pH and its Control

Definition of pH:

The acidity or alkalinity of a reaction mixture is most important. It can control the rate of reaction, the nature of the species present and even subjective properties such as taste. The original definition of pH (Sorensen, 1909) related it to the concentration of hydrogen ions. Two facts should be recognized. First, like many ions in solution, the hydrogen ion does not exist in aqueous solutions as a ‘bare’ H+ species, but as a variety of hydrated ions, such as H₃O+. Second, the determination of pH is often carried out by methods that measure the activity of the hydrogen ions, a(H₃O+)

a(H₃O⁺) = c(H₃O⁺)γ_± or pH = -log[a(H₃O⁺)]

where c(H₃O⁺) is the molar concentration of hydrogen ions, and γ_±} is the mean ionic activity coefficient of the ions in solution (see Topic C1).

At low concentrations (<10^-2 molar), γ_±} is close to 1, and the difference between concentration and activity is small for uni-univalent electrolytes.

The practical (or operational) definition of pH recognizes that it is determined using electrochemical cells having an electrode selective to hydrogen ions. This has been discussed in Topics C2 and C3, but a typical cell is:

Reference electrode || Solution X | glass electrode

This gives an output e.m.f , E_X,

E_X = E* + (RT/F) ln [a(H₃O⁺)_X]

The constant E* depends on the exact nature of the reference and glass electrodes, and is best eliminated by calibration with a standard solution S which has a pH that is accurately known.

E_S = E* + (RT/F) ln [a(H₃O⁺)_S]

Subtracting these and converting the logarithms gives a practical definition of pH:

pH(X) = pH(S) + (E_S-E_X)/(RT ln(10)/F)

Typical calibration buffers are discussed below.

The pH Scale:

In all aqueous solutions, pH values may range between about 0 and 14 or more as shown in Figure 1. Molar solutions of strong mineral acids, such as Hcl, HNO₃ or H₂SO₄ have pH values less than 1. Weak acids, such as ethanoic or citric acid in decimolar solution have a pH of around 3.

A useful standard is 0.05 M potassium hydrogen phthalate which, at 15°C has a pH of 4.00. Although pure water is neutral and has a pH of 7.00, freshly distilled water rapidly absorbs carbon dioxide from the air to form a very dilute solution of carbonic acid, and therefore has a pH of around 6.

Another standard occasionally used is 0.05 M borax (sodium tetraborate, Na₂B₄O₇), which has a pH of 9.18 at 25°C.

Dilute alkalis such as ammonia or calcium hydroxide (lime water) have pH values near to 12, and for molar caustic alkalis, such as NaOH, the pH is over 13.

Buffers:

As many reactions depend greatly upon the concentration of hydrogen ions in the solutions being used, it is important to control the pH. This is usually achieved by using a solution which has a pH that is accurately known and that resists any change in pH as solvent for the experiment. Such solutions are called buffers.

The equilibria that govern the reactions of weak acids or bases in aqueous solution will resist attempts to change them. This is known as Le Chatelier’s principle. For example, the dissociation of ethanoic acid obeys the equation:

CH₃COOH = [CH₃COO^- + H₃O⁺

and an equilibrium constant is written (in terms of concentrations)

K_a = c(Ac^-) \ c(H₃O⁺)/c(HAc) = 1.75 \ 10^-5

using the abbreviation Ac for the CH₃COO^- group. Converting to logarithmic form, and recalling that pK = -log (K):

pH = pK_a + log [c(salt)/c(acid)]

This is the Henderson-Hasselbalch equation.

If we make a mixture containing both the free acid, HAc, and its salt sodium ethanoate, NaAc, then the equilbrium and the concentrations of acid and salt will determine the concentration of hydrogen ions and the pH.

Example 1

For a mixture of 50 cm³ of 0.1 M HAc with 40 cm³ of 0.1M NaAc, giving a total volume of 90 cm³,

c(H₃O⁺) = 1.75 \ 10^-5 \ [(50 \ 0.1/90)/(40 \ 0.1/90)]

= 2.19 \ 10^-5 M, so that

pH = 4.66

Addition of acid to this buffer shifts the above equilibrium to the left and most of the added hydrogen ion combines with the anion. Adding 10 cm³ of 0.1 M HCl lowers the pH only to about 4.45. If this amount of acid were added to 90 cm³ of water, the pH would be 2.0. Similarly, when alkali is added, the hydroxyl ions react with the acid to produce more salt. 10 cm³ of 0.1 M NaOH will raise the pH only to around 4.85. If this amount of alkali were added to 90 cm³ of water, the pH would rise to 12.

