubility data to determine the pKa was much more applicable.
A derivation of the Henderson-Hasselbalch equation allows us to determine the pK a from solubility data, the graphical representation is shown in Figure A plot of the pH dependence of the solubility of an acid with pK a 4. Here S 0 is equal to the intrinsic solubility. By extrapolating these two functions and calculating the intercept, the pK a can be calculated:. In the later years, pK a values for zwitterionic compounds were determined 85 and a solid method for the bi-functional bases and acids was formulated.
Under certain conditions the pH does not change under addition of more titrant. This pH is known as the Gibbs pK a. Nowadays, the solubility data are used to determine pK a values for a wide range of drugs, where the pK a value is of great interest.
Therefore, solubility measurements for pK a determinations can be used for sparingly soluble compounds which have a chromophore near the ionization center. Well before , it was already known that a change in acidity could lead to color changes of natural substances.
If this is fulfilled, then the spectra of the dissociated and the non-dissociated form can be expected to differ. In principle any wavelength can be used for the determination of pK, except at the isosbestic point at which wavelength of both forms have the same molar absorptivity. The best choice however is a wavelength at which the molar absorbtivities are as different as possible. The method was further improved by measuring the absorption of two different wavelengths at a variable pH.
The ratio in absorption at those two wavelengths is plotted against the pH. In this way, a sigmoid curve is obtained and the pK a can be determined from the inflection point as normal. One of the wavelengths has to be assigned to the chromophore and the other wavelength should be invariant under change of pH if this is possible.
This was then further elaborated by Flexser et al 89 in by determining different ionization constants. In the s, Wigler et al 90 , 91 were the first to determine pK a values of di-protic compounds.
Up to this point, the pK a values calculated required prior knowledge of experimental data, such as the absorption coefficients of the neutral and ionized compound. By measuring over a whole wavelength range, Allen et al 92 were able to determine the pK a values without this prior knowledge. The measurements could also be done much faster. This method showed good concurrence with previous single wavelength methods 93 and was later highly automated by Saurina et al.
It can be argued that fluorometry is a specific form of spectrometry as any fluorescence is the result of light absorption, while the reverse is not the case. The use of fluorescence spectroscopy to determine pK a values depends on the difference in the fluorescence spectrum between a free acid or base and its conjugated form.
While fluorometry can potentially be more sensitive and selective than conventional spectrometry, it has the disadvantage of being only applicable to fluorescent analytes. Additionally, it is known that the pH dependence of fluorometry often does not agree with those obtained from spectrometry or other methods. The reason for this is that the former depends on excited state proton exchange as well as the ground-state equilibrium. In spite of these challenges, a successful determination of the ground-state pK a values of sparingly soluble N-heterocyclic bases was accomplished by Rosenberg et al.
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