The acid dissociation constant (pKa) is among the most frequently used physicochemical parameters, and its determination is of interest to a wide range of research fields. We present a brief introduction on the conceptual development of pKa as a physical parameter and its relationship to the concept of the pH of a solution. This is followed by a general summary of the historical development and current state of the techniques of pKa determination and an attempt to develop insight into future developments. Fourteen methods of determining the acid dissociation constant are placed in context and are critically evaluated to make a fair comparison and to determine their applications in modern chemistry. Additionally, we have studied these techniques in light of present trends in science and technology and attempt to determine how these trends might affect future developments in the field. Fourteen methods of determining the acid dissociation constant are placed in context and are critically evaluated to make a fair comparison and to determine their applications in modern chemistry. Additionally, we have studied these techniques in light of present trends in science and technology and attempt to determine how these trends might affect future developments in the field. Although Henderson defined K in terms of a concentration ratio in 1908, it was not until 1916 that Hasselbalch 7 proposed their now famous equation (1) , which remains the most commonly used equation to calculate pK a values: the Henderson-Hasselbalch equation. It relates pH and pK a to the equilibrium concentrations of dissociated acid [A − ] and non-dissociated acid [HA] respectively: (1) pH = pK a + log ( [ A - ] / [ HA ] ) In many experimental methods to determine pK a values, a certain parameter is measured as a function of pH. This results in a characteristic sigmoid curve ( Fig. 1 ) from which the pK a may be determined by locating the inflection point. The degree of dissociation α for acids is defined as: (2) α = [ A - ] / ( [ HA ] + [ A - ] ) Combining Equations 1 and 2 leads to (for anions): (3) Log ( α / ( 1 - α ) ) = pH - pK a However, for concentrated solutions or pK a ’s near the extremes of the pH scale, it has been shown that there are significant differences between the predicted and actual concentration of the hydrogen ion. 8 Since the Henderson-Hasselbalch equation only gives accurate results for dilute acids in aqueous solutions, another formula for the quantification of acid strength was developed by Hammett. 9 Instead of measuring the concentration of the species present in solution, Hammett described the strength of an acid as the relation between the hydrogen ion activity (a) and the activity coefficients (f) of the various species in solution. However, difficulty associated with accurate determination of the parameters in this model has kept it from being as widely used as the Henderson-Hasselbalch equation. Influences on pK a In spite of being universally referred to as a constant, the dissociation constant pK a is not in fact truly constant; it depends on temperature (T), ionic strength (I), and the solvent dielectric constant (ɛ). This yields the sum shown in Equation 8 : (8) Λ 0 HA = Λ 0 NaA + Λ 0 HCl - Λ 0 NaCl Once the limiting conductance is known, the degree of dissociation (α) for a weak electrolyte is given by α = Λ/Λ 0 . An apparent dissociation 26 In order to obtain the true thermodynamic acid dissociation constant K a , one has to correct for the activity of the ions: (9) K ′ = Λ 2 · c / ( Λ 0 · ( Λ 0 - Λ ) ) 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. 28 In contrast to the earlier period, which focused mainly on obtaining thermodynamic dissociation constants, experiments performed after this period were additionally concerned with correlating this data with the structure of the organic acids being studied. 29 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 1970s, when two new conductance equations were published. These equations enabled the study of asymmetrical electrolytes, and even mixtures of electrolytes. Solubility In 1945, 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. 82 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. 83 A derivation of the Henderson-Hasselbalch equation allows us to determine the pK a from solubility data, the graphical representation is shown in Figure 10 . (18) log S = log S 0 + log ( 10 - pK - pH + 1 ) Here S 0 is equal to the intrinsic solubility. When pH >> pK a or pH << pK a assumptions can be made and linear log S/pH functions are obtained. By extrapolating these two functions and calculating the intercept, the pK a can be calculated: (19) log S = ( log S 0 - pK a ) + pH 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. 86 Avdeef 84 found a special way of determining the pKa.

