Potentiometric pH meters measure the voltage between two electrodes and display the result converted into the corresponding pH value. They comprise a simple electronic amplifier and a pair of electrodes, or alternatively a combination electrode, and some form of display calibrated in pH units. 

pH:

pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution. The pH scale usually ranges from 0 to 14. Aqueous solutions at 25°C with a pH less than 7 are acidic, while those with a pH greater than 7 are basic or alkaline.

The pH is then calculated using the expression: pH = - log [H3O+]. 

A pH meter measures essentially the electro-chemical potential between a known liquid inside the glass electrode (membrane) and an unknown liquid outside. Because the thin glass bulb allows mainly the agile and small hydrogen ions to interact with the glass, the glass electrode measures the electro-chemical potential of hydrogen ions or the potential of hydrogen. To complete the electrical circuit, also a reference electrode is needed. Note that the instrument does not measure a current but only an electrical voltage, yet a small leakage of ions from the reference electrode is needed, forming a conducting bridge to the glass electrode. A pH meter must thus not be used in moving liquids of low conductivity (thus measuring inside small containers is preferable).

The pH meter measures the electrical potential (follow the drawing clock-wise from the meter) between the  mercuric chloride of the reference electrode and its potassium chloride liquid, the unknown liquid, the solution inside the glass electrode, and the potential between that solution and the silver electrode. But only the potential between the unknown liquid and the solution inside the glass electrode change from sample to sample. So all other potentials can be calibrated out of the equation

Dissociation constant: 

Dissociation constant (Kw) is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex falls apart into its component molecules, or when a salt splits up into its component ions. 

pH Range:

The pH scale is often said to range from 0 to 14, and most solutions do fall within this range, although it's possible to get a pH below 0 or above 14. Anything below 7.0 is acidic, and anything above 7.0 is alkaline, or basic.

Buffer solution :

A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. ... Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. 

Glass electrode

A glass electrode is a type of ion-selective electrode made of a doped glass membrane that is sensitive to a specific ion. The most common application of ion-selective glass electrodes is for the measurement of pH. The pH electrode is an example of a glass electrode that is sensitive to hydrogen ions. Glass electrodes play an important part in the instrumentation for chemical analysis and physico-chemical studies. The voltage of the glass electrode, relative to some reference value, is sensitive to changes in the activity of certain type of ions. 

The glass electrode consists of a thin glass bulb containing dilute HCl, into which is inserted an Ag–AgCl wire, serving as the electrode with a fixed voltage. The HCl solution is separated from the test solution by a membrane of special glass, usually a lithium silicate of particular composition. 

Reference electrode

The standard hydrogen electrode, or SHE, is composed of an inert solid like platinum on which hydrogen gas is adsorbed, immersed in a solution containing hydrogen ions at unit activity. The half-cell reaction for the SHE is given by

2H+(aq)+2e−⇌H2(g)

and the half-cell potential arbitrarily assigned a value of zero (E0 = 0.000 V).

Practical application of the SHE is limited by the difficulty in preparing and maintaining the electrode, primarily due to the requirement for H2 (g) in the half-cell. Most potentiometric methods employ one of two other common reference half-cells – the saturated calomel electrode (SCE) or the silver-silver chloride electrode (Ag/AgCl).

1. Saturated Calomel Electrode (SCE)

The SCE is a half cell composed of mercurous chloride (Hg2Cl2, calomel) in contact with a mercury pool. These components are either layered under a saturated solution of potassium chloride (KCl) or within a fritted compartment surrounded by the saturated KCl solution (called a double-junction arrangement). A platinum wire is generally used to allow contact to the external circuit. The half reaction is described by

                                                              Hg2Cl2(s)+2e−⇌2Hg(l)+2Cl−(sat’d)

with an E0 value of +0.244 V. A common arrangement for the SCE is shown above, left side. In this arrangement, a paste is prepared of the calomel and solution that is saturated with KCl.

The solution over the paste is also saturated with KCl, with some solid KCl crystals present. Contact to the measurement cell is made through a porous glass frit or fiber which allows the movement of ions, but not the bulk solution. In many electrodes designed for potentiometry, the reference half cell is contained within the body of the sensing electrode. This arrangement is referred to as a “combination” electrode.

