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MAIN >> SERVICE >> Training >> How a pH-meter works?
How a pH-meter works?Print
What is pH?

 

The measurement of pH is one of the most often used in chemistry. The correct expressions for pH are “acidity index” or sometimes “hydrogen index”.The formal definition of pH is given by the equation:

 

рН= -lg aH+, (1)

where aH+ is the thermodynamic activity or the effective concentration of the hydrogen ions in the given solution. The thermodynamic activity is the concentration of the hydrogen ions, corrected for the non-ideality of the solution.

 

The correcting multiplier, which transforms the concentration into activity is called the activity coefficient.

 

aH+ = γ[H+], (2)

 

where [H+] is the molar concentration of hydrogen ions in the solution. The multiplier γ in many cases can be calculated theoretically. For diluted solutions the multiplier γ is close to unity and in many simple cases is neglected. In the present note we omit it, because it is not connected with the primciple of the operating of a pH meter.

 

pH  uses a logarithmic, rather than linear scale because of two main reasons. First, the concentration of hydrogen ions is varied in practical systems, say, while acid-base titrations, in a very wide range 12 to 14 orders of magnitude (that is 10 to the 12th or 1o to the 14th power times). The second reason is that the instrumental measurements produce the output voltage that is varies linearly versus the logarithm of the concentration, rather than versus the concentration itself. So the application of the logarithmic scale, which allows to avoid very big numbers and is compatible with the instrumental methods finds a wide range of applications in chemistry and neighboring branches of science and technology.

 

 How is pH measured instrumentally. The primciple of operating of the system as a whole unit.

 

At present the main means of the pH measurements is the use of a special instrument, the pH meter.

The principle of the operating of such an instrument is potentiometric one, i.e. the measured value is the voltage between two electrodes, immersed into the tested solution.Normally the voltage between such electrodfes is changed by tens and hundreds of millivolts.

 

Thus pH met5er is actually a specialized voltmeter. The peculiarity of this voltmeter is a very low input current? So that it can measure the voltage from very different electrodes, including glass electrodes, which would not let big current flow. In addition, the pH meter can  process the voltage thus measured and transform it into pH (and in more sophisticated models into some other values, say the Turner degrees for the acidity of milk.)

 

Consider the functions of the pH meters in more details. Two electrodes are immersed into the solution, that are the indicator (work) electrode and the reference electrode. The potential of the indicator electrode versus the solution is linearly dependent versus pH of the solution (it is explained below.)

Uind= а + b*pH (3)

 

Here a and b are the constants, depending only versus the temperature of the solution.

 

The potential of a perfect pH-electrode does not depend upon the concentration of other ions. It is called the selectivity of the indicator electrode to hydrogen cations. Thus the pH-electrode can be classified as an ion-selective electrode.

 

The analytical response (the pH–dependent potential drop) origins from the interface of the membrane of the indicator electrode and the tested solution. It is transmitted to a metal wire in the construction of the indicator electrode and then to the input of the pH-meter, which is actually a special voltmeter. However the voltmeter cannot measure the potential of a single electrode. So one needs also a reference electrode, which is attached to the second input of the pH-meter.

 

The role of the reference electrode is to provide the constant reference potential versus the solution. It establishes a constant potential difference between the point in the solution, where it is inserted in and its output. The potential of the refernce electrode does not depend upon the potential of other ions. It is a whole device, using a series of scientific and technological solutions.

 

If we insert the reference electrode into the solution? A constant potential difference Uref is generated between the solution and the output of the reference electrode. This potential is applied to the second input of the pH-meter (reference input)/ The potential drop in the solution equals zero, because no current flows (and if flows, it interferes the pH measurement).

 

Thus, the potential between the inputs of the pH-meter, that is the measured potential, is given by the expression:

 

DU = Uind – Uref = a+b*pH = c+ b*pH (4)

 

Thus there exists a linear relationship between the pH or the tested solution and the measured voltage.

 

The constants c and b for the expression (4) are determined with the help of standard solutions with the known pH value. These constants are saved in the memory of the processor. Since then the instrument can automatically transform the measured value of the measured potential DU into the actual pH of the tested solution. The measurement can be continuous, for example while monitoring the tap water. It can also regulate the supply of the acid or alkali into the solution in order to establish a wanted value of pH (for example for a pH-stat)

 

How the indicator electrode works 

 

Let us consider in more detail the work of the pH-sensitive electrodes and trace the origin of eq. (3)

 

The pH-electrode is performed in the shape of a glass tube with a thin-walled glass ball at one end.. The wall of this ball is a pH-sensitive membrane. A silver wire, covered with a dense layer of silver chloride is place at the other end of the tube and serves to be the output of the electrode.  The tube is filled with 0.1 molar solution of hydrochloric acid, so that acid completely, without bubbles fills the ball and the wire is deeply inserted into the solution. The bubbles in the solution interfere the normal operating of the system because they effect the contact between the wire and the glass ball, which is conducted by the acid. So sometimes the “broken” glass electrode is readily repaired by simple shaking. Thus the electrochemical circuit within the pH electrode can be presented as follows:

 

AgAgCl HCl (0,1 M)glass membraneouter solution, ( рНout, [H+]out) (5)

 

Denote the potential difference between Ag and AgCl DU1, between AgCl and HCl (0,1 M) DU2, between HCl (0,1 M) and outer bulk solution DU3.

