experimental data acquisition
Immerse pH and reference electrodes in a standard pH solution, ideally under temperature control and a CO2-free atmosphere. Read the electric potential. Repeat this for at least two more pH standard solutions.
The device known as a pH electrode
transduces H+ membrane potential to electric potential.
This is accomplished by coupling a H+-selective membrane with a Ag/AgCl electrochemical concentration cell; the basic scheme
is presented in Figure
The general thermodynamic expression for the chemical potential of a process with reaction quotient Q is shown in equation 1 where ΔG0 is the standard Gibbs energy for the process, R is the ideal gas constant and T is the temperature. If the chemical process involves charge transfer then its chemical potential may be expressed as an electric potential ΔE, equation 2, where F is the Faraday constant and n is the charge number of the ion, or the number of moles of charges transferred per mole of the advancement of the process. Substitution of equation 1 into equation 2 yields equation 3, known as the Nernst equation, where ΔE0 is the standard potential. The observed potential ΔE of a pH electrode is the sum of the series of potentials shown in equation 4 where ΔEAg/AgCl_cell is the potential of the Ag/AgCl concentration cell and ΔEinterfaces is the collective potential that develops at the several interfaces of the system due to their asymmetries. Since the only potential that changes from one solution to another is ΔEH+membrane then the observed potential may be expressed by equation 5, using equation 3 to express ΔEH+membrane and expanding Q to show the inner and outer hydrogen ion concentrations. The use of concentrations instead of activities is an approximation justified by its very low values. Since the membrane is assumed to be H+-selective then the measured potential is defined only by hydrogen ions. The value of n is +1 for the hydrogen cation.
Changing the natural logarithms to decimal logarithms, the electric potential measured by a pH electrode is described by equation 6, where ΔEconstant is explained in equation 7. Notice that this, temperature dependent, constant potential is the reference potential against which the H+ potential is measured. Since equation 6 is linear on the parameters with variables E and pH, linear regression over these variables enables to estimate the specific parameter values of the electrode and therefore to obtain the quantitative relationship between potential and pH for an electrode. While the y-intercept of equation 6, ΔEconstant, is electrode dependent, the slope is theoretically defined as -2.303RT/F and should be independent of the electrode.
example and discussion
Figure 2 shows student calibration results for three different pH electrodes. Three aspects about the electrodes are evaluated after calibration: linearity of response, sensitivity and asymmetry potential.
Linearity of response is a critical feature because it enables correct prediction of pH values using equation 6. All three electrodes respond linearly and interpolation should be very precise. However, care should be taken when extrapolating for more than two pH units outside the extreme pH standards used.
Calibrations were performed at 298 K and so the slope is expected to have a value of -59.1 mV/pH-unit for all electrodes. The sensitivity of an electrode can be defined as the ratio between the experimental slope and the theoretical slope and all three electrodes perform near 97%, which is good. The experimental slope is a measure of how strongly the electrode reacts to a pH difference between the two sides of its membrane. A loss in sensitivity indicates some problem with the electrode, or simply ageing, but if response linearity is maintained then pH values are still correctly predicted by linear regression, although noise instability will be noticeable.
The asymmetry potential is calculated, after calibration, as the potential for pH = 7. As can be seen in Figure 2, the asymmetry potential may vary due to different Econstant values because it depends on the specific values for the terms in equation 7. The asymmetry potential changes if the inner electrode solutions change or the porous junction of the reference electrode gets dirty, for example. Often, new electrodes present approximately zero potential for pH = 7 (Figure 2, diamond red markers) but that is not a necessary condition for good electrode performance.
Figure 1 – Schematics of a potentiometric pH measuring system, or pH-meter. It includes a measuring electrode, a reference electrode and a potentiometer. The reference electrode closes the electric circuit with an ion-permeable porous junction which also maintains the neutrality of the solutions. Usually, the two electrodes are combined in one piece where the reference electrode partially surrounds the measuring electrode. This is called a combined pH electrode but it is normally referred to simply as pH electrode. Hydrogen ions may not actually succeed in crossing the membrane beyond a superficial hydrated thin layer since the potentiometer counteracts a net transport. Nevertheless, the in-out H+ concentration difference is conveyed by ions in the inner dry glass.