2. Silver/Silver Chloride (Ag/AgCl)

The silver/silver chloride reference electrode is composed of a silver wire, sometimes coated with a layer of solid silver chloride, immersed in a solution that is saturated with potassium chloride and silver chloride. The pertinent half reaction is

                                                                      AgCl(s)+e−⇔Ag(s)+Cl−(sat’d)

with a value for E0 of +0.222 V. The actual potential of the half-cell prepared in this way is +0.197 V vs SHE, which arises because in addition to KCl, AgCl also contributes to the chloride activity, which is not exactly unity. A schematic of the Ag/AgCl reference electrode is shown at right in the previous figure.

Both the SCE and the Ag/AgCl reference electrodes offer stable half-cell potentials that do not change over time or with temperature. In addition, the loss of electrolyte to evaporation does not change the saturated nature of the solution, nor the potential. One must be aware that the contact junctions of the half cells by nature slowly leak fill solution into the external solution in which they are found. As such, there are instances where measurements of certain ions, like chloride, might be affected by the ions introduced to the measurement solution by leakage. The double junction design prevents this problem by placing a second solution between the reference half cell and the measurement solution.

Combination electrode

The majority of today's pH electrode types are known as combination electrodes. Combination electrodes have the glass Hydrogen Ion (H+) sensitive electrode and an additional reference electrode all in one housing. 

The combination or pH electrode measures the difference in potentials between the two sides in the glass electrode. To measure the potentials it must be a closed circuit. The circuit is closed through the internal solutions of the electrode and the external solution that is being measured and the pH meter.

As the electrode is immersed in the test solution the glass bulb senses the hydrogen ions as a millivolts (mV) due to the positive charge of the hydrogen ions. The electrolyte or internal solution picks up the mV signal from the glass bulb. That signal is then passed to the internal electrode. The Ag/AgCl wire then passes that signal to the electrode cable that leads to the meter.

The reference electrode containing electrolyte or filling solution generates a constant mV, which is transferred to the Ag/AgCl wire. The wire then passes the signal, which can be considered a "control" being measured to the electrode's cable.

The circuit is closed by a minute amount of internal solution from the reference electrode flowing through a porous membrane made of a ceramic wick. This membrane or junction as it is called is located the electrode body.

The pH meter measures the difference between the internal electrode and the reference electrode in millivolts DC. This mV reading is then read by the meter and is displayed in pH units.

All pH electrodes require calibration from time to time. A two point calibration characterizes an electrode with a specific pH meter. Once an electrode is characterized, the electrode/meter pair can be used to determine the pH of a solution. Please follow the step-by-step procedure outlined below to perform a two point calibration. A 7.00 pH buffer solution and a 4.01 pH buffer solution are required.

1. Rinse the electrode thoroughly with DI water to remove all traces of storage solution, process medium, or previous test solution. Thoroughly rinse the electrode after each buffer test to prevent carry over contamination of the pH buffer solutions. Gently blot the electrode on a soft tissue to remove the excess rinse water. Do not rub the bulb since it can cause a static charge build-up.

2. Insert the electrode and the automatic temperature compensator (ATC) in 7.00 pH buffer solution. Allow 30 seconds for the electrode/ATC to reach thermal equilibrium with the buffer solution. Adjust the pH meter with the standardize/zero control for a pH indication equal to 7.00.
   Note: If the meter does not have an ATC, place a thermometer along with the electrode in the 7.00 pH buffer solution. Allow 30 seconds for the pair to reach thermal equilibrium with the buffer. Adjust the temperature dial on the meter to correspond with the thermometer reading. Then adjust the pH meter with the standardize/zero control for a pH indication equal to 7.00.

3. Repeat Step 1, and insert the electrode and the ATC in a 4.01 buffer solution. Allow 30 seconds before adjusting the pH meter with the slope/span control for a pH indication equal to 4.01.

4. Repeat Steps 2 and 3 to maximize the precision of the calibration.