Computer Simulation of the Effect of Temperature on pH zyx JAMES E. KIPPX AND DAVID F. SCHUCK Received March 8, 1995, from the zyxwvutsrq William Graham Science Center, Baxter Healthcare Corporation, IV Systems Division, Round Lake, Illinois 60073. Accepted for publication August 1, 1995@. Abstract 0 The effect of temperature on solution pH was simulated by computer (program PHTEMP). We have determined that the change in pH due to shifts in acid-base equilibria (ApH = pH(6O"C) - pH(25"C)) can be substantial for compounds such as aliphatic amines that have high enthalpies for acid dissociation. This is of particular significance during elevated temperature experiments in which changes in the p& values of formulation components, and hence the solution pH, can accelerate decomposition as compared to those formulations where sensitive functionality is absent. PHTEMP afforded the following results at initial pH = 7 (25 "C): (a) 0.1 zyxwvutsr M triethylamine zyxwvutsrq (AHS = 10.4 kcal/mol) ApH zyxwvutsrqp x -0.8; (b) 0.1 M acetic acid (AH" = -0.1 kcal/mol) ApH x 0; (c) 0.1 M sulfuric acid (AH", = -12 kcal/mol; AW2 = -5.4 kcal/mol) ApH x -0.4. Solutions of general pharmaceutical interest were also studied and included a 12-component amino acid mixture, 0.1 M glycine, and 0.1 M triethylamine in either 0.02 M citric acid or 0.05 M TRlS buffer. In each case the pH change with temperature was dependent on the concentrations of components, the enthalpies for each acid dissociation, and the starting pH. At lower pH (<4), PHTEMP predicts that ApH is typically smaller than at higher pH (>9). These results are interpreted as the effect of a relative change in hydronium ion activity, AH+/H+(initial), due to temperature-induced shifts in equilibria (acid dissociation, water autoprotolysis). This relative change must become larger as H+ decreases (pH increases). The output of PHTEMP was experimentally verified with 0.1 M glycine and with a multiple component amino acid solution. In both cases, agreement with prediction was excellent. The results of this investigation underscore the need to critically review formulation choices for both thermodynamic and traditional kinetic effects on the resulting product stability. Introduction zyxwvuts The measurement and control of solution pH is critical in pharmaceutical development. Accelerated screening of can- didate formulations is often conducted at temperatures far higher than that of the anticipated product storage condition. High-temperature data may be fitted to a temperature- dependent kinetic model (e.g., Arrhenius or Eyring) in order to predict stability at the product storage temperature, or the results may be used qualitatively to ascertain the effects of solution parameters (e.g., pH, ionic strength, buffer strength) on stability. It may be erroneously assumed that the effects of temperature on pH can be neglected. For example, test solutions could be adjusted to a given pH at room temperature and decomposition carried out at elevated temperature. Similarly, pH may be improperly neglected because of the experimental difficulty associated with pH measurements at elevated temperatures. We present the results of simulations using a computer program (PHTEMP) that is used to predict the change in pH due to shifts in equilibria and solute activities with temper- ature in single and multiple component formulations. We have found such simulations useful in evaluation of buffer @Abstract published in zyxwvutsrqpo Advance ACS Abstracts, September 15, 1995. systems for temperature sensitivity in situations where pH measurement at very high temperature is impractical. The effect of temperature on measured pH depends on the temperature dependence of the electrode response (Le., equi- libria shifts within the electrode and changes in junction potentials) and on shifts in solution equilibria within the sample. Introductory physical chemistry texts typically dis- cuss the Nernst slope' to describe the temperature dependence of the electrode, while changes in solution equilibria with temperature are extensively described in classroom chemistry texts and in classic compendia on pH measuremenL2 Because of the mathematical complexity of predicting the temperature dependence of multiple component systems, most of these treatises are limited to relatively simple systems. A computer program (PHTEMP) was written to predict the temperature dependence of acid-base equilibria, wherein multiple solution components with multiple contributing equilibria are present. PHTEMP is based on an earlier program3(PHCALC) which calculates ionic equilibria at fured temperature (25 "C) of any solution comprised of up to 54 acids and bases, including polyprotic acids. In PHTEMP, the equilibrium constants at any user-selected temperature are determined from the van 't Hoff equation using published thermodynamic values zyxw (K, at 25 "C and the standard acid- dissociation enthalpy, AH").4 As in PHCALC, PHTEMP sets up the system of mass balance, charge balance, and equilib- rium equations in a matrix, and solves the matrix equation to obtain estimates of the concentrations of all solution species. The calculated concentrations are used to determine ionic strength (I, in mom) and hence activity coefficients, z yi, at any given temperature by use of an extended form of the Debye Hiickel e q ~ a t i o n : ~ hi2& log yi = - 1 + Bai& Parameters A and B are defined as B = e(2N,,leoer,AkT11'2 (3) Constants e, No, k, e,, and er,A, T, and zyx zi are the elementary charge, Avogadro's constant, Boltzmann's constant, free charge permittivity in vacuo, solvent dielectric constant, temperature (degrees Kelvin), and charge of ion i, respectively. The ionic size (ai) is an empirical parameter that is entered by the user as an average value. The ionic strength, I, is defined as where ci and zi are the concentration (molarity) and charge of each ionic species present in solution. The programming strategy of PHTEMP is otherwise identi- cal to PHCALC. We have used PHTEMP to estimate the change in pH for a temperature increase from 25 to 60 "C as a function of the initial pH. The following solutions were studied: (a) single 0 1995, American Chemical Sociev and American Pharmaceutical Association 0022-3549/95/3184-1347$09.00/0 Journal of Pharmaceutical Sciences / 1347 Vol. 84, No. 11, November 1995