The second ionization constant of malonic acid in aqueous solution was determined at 0° to 60° C from measurements of the electromotive force of galvanic cells without liquid junction. Solutions containing sodium acid malonate, sodium malonate, and sodium chloride were employed for these determinations.From the values of the ionization constants, the closest distance of approach, or the so-called diameters, of the ions in the solution was calculated for the different temperatures. These ionic diameters, the electromotive forc e, and the known molalities were then employed to calculate pH values of the solutions. The ionization constant at the different temperatures was determined from the experimental data by three different methods, using a least-square calculation in each. The values are different for the various temperatures, and may be computed for temperatures from 0° to 60° C, inclusive, by the equation 1053.08 log K 2= --T -+20.3223 log T-0.05838 T+0.0000236 T2-37.1402.Equations were formulated to express the variation of pH as a function of the ionic strength of the solution, to give the heat of ionization of the acid malonate ion, and to give the difference in the specific heats of the ions and the undissociated acid malonate ion at each temperature. The change in free energy and entropy for the ionization of the acid malonate ion were also calculated for each temperature. All of these quantities are of importance in arriving at explanations for the variation of hydrogen-ion activity with temperature.It has been found that solutions containing equal concentrations of sodium acid malonate, sodium malonate, and sodium chloride, each varying from 0.001 to 0.044 molal, have pH values ranging from 5.272 to 5.761 at 0° to 60° C. These solutions are suitable for use as pH standards.

Electrometric titration of 0.1 M malonic acid by 0.1007 N sodium hydroxide was completed at 25° C for the determination of the pH titration curve and the calculations of the primary and secondary dissociation constants. The treatment of the data embodied the application of the Henderson equation for liquidjunction potential, the Debye-Huckel theory of inter ionic attraction, and the Guggenheim-Huckel expression for the variation of the ionic activity coefficients with concentration. The dissociation constants found for malonic acid at 25° C are K, = 2.06XlO-3 and K2= 2.94 X IO-6.

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ABSTRACT

N THE electrometric measurement of the pH values of buffered solutions more dilute than 0.0001 M by means of quinhydrone and hydrogen electrodes the resistance of the solution, escape of carbon dioxide, acid properties of the quinhydrone, and polarization of the electrodes are so disturbing that the e. m. f. readings may vary as much as 5 to.30 millivolts or 0.1 to 0.5 pH