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Chapter: 3 Chemistry
    Section: 3.9 Electrochemistry
        SubSection: 3.9.5 pH values



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3.9.5 pH Values

The concept of pH is unique amongst the commonly encountered physicochemical quantities, in that its definition,

spacer pH = − lg aH spacer(1)

involves a single ion quantity, the activity of the hydrogen ion, which is immeasurable by any thermodynamically valid method and requires a convention for its evaluation. In terms of molality, eqn (1) may be rewritten

spacer pH = − log(mH γH / m0) spacer(2)

where m0 is an arbitrary constant representing the standard state condition and equal to 1 mol kg−1, mH is the molality of hydrogen ion and γH is the single ion activity coefficient of the hydrogen ion. Arising from the non-experimental determinability of single ion activities, the definition and determination of pH depend on the assignment of pH values to standard solutions together with the determination of pH difference by a cell with liquid junction.

The electromotive force, emf, E(X) of the cell with liquid junction:

spacer Reference electrode | KCl (aq., conc.) || Solution X | H2(g) | Pt spacer(Cell I)

is measured, and likewise that E(S) of the cell:

spacer Reference electrode  | KCl (aq., conc.) || Solution S | H2(g) | Pt spacer(Cell II)

The temperature of both cells (I and II) must be equal and uniform throughout, and the hydrogen gas pressures identical. The two bridge solutions are any molality of KCl not less than 3.5 mol kg−1 (4.2 mol dm−3) provided they are the same. The reference electrode may be silver/silver chloride or calomel.

The pH of the solution X, pH(X) is then related to the assigned pH of the solution S, pH(S), by the definition:

spacer pH(X) = pH(S) + [E(S) − E(X)] / (RT/F) ln 10 spacer(3)

where R is the gas constant, T the thermodynamic temperature, F the Faraday constant. The quantity k = (RT/F) ln 10 is called the slope factor. As a consequence of this definition of pH, any difference in liquid junction potential between cells I and II is subsumed into the value of pH(X).

A Working Party of IUPAC, after extensive considerations over five years, recently produced a report (1) which sets pH firmly within the International System of Units (SI). A summary of these important developments is given below.

Since pH is a single ion quantity, it is not determinable in terms of a fundamental (or base) unit of any measurement system, and there is therefore difficulty in providing a proper basis for the traceability of pH measurements. A satisfactory approach is now available in that pH determinations can be incorporated into the International System (SI), provided they can be traced to measurements made using a method that fulfils the definition of a 'primary method of measurement'.

The essential feature of a primary method is that it must operate according to a well-defined measurement equation in which all of the variables can be determined experimentally in terms of SI units. Any limitation in the determination of the experimental variables, or in the theory, must be included within the estimated uncertainty of the method if traceability to the SI is to be established. If a convention were used without an estimate of its uncertainty, true traceability to SI would not be established. The electrochemical cell without liquid junction, known as the Harned cell,

spacer Pt | H2 | buffer S, Cl | AgCl | Ag spacer(Cell III)

fulfils the definition of a primary method for the measurement of a quantity called the acidity function, p(aHγCl), which is related to pH, and subsequently to the pH, of carefully chosen buffer solutions.

Values of the slope factor (k) at 0 – 50 °C
 °C   0   5   10   15   20   25   30   35   40   45   50 
k/ mV 54.20 55.19 56.18 57.17 58.17 59.16 60.16 61.14 62.14 63.13 64.12

Primary standards

pH values have been assigned by the Harned cell without transference method (III) to seven buffer solutions which meet certain criteria of reproducibility of preparation and properties. These solutions are called primary pH standards (PS). When two PS solutions are used in cells II, the experimental value of the slope will not be exactly in accord with the slope factor value, and, moreover, the experimental value could change if additional primary standard solutions were to be used. Hence the pH value determined for an unknown solution can be slightly dependent (± 0.02) on the choice of primary standard. Details of solution compositions, and pH(PS) values assigned, are given in the table below.