Determination of the physicochemical properties, especially the lipophilicity (expressed as the logarithm of distribution coefficient, log D) and dissociation constant (pKa), is of great importance in the early stage of environmental risk assessment for an ionizable compound without these data. Currently, the log D and pKa values of dialkyl phosphinic acids (DPAs), the environmental hydrolysates of aluminum dialkyl phosphinates (ADPs) that is one class of emerging phosphorus-containing flame retardants, are not available. In this study, the log D and pKa values of three DPAs including methylethylphosphinic acid (MEPA), diethylphosphinic acid (DEPA) and methylcyclohexyl phosphinic acid (MHPA), were simultaneously determined by negligible depletion hollow fiber supported liquid phase microextraction (nd-HF-LPME) followed by ultra-performance liquid chromatography coupled with tandem mass spectrometry (UPLC-MS/MS). The pKa and log D of DPAs were determined by curve-fitting the experimental data with equations derived on the basis of the Henderson-Hasselbalch equation and compared with model calculated data. For MEPA, DEPA and MHPA, the pKa values were close and around 3, but the log Ds were strongly pH-dependent with values from -5.01 to 1.01. The log KOW of the neutral form (logKOW,HA) and ionic form (logKOW,A) were in the range of -0.67-1.02 and -3.86--1.33, respectively. The experimentally determined pKa values were highly in good agreement with ACD/pKa predicted values and the measured log KOW,HA values were closely related to KOWWIN calculated ones, suggesting ACD/pKa and KOWWIN are good alternative methods to estimate pKa and log KOW of DPAs, respectively. As far as we know, this is the first report on the pKa and log D data for DPAs, which are fundamental for the product design and evaluating the environmental behavior and effects of DPAs and ADPs.

Henderson-Hasselbalch relation is generally the simplified theoretical framework used to introduce students to acid-base titration. However, it is not always valid and its limitations should be made clear to chemistry students. The appropriate parameter to evaluate its validity is K a /C 0 , in connection with Ostwald dilution law. For more advanced students, it is possible to deduce analytical expressions that always fit accurately acid-base titrations and allow an evaluation of Henderson Hasselbalch relation. Gran plot appears as a particularly sensitive technique to the breakdown of Henderson Hasselbalch relation.

CO2, HCO3, SID, and total weak acids have been defined as pH’s independent variables. However, according to Gamble, HCO3 should be equal to the difference between the sum of cations and the sum of anions besides HCO3. Therefore, if this mathematical expression is substituted for HCO3 in the Henderson-Hasselbalch equation, all independent variables of pH can be demonstrated. Our aim is to test this theory in this study. This prospective observational study was conducted between 2019 and 2020. All admitted patients to the intensive care unit who were >18 years old were included. Demographic data Therefore, if this mathematical expression is substituted for HCO 3 in the Henderson-Hasselbalch equation, all independent variables of pH can be demonstrated. Our aim is to test this theory in this study. This prospective observational study was conducted between 2019 and 2020. All admitted patients to the intensive care unit who were >18 years old were included. Demographic data, blood gas parameters, albumin, magnesium, and inorganic phosphorus levels, and outcomes were recorded twice (at admission and at the 24 th hour). The multivariate linear regression model was used to determine pH’s independent variables. Yet, according to the Gamble equation, HCO 3 should be equal to the difference between all cations’ ionic charges (Na, K, Ca, Mg) and all anions’ ionic charges other than HCO 3 (Cl, albumin, inorganic phosphorus (P i ) , and unmeasured anions (UA)). In 2005, Schück finally derived the new Henderson-Hasselbalch equation by substituting Stewart’s independent variables for HCO 3 but there was no mention of the independent variables of [H + ] in his study [ 12 ]. Unexpectedly, he used Stewart’s independent variables