Weak bases and their salts behave in much the same way. For example, ammonia and ammonium chloride:

NH₃ + H₂O = NH₄⁺ + OH^-

Kb = c(OH^-) x c(NH₄ +) / c(NH₃) = 1.75 \ 10^-5

or, rewriting the Henderson-Hasselbalch equation:

pOH = pK_b + log[c (salt)/c(base)]

or, since pH + pOH = 14.0

pH = 14.0 - pK_b - log[c(salt)/c(base)]

For a mixture of equal amounts of 0.1 M ammonia and 0.1 M ammonium chloride

pH = 14.0 - 4.75 = 9.25

A most useful range of buffers is obtained by using salts of a dibasic (or tribasic) acid such as phosphoric acid, H₃PO₄ - for example, potassium dihydrogen phosphate, KH₂PO₄, and disodium hydrogen phosphate, Na₂HPO₄. The equilibrium involved here is:

H₂PO₄^- = H₃O⁺ + HPO₄^2-

For this equilibrium, the second dissociation constant of phosphoric acid, K_a2, is close to 1 \ 10^-7, or pK_a2 = 7. Figure 2 shows the effect of adding acid or alkali on the pH of a mixture containing 50 cm³ each of 0.1 M KH₂PO₄ and 0.1 M Na₂HPO₄, which originally has a pH of 7.0. Adding 0.001 moles of acid to 100 cm³ of water would lower the pH to 2.

The more concentrated the buffer, the greater will be its buffer capacity. This is the amount of acid (or alkali) that, when added to 1 liter of buffer, will change its pH by 1 unit. In the above example, the buffer capacity is about 0.04 moles. If we had used a more concentrated buffer, the capacity would be greater. Very dilute buffers have little buffer capacity, and hence have limited use.

Table 1 gives a selection of buffers and standard solutions that are useful for pH control. These solutions and others are often used to calibrate pH meters.

pH Measurement:

Two important methods exist for pH measurement: visual, using indicators, and potentiometric, by means of electrochemical cells.

Indicators for pH measurement are weak acids (or bases) where the color of the acid form is different from that of the salt.

HIn = H₃O⁺ + In^‑

Colour1 Colour2

The dissociation constant of the indicator, K_In, is given by

K_In = c(H₃O⁺) \ c(In^-)/c(HIn)

For example, for methyl orange (Fig. 3):

Acid form, red = Alkaline form, yellow + H⁺

As with buffers, the equilibrium and the concentration of hydrogen ions will govern the ratio of color 2 to color 1.

Example 2

With the indicator bromocresol green, where K_In = 1.6 \ 10^-5, or pK_In = 4.8 and color 1 (acid) is yellow, while color 2 (salt) is blue, a solution of pH 4.0 will give:

log [c(In^-)/c(HIn)] = log [c(color 2)/c(color 1)] = pH - pK_In = -0.8

Therefore, c(color 2)/c(color 1) = 0.16, which means about 14% blue, 86% yellow, or visually a very yellowish green. When the pH is equal to the pKIn, there are equal amounts of each form making a green color.

A wide range of indicators is available for titrations and other purposes and these are discussed further in Topics C5 and C7.

This provides a useful and rapid method of estimating pH by eye; for example, using litmus paper which is red below about pH 6 and blue above pH 8. Both wide range and narrow range indicator papers are available to enable a rapid estimation of pH. However, to determine the pH accurately using indicators, careful spectrometric comparison would be needed and this is a time-consuming method that is rarely used.

The pH meter uses a reference electrode and a glass electrode with a highresistance voltmeter and affords a rapid and accurate method of measuring pH (Fig. 4). The calomel reference electrode is decribed fully in Topic C3.

The glass electrode is an example of a membrane ion-selective electrode and is described in Topic C3. It responds to hydrogen ions:

E(glass) = E* + (RT/F) ln [a(H₃O⁺)X]

Therefore the complete cell

Pt | Hg | Hg₂Cl₂ (s) | KCl (sat, aq) || Solution X | glass membrane | AgCl | Ag has an e.m.f. at 25°C equal to:

E (cell) = (E* - 0.241) + (RT/F) ln [a(H₃O⁺)_X]

By using one of the standards described above, for example, 0.05 M potassium hydrogen phthalate, which has a pH at 25oC of 4.008, we may eliminate E* and measure the activity of hydrogen ions, and hence the pH, in the unknown solution X.

pH(X) = pH(S) + (E_S - E_X)/(RT ln(10)/F)

pH Control:

It is often necessary to control the pH of a solution, especially if hydrogen ions are being generated or consumed, or if the nature of the species being analyzed changes with the pH. A few examples will illustrate this problem.

(i) In recording the UV spectrum of a solution of a weak acid, such as a phenol, the peak maxima occur at different wavelengths in an acid medium compared with those in a basic medium. Comparisons may best be made using a constant pH buffer.

(ii) In complexometric titrations (see Topic C7), such as the determination of magnesium by EDTA, the complex is formed readily and completely at high pH, so the titration is carried out using an ammonia-ammonium chloride buffer to keep the solution at pH 10.

(iii) As noted in Topic C3, the fluoride electrode detects free F^- ions very well, but OH^- ions interfere, and H⁺ ions form undissociated H₂F₂. It is therefore essential to make measurements in a buffer of about pH 5-6.

pH is most often controlled by performing the analysis in a suitable buffer solution. Occasionally, where a reaction produces an acid (or alkali) the technique of pH-stat titration may be used. Here, the acid produced is detected, and sufficient alkali added to return the pH to the optimum value.