December 1997 pH in a tank Carlos Fuhrhop, Jaime Glaría, Juan Orellana, Cristián Saavedra Department of Electronic Engineering, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaiso, Chile _________________________________________________________________________________________________________ Abstract This communiqué reviews some of the hydrogen potential theory in aqueous solutions as a preparation for a real case, which is omitted. It migrates to a non-standard “excess of hydrogen” in order to somewhat alleviate the severe non-linearity usually appearing in the regulation of hydrogen potentials. Key words- pH regulation, PI regulation, simulation. _________________________________________________________________________________________________________ 1. INTRODUCTION Regulation of the concentration of acids and basis in aqueous solutions is a capital quest in diverse fields; e.g., water and sewage treatment, food technology, medicine and chemical industry. For such regulation, hydrogen potentials (pH) are measured by means of selective electrodes that develop proper voltages if due arrangements are made. One of those electrodes was used experimentally by Böttger to follow changes in acidity as early as 1897. The expression “pH” was coined by Sorensen in 1909, standing for “power of hydrogen” in the following manner: [ ] ( ) + - = H pH log where the brackets indicate the concentration of (hydrogen) ions, in [mol/l]. In our days, that definition has been modified and complemented to fit present knowledge more accurately: [ ] ( ) + - = O H pH 3 log [ ] ( ) - - = OH pOH log Besides the internal difficulties concerning electrodes, which we shall neglect, an official problem with the regulation of the concentration of acids and basis lies on the severely non-linear nature of the above equations. This report suggests a change that might help. 2. A LINK It is known that pOH and pH are linked by table 1, where T stands for temperature in [ o C] (Lide, 1992). Table 1: Temperature and potentials T pOH+pH T pOH+pH 0 14.938 55 13.152 5 14.727 60 13.034 10 14.528 65 12.921 15 14.340 70 12.814 20 14.163 75 12.712 25 13.995 80 12.613 30 13.836 85 12.520 35 13.685 90 12.498 40 13.542 95 12.345 45 13.405 100 12.265 50 13.275 Simple work yields: m m m m pH m m m m pOH pH O H O H pOH OH OH ⋅ ⋅ = ↔       ⋅ - = ⋅ ⋅ = ↔       ⋅ - = - - + + - - - - 2 3 3 2 10 9023 . 1 567 . 52 log 10 7007 . 1 798 . 58 log (1) where m OH- , m H3O+ and m represent the total masses in [kg] of the hydroxyl ions (OH - ), the hydronium ions (H 3 O + ) and the whole solution, respectively (assuming that the overall density in [kg/m 3 ] is 1000). (1) transforms table 1 into table 2. Table 2: Temperature and concentrations T m m m m OH HO - + ⋅ 3 T m m m m OH HO - + ⋅ 3 0 6.109⋅10 -10 55 47.75⋅10 -10 5 7.789⋅10 -10 60 54.70⋅10 -10 10 9.794⋅10 -10 65 62.30⋅10 -10 15 12.16⋅10 -10 70 70.46⋅10 -10 20 14.91⋅10 -10 75 79.24⋅10 -10 25 18.09⋅10 -10 80 88.81⋅10 -10 30 21.73⋅10 -10 85 98.85⋅10 -10 35 25.85⋅10 -10 90 109.9⋅10 -10 40 30.48⋅10 -10 95 120.2⋅10 -10 45 35.88⋅10 -10 100 132.6⋅10 -10 50 41.44⋅10 -10 Table 2 produces figure 1, where: x m m m m O H OH = ⋅ + - 3 (2) 0.00E+00 2.00E-09 4.00E-09 6.00E-09 8.00E-09 1.00E-08 1.20E-08 1.40E-08 0 10 20 30 40 50 60 70 80 90 100 T x Fig. 1: Temperature and concentrations