Typical Values of pH(PS) for Primary Standards at 0 - 50 °C

Primary Standards (PS) 0 5 10 15 20 25 30 35 37 40 50
saturated potassium hydrogen                      
tartrate (at 25 deg C)           3.557 3.552 3.549 3.548 3.547 3.549
0.05 mol kg-1 potassium                      
dihydrogen citrate 3.863 3.84 3.82 3.802 3.788 3.776 3.766 3.759 3.756 3.754 3.749
0.05 mol kg-1 potassium                      
hydrogen phthalate 4 3.998 3.997 3.998 4 4.005 4.011 4.018 4.022 4.027 4.05
0.025 mol kg-1 disodium                      
hydrogen phosphate +                      
0.025 mol kg-1 potassium 6.984 6.951 6.923 6.9 6.881 6.865 6.853 6.844 6.841 6.838 6.833
dihydrogen phosphate                      
0.03043 mol kg-1 disodium                      
hydrogen phosphate +                      
0.008695 mol kg-1 potassium 7.534 7.5 7.472 7.448 7.429 7.413 7.4 7.389 7.386 7.38 7.367
dihydrogen phosphate                      
0.01 mol kg-1 disodium                      
tetraborate 9.464 9.395 9.332 9.276 9.225 9.18 9.139 9.102 9.088 9.068 9.011
0.025 mol kg-1 sodium                      
bicarbonate + 10.317 10.245 10.179 10.118 10.062 10.012 9.966 9.926 9.91 9.889 9.828
0.025 mol kg-1 sodium carbonate                      

Secondary standards

Secondary standards (SS) are also defined, and values are also assigned by means of the Harned cell (III). These secondary standards do not for some reason of detail fulfil the criteria for primary standards in terms of reliable chemical quality.

Calibration Procedures: choice of standard reference solution

Some useful data for standard buffers are given in the table below

Summary of Useful Properties of some Primary and Secondary Standard Buffer Substances and Solutions

Salt or Solid Substance Molecular Molality/ Molar Density/ Mass/g Dilution pH Temp.
  formula mol kg-1 mass/ g dm-3 to make value coefficient
      g mol-1   1 dm3 DpH½ /K-1
potassium tetroxalate KH3C4O8.2H2O 0.1 254.191 1.0091 25.101    
potassium tetraoxalate KH3C4O8.2H2O 0.05 254.191 1.0032 12.62 0.186 0.001
potassium hydrogen KHC4H4O6 0.0341 188.18 1.0036 6.4 0.049 -0.0014
tartrate (sat at 25 oC)              
potassium dihydrogen KH2C6H5O7 0.05 230.22 1.0029 11.41 0.024 -0.022
Potassium hydrogen KHC8H4O4 0.05 204.44 1.0017 10.12 0.052 0.00012
disodium hydrogen Na2HPO4 0.025 141.958 1.0038 3.5379 0.08 -0.0028
orthophosphate +              
potassium dihydrogen KH2PO4 0.025 136.085   3.3912    
disodium hydrogen Na2HPO4 0.03043 141.959 1.002 4.302 0.07 -0.0028
orthophosphate +              
potassium dihydrogen KH2PO4 0.00869 136.085   1.179    
disodium tetraborate Na2B4O7.10H2O 0.05 381.367 1.0075 19.012    
disodium tetraborate Na2B4O7.10H2O 0.01 381.367 1.0001 3.806 0.01 -0.0082
sodium bicarbonate NaHCO3 0.025 84.01 1.0013 2.092 0.079 -0.0096
+ sodium carbonate Na2CO3 0.025 105.99   2.64    
calcium hydroxide Ca(OH)2 0.0203 74.09 0.9991 1.5 -0.28 -0.033
(sat. at 25 oC)              

1. If pH is not required to better than ±0.05 any standard reference solution can be selected.

2. If pH is required to ±0.002, and interpretation in terms of hydrogen ion concentration or activity is desired, choose a standard reference solution to match the unknown as closely as possible in terms of pH, composition and ionic strength.

3. A bracketing procedure may be adopted whereby two standard reference solutions are chosen for which the pH values, pH(S1) and pH(S2), lie on either side of pH(X). Then, if the corresponding potential difference measurements are E(S1), E(S2) and E(X), pH(X) is obtained from

pH(X) = pH(S1) + [ E(X) − E (S1) ] / %k                                                      (4)

where %k = 100[E(S2) − E(S1) ] / [ pH(S2) − pH(S1) ] is called the apparent percentage slope.
This procedure is very easily done on some pH meters simply by adjusting downwards the slope factor control when the electrodes are in in S2.
The purpose of the bracketing procedure is to compensate for deficiencies in the electrodes and measuring system.

Interpretation of pH(X) in terms of hydrogen ion concentration

The determined pH(X) has no simple interpretation in terms of hydrogen ion concentration, but the mean ionic activity coefficient of a typical 1:1 electrolyte can be substituted into equation (2) to obtain hydrogen ion concentration subject to an uncertainty of 3.9% in concentration corresponding to 0.02 in pH.


1. R.P. Buck, S. Rondinini, A.K. Covington, F.G.K. Baucke, C.M.A. Brett, M.F. Camoes, M.J.T. Milton, T.Mussini, R. Naumann,, K.W. Pratt, P. Spitzer, and G.S. Wilson Pure Appl. Chem. 2002, 74, 2105.

A.K. Covington


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