 

The potential difference between Ag and AgCl is determined by the fast exchange of silver cations at this interface and is constant and stable, because the composition of the both  Ag and AgCl is constant. Thus DU1 is constant

 

The potential difference between AgCl and HCl (0.1 m) is determined by the equilibrium, caused by the fast exchange of chloride ions at this interface and is constant and stable, because the composition of the both AgCl and HCl is constant and also because of the constant solubility product of AgCL.

The potential-determing reaction can be written as follows:

 

Cl- in AgCl  Cl- in HCl  (6)

 

The potential drop in this case can be expressed by a famous Nernst equation:

 

DU2 = DU20 + (RT/F) ln ([Cl-] in AgCl  /[ Cl-] in HCl   (7)

 

Here the notations are standard for Nernst equation.

Thus DU2 is constant

Only one term namely DU3 remains of the successively attached elements of the electrochemical chain.

 

It is the potential drop on the glass membrane. The type of the glass is selected so, that only hydrogen ions penetrate through the membrane. The other ions would not penetrate through this membrane.

 

The multiple experimental research have shown, that this potential difference is determined by the expression:

 

DU3 = (RT/F) ln ([H+]out /[ H+] in HCl (8)

 

No perfect theory to explain this fact is available so far, though several good explanations exist.

 

The logarithm of the ratio equals to the difference of the logarithms:

DU3 = (RT/F)ln ([H+]out - (RT/F) ln [ H+] in HCl (9)

The second term in eq.(9) does not depend upon the concentration of hydrogen ions, so we can consider it to be a constant.

Thus, the total potential of the pH electrode versus the solution can be expressed as follows:

 

Uind = DU1 +DU2+DU3=DU1 +DU2 - (RT/F) ln [ H+]in HCl + (RT/F) ln ([H+] out) =
= a +(RT/F) *2,303*lg([H+] out) = a -(RT/F) *2,303*
рН out = a + b рНout (10)

 

So we have derived eq.(3).

The following notatiopns are used:

 

a= DU1 +DU2 - (RT/F) ln [ H+] in HCl

and

 

b =-(RT/F) *2,303.

 

We also used the following expression to turn from natural logarithms to decimal ones:

 

Lnx= 2.303 lgx

 

 

How the reference electrode works?

 

Consider now in more detail the work of the reference electrode. The most widely used in the laboratory is so-called saturated silver-chloride electrode.

 

The reference electrode is performed in the shape of a glass tube with a filtering element of porous ceramics, porous glass asbestos or other fibers at one end.. This element is called an electrochemical bridge. It is needed to provide the electric contact of the inner solution with the outer tested solution but with the lrate of the leak of the inner solution to be very slow. . A silver wire, covered with a dense layer of silver chloride is place at the other end of the tube and serves to be the output of the electrode.  The tube is filled with the saturate (or concentrated with the concentration fixed) solution of potassium chloride, so that the salt solution completely, without bubbles fills the tbe and the wire is deeply inserted into the solution. The bubbles in the solution interfere the normal operating of the system because they effect the contact between the wire and the electrochemical bridge, which is conducted by the salt solution. So sometimes the “broken” reference electrode is readily repaired by simple shaking. Thus the electrochemical circuit within the reference electrode can be presented as follows:

 

AgAgCl KCl (sat)filtering membraneouter solution, ( рНout, [H+]out) (5)

 

Denote the potential difference between Ag and AgCl DU1, between AgCl and KCl (sat) DU4,between KCl (sat) and outer bulk solution DU5

 

As follows from the considerations equivalent to ones for the pH-electrode, DU1 is a constant, being the same as for the pH-electrode with the same temperature dependence. DU4 is also a constant, which is close to DU2, but not equal to it because the silver/silver chloride wire is inserted into hydrochloric acid in the pH-electrode and into poitassium chloride in the reference electrode.

 

However in the both cases the equilibrium is determined by the exchange between the crystal and the solution with chloride ions. Chloride is redistributed till the electric potential would balance the difference in the energies of chemical nature. After that the potential difference would not change DU4= const.

 

Only one term namely DU5 remains of the successively attached elements of the electrochemical chain.

 

It is the potential drop on the filtering element. There exists a theoretical equation of Albert-Sergeant for the potential drop on the tube, where the concentrated salt diffuses into the diluted solution (it is the case):

 

DU5 = (RT/F) ln (Λ+/Λ-) (12)

 

Here Λ+ and Λ-) are the equivalent electric conductivities of the cation of the salt (that is potassium in our case) and thew anion (chloride in our case).

 

The peculiarity of potassium and chloride is that for such a pair Λ+ = Λ- ,and the expression under the logarithm turns into unity, and the value of the logarithm turns into zero, because the logarithm of unity is zero. Thus DU5=0.

 

Thus the overall potential of the reference electrode versus the solution can be calculated as:

 

U ref.= DU1 +DU4 = const (13)

 

Such a stability of the potentialo of the output contact of the reference electrode versus  the point in the solution, where its electrochemical bridge is inserted is the basis to use this electrode as a reference point in potential measurements. 

 

 

 
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