Home Reading Skoog et al. Fundamentals of Analytical Chemistry. Chapter 10, 21

slope = Include E IRE, E ERE, E j pH E cell (25 0 C) Calibration plot

Concentration and activity pH = -logC H + Diluted solutions [C] = mole/L

Concentration and activity pH = -logC H + Diluted solutions Concentrated solutions Activity (Apparent concentration)

Concentration and activity By convention we accept that equation is true at any concentration. pH = -loga H + Operational definition of pH

Concentration and activity      activity coefficient For diluted solutions a = C

Activity coefficient of an individual ion is a theoretical quantity. Ions exist in solutions only in combinations with oppositely charged co-ions. Therefore we cannot experimentally measure the activity coefficient of an individual ion. In experiment, we can only able to determinate the mean activity coefficient, averaged by all the ions in the solution. The mean activity coefficient of the electrolyte K m A n is defined as Experimental Value Theoretical value

For a 1:1 electrolyte KA the mean activity coefficient is equal to

Calculation of the activity coefficient The total concentration of ions in a solution is characterized by a quantity called ionic strength ( I ) C i = molar concentration of ionic species i z i = charge of ionic species i

Example: Calculate ionic strength of 1M solution of HCl C H = 1M; C Cl = 1 M; z H = 1; z Cl = 1

Debay – Hückel equation For water solutions at T = 25 o C A = 0.51, B = 3.3 r i = effective diameter of the hydrated ion i in nanometers. It is close to 0.3 nm for most single charged ions. A and B are coefficients depending on the solvent and temperature.

Ion-selective electrode Ion-selective electrodes measure the activity of ions. Correspondingly the potentiometric equation for them reads pX = -logC X

Ion-selective electrode Glass electrodes Liquid membrane electrodes Solid-state crystalline electrodes Li +, Na +, K +, NH 4 + Ca 2+, K +, Water hardness (Ca 2+ + Mg 2+ ), Cl -, NO 3 - Cu 2+, Cd 2+, Pb 2+, Ag + /S 2-, Cl -, F -, I -, CN -

Ion-sensitive glass electrodes H+H+ H+H+ H+H+ H+H+ H + responsive glassNa + responsive glass Na +

Ion-sensitive glass electrodes Cole-Parmer® potassium- selective electrode

Ion-sensitive glass electrodes Ion conductive glasses are ion-exchangers. When such glass is brought to contact with a solution of electrolyte, equilibrium is established: Glass-A + + B + = Glass-B + +A + soln Any aqueous solution contains hydrogen-ions. So, most frequently, this ion- exchange equilibrium is between H + and a metal cation. Glass-H + + B + = Glass-H + +A + soln

Ion-sensitive glass electrodes E IRE E b = E 2 – E 1 E ERE EjEj E b = L‘ log(a+k H,B b) a, b = activity of hydrogen-ion and the cation in the solution k H,B = selectivity coefficient The selectivity coefficient is a measure of the response of an ion-selective electrode to other ions.

E b = L‘ log(a+k H,B b) 1. k H,B ≈ 0E b ≈ L‘ log(a)=L‘ pH 2. k H,B >> 0E b ≈ L‘ log(k H,B b)=L‘‘ pB L ‘‘ = L ‘ *log(k H,B ) pH-glass Ion-selective glass

Ion-sensitive glass electrodes

Liquid membrane electrodes Porous plastic membrane holding liquid ion-exchanger Ag wire Plastic tubing Aqueous solution sat’d AgCl + B + Liquid ion- exchanger

Liquid membrane electrodes

Solid-state electrodes Solid-state electrode has principally the same design as glass membrane electrodes except the membrane is made from cast pellets of crystalline material rather than from conducting glass. Solid membrane must contain mobile ions, to which it is responsive. MaterialSelective ion AgF, LaF F - AgClCl - AgII+I+ Ag 2 SS 2+, Ag + CdS/Ag 2 SCd 2+ PbS/Ag 2 SPb 2+

Solid-state electrode

Potentiometric titration Potentiometric titration is a titration technique. It differs from classic titration only in a method of indicating the titration endpoint. Can be used for 1.Acid/base titration 2.Red/Ox titration 3.Complexometry Benefits: 1.More sensitive 2.Can be automated 3.Can be used for turbid or strongly coloured solutions 4.Can be used if there is no suitible indicator

Set-up for potentiometric titration Burette Electrode Potentiometer

Automatic titration Pump-burette Cell Electrodes Reservoirs

There are two distinguishable situation in potentiometric acid/base titration: 1. Titration of a strong electrolyte by a strong electrolyte 2. Titration of a weak electrolyte by a strong electrolyte

Titration of a strong acid by a strong base V eq

Consider the following graph: Titration of a weak acid by a strong base pK a V eq /2 V eq

Consider the following graph: + In this region H + dominates, the small change in pH is the result of relatively small changes in H + concentration.

Consider the following graph: In this region, relatively small changes in H + concentration cause large changes in pH, The midpoint of the vertical region is the equivalence point.

Consider the following graph: In this region OH - dominates, the small change in pH is the result of relatively small changes in OH - concentration.