and AG corr together to define the metabolic components. In this study, we sought to determine all independent variables of [H + ] using the Gamble and Henderson-Hasselbalch equations and we hypothesized that there were ten independent variables of pH. Materials and methods Study design This prospective observational study ran from 24 May 2019 to 1 June 2020 after local ethics committee approval (Acıbadem University and Acıbadem Healthcare Institutions Medical Research Ethics Committee -ATADEK- 2019-10/9, Chief: Prof Dr Ismail Hakkı Ulus). Theory According to the Henderson-Hasselbalch equation, there are two independent variables of pH: (Eq 1) p H = 6.1 + log H C O 3 0.03 × P a C O 2 Gamble JL claimed that the sum of cations equaled the sum of anions in the plasma:[ 6 ] (Eq 2) N a + K + C a + M g = C l + l a c t a t e + H C O 3 + [ A l b − ] + [ P i − ] + [ U A ] According to Gamble’s equation, HCO 3 can be written as below. (Eq 3) H C O 3 = N a + K + C a + M g − C l − l a c t a t e − [ A l b − ] − [ P i − ] − [ U A ] This mathematical expression can be written as a form of the Henderson-Hasselbalch equation instead of in terms of HCO 3 . Since UA’s ionic charge is calculated using SIG [ 14 ], the Henderson-Hasselbalch equation can be revised as below: (Eq 4) p H = 6.1 + log N a + K + C a + M g − C l − l a c t a t e − [ A l b − ] − [ P i − ] − [ U A ] 0.03 × P a C O 2 p H = 6.1 + log N a + K + C a + M g − C l − l a c t a t e − [ A l b − ] − [ P i − ] − [ S I G ] 0.03 × P a C O 2 We tested whether all parameters in the last Henderson-Hasselbalch equation were independent variables of pH. Statistical analysis Descriptive data are presented as mean±sd, median (quartiles), and percentages. The Kolmogorov‒Smirnov test was used to detect normality. According to our results supported our hypothesis, we detected ten independent variables of pH To detect whether there are compensation disorders and mixed disorders, rule-of-thumb equations and expected (standard) HCO 3 are calculated again and assessed; then, a decision about acid-base status is made [ 19 , 21 , 23 ]. For these reasons, the traditional approach has substantial limitations. Firstly, HCO 3 is a calculated variable and cannot be an independent variable for pH. Therefore, other parameters derived from HCO 3 , which are SBE and AG, cannot be independent variables as well. Furthermore, AG should be fully corrected, but if it is fully corrected, it becomes exactly the SIG of Stewart’s approach. For this reason, the measures of agreement between albumin-corrected AG and SIG may be weak ( Table 3 ). Therefore, metabolic acid-base disturbances are tried to be understood by using these dependent variables. Secondly, it is perceived as if the H 2 CO 3 -HCO 3 buffer system is the only system for [H] production. Thus, other probable metabolic variables that affect water dissociation are ignored or overlooked. Further, according to this approach, respiratory disturbance (CO 2 ) is compensated for by only metabolic components (HCO 3 ) and vice versa [ 19 , 23 ]. Stewart approach and then: New calculated independent variables and corrections Stewart’s approach creates a solution to metabolic acid-base disturbances by using the electroneutrality law, which Gamble summarizes [ 6 , 7 , 18 ]. In this approach, the independent variables of pH are CO 2 , SID, and A TOT . SIG was also added to Stewart’s independent variables [ 14 , 18 ]. SID, A TOT , and SIG are calculated variables, whereas CO 2 is a measured variable in this approach. In this situation, SID and A TOT also relate to their components in both equations [ 18 ]. These relationships can cause some problems. Buffers (albumin and ionic phosphorus) Albumin and P i are named as weak acids in Stewart’s approach [ 7 , 18 ]. They do not affect [H] on water dissociation but bind hydrogen ions when hydrogen ions increase in the plasma and vice versa ( Fig 4 ). Indeed, these buffers’ ionic charges are affected by the pH in accordance with their ionic charge formula [ 12 , 18 ], but at the same time, they are also independent variables of pH ( Table 2 ). This indicates that even though albumin and Pi serum levels do not change, their ionic charges vary when pH increases or decreases.