Chemical Standards Research
We are currently working on the research area:
pH measurement by Harned Cell: The primary method for pH determination
pH is a fundamental physical constant which is used in a bewildering array of scientific disciplines and every-day activities. Traceable pH measurements are achieved by using a standard method; an electrochemical cell comprising a hydrogen gas working electrode coupled with a silver/silver chloride reference electrode without transference. This apparatus is commonly referred to as a “Harned Cell”. The expanded uncertainty for this method is U(pH) = 0.006 with a coverage factor of 2 giving a confidence interval of 95%.
The theory of traceable pH measurements
pH is a fundamental physical constant that is apparent in a bewildering array of natural phenomena and man made processes. From household cooking to large scale industrial processes, from human physiology to agriculture. It is therefore quite surprising that most scientists have only a very basic understanding of the theory behind pH measurements. The most simplistic understanding is that the pH is related to the activity of hydrogen ions in solution according to;
where a represents activity units which are related to concentration via;
where γ represents the activity coefficient and m represents the (molal) concentration scale. This definition of pH ignores the fundamental problem of pH measurements and solution chemistry in general: The activity coefficient (and hence the activity) of a single ion cannot be measured of theoretically calculated.
The traceability of pH measurements is only made possible through the use of a standard method that has been shown to meet the requirements of a primary method.
The primary method used for pH method is an electrochemical cell, without transference, comprising a hydrogen gas electrode in a standard buffer solution containing added chloride ions with a silver/silver chloride reference electrode. This cell is most commonly referred to as a “Harned” cell and is represented schematically as;
The following reactions occur spontaneously within a cell of this type;
combined;
Applying the Nernst equation to this reaction yields the following equation for the cell potential;
which can be rearranged to give the Acidity function;
at zero chloride molality
This parameter is determined by measuring the potentials generated by five Harned cells containing the buffer solution, each with a different molality of added chlorine. The resulting potentials are plotted and linearly extrapolated to zero chloride molality. Provided the total change in ionic strength between the five solutions is less than 20%, the curve should be linear and should obey the following basic equation;
where S is an empirical, temperature dependant constant
at zero chloride molality
The activity coefficient of a single ion is an inaccessible quantity. However, using the Debye-Hückel theory and the Bates-Guggenhiem convention is possible to determine the activity coefficient according to;
where A is the temperature dependant Debye-Hückel constant. Values of A with temperature are given in Appendix E. a is the “Distance of closest approach” and Ba is given the value of 1.5 at all temperatures in accordance with the Bates-Guggenheim convention.
pH measurement using the Harned cell
Combining equations (4), (6) and (7) we arrive at the measurand equation for pH values from the Harned Cell;
A detailed description of the method used to make pH measurements with the Harned cell is given in Appendix B.
Sources of uncertainty in Harned Cell measurements.
There are four steps in determining pH according to the primary (Harned cell) method:
- Determination of the standard potential of the Ag/AgCl electrode.
This parameter is determined by measuring the potential produced in a cell containing an accurately known hydrogen ion concentration (typically 0.01 ml.kg-1) and using the Nernst equation to calculate Eo. The crucial parameter in determining the standard potential in the molality of the HCl solution (See section 3.1). Other parameters include the uncertainty in the potential reading (E), temperature (T), atmospheric pressure (P), bias potential (ΔE) and the activity coefficient (γ).
- Determination of the acidity function in the buffer filled cells.
The parameters in this step are: The uncertainty in the standard potential (step 1.), measured potential (E), temperature (T), atmospheric pressure (P) and bias potential (ΔE). The molality of the chloride solutions is also a crucial parameter (See section 3.2 and 3.3).
- Extrapolation to zero chloride molality.
The zero chloride potential is determined by least squares regression.
- Uncertainty in Bates-Guggenheim convention.
The uncertainty in the Bates-Guggenheim convention is estimated to be 0.01.