…is concerned with the properties of of and with processes that occur at electrodes …..all of which involve the transfer of electrons. THE CHARGE AND CURRENT

•Electrochemistry studies the processes which involve charge •The charge is a source of electric field

Element of charge: 1.602·10-19 C The energy change is ±1.602·10-19 J if we move the charge across the potential drop of 1V If we do the same with 1 mol of charges, we obtain…

A B 1V + -

-

dQ The current is the change of charge per time I  dt Transport of charge Q and matter ( n (mol))

Q  Nze N  n.N A

Q  n.z.N A.e

1 Faraday’s constant F  N A.e  96484Cmol m Q  n.z.F Q  I.t n  M FARADAY’S LAW (1834)

“The chemical power of a current of electricity is in direct proportion to the absolute quantity of electricity which passes” “Electrochemical Equivalents coincide, and are the same, with ordinary chemical equivalents” m Q  M zF

MIt m  zF Solutions of electrolytes dissociation and of electric conductivity of electrolytes strong electrolytes weak electrolytes activity coefficients ionic strength solubility product

Acids and bases Ionic product of water pH Dissociation constants of weak and bases

Electrochemical cells and electrodes EMF and electrode potentials -selective electrodes Solutions of Electrolytes: Electrolytes Strong Weak

The degree of dissociation: c'   c HCl CH3COOH c’ – dissociated part c - total concentration – of cations and anions resulting from the substance dissociation

Strong electrolyte – fully (almost) dissociated strong acids, bases or their salts (e.g. NaCl, HCl, KOH,…)

  HCl  H 2O  H3O  Cl   0.5

Weak electrolyte – partly (slightly) dissociated substance

(e.g. CH3COOH, NH4OH)

  CH 3COOH  H 2O CH3COO  H3O 0.01   0.5 Charge number of ions z :

Cations: Na+ z = 1 Anions: Cl- z = -1 Mg2+ z = 2 -2 SO4 z = -2

Zwitterions: z = 0 Ampholytes are molecules containing both acidic and basic groups (e.g. aminoacids)

The principle of electroneutrality: in an electrolytic solution the concentrations of all the ionic species are such that the solution as a whole is neutral

 positive charge = negative charge  Svante August Arrhenius (19 February 1859 – 2 October 1927)

Nobel prize for in 1903

1887 – theory of electrolyte solutions AB  A  B An equilibrium in solution between undissociated molecules AB and the ions A+ and B- Dissociation:

-binary electrolyte (2 ions): NaCl  Na  Cl    2

2  -ternary (3 ions): CaCl2 Ca  2Cl   3 3  -quaternary (4 ions): FeCl3  Fe  3Cl   4

Stepwise dissociation:

  H3PO4  H  H 2 PO4   2 H 2 PO4  H  HPO4 2  3 HPO4  H  PO4

Na2 HPO4 ,CaHPO4 , K3PO4  The colligative properties of electrolytes

Freezing point depression T  iKk .cm Boiling point elevation T  iKe.cm   icRT Osmotic pressure i – van’t Hoff’s coefficient Nonelectrolytes: i    - osmotic coefficient

Electrolytes: i .  - number of ions In diluted solutions:  = 1 Electrolytes e.g.:  Na2SO4 2Na  SO4   3

Dissociation of electrolytes, due to disintegration of molecules to ions, affects significantly colligative properties of solutions Solvents and Solvation

o solvent  r (25 C) N-methyl-formamide 187 formamide 109

H2O 78,3

CH3OH 32,6 Anhydrid acetic 20 pyridine 12,3

CH3COOH 6,15 etylether 4,3 benzene 2,3 N-hexane 2,0 1 e2 Columb’s law: F   .    0 r 4  R2  - permitivity 0 r NaCl:

Energy is required to pull apart atoms, ions, or molecules that are attracted to each other. But when atoms, ions, or molecules come together, energy is released. One way to say it is, “It takes energy to break bonds, and energy is released when bonds are formed.” 1. Dissociation and Solvation of ions:

Na g Cl  g

1 1 kr H  779kJmol  solv H  775kJmol  H 2Ol endothermic exothermic

 H Ol    NaClcrystal2  Na aq Cl aq 1 dis H  3,87kJmol

dis H  kr H  solv H

Enthalpy of dissolution a) Salts: NaCl, KCl, NH4Cl, etc. Endothermic dissolution dis H  0 b) Dissolution of non-ionic substances (gas, liquid) - electrolytic dissociation and hydration of ions:   HClg H 2Ol H3O aq Cl aq

  H 2SO4 l H 2O  H3O aq HSO4 aq   2 HSO4 aq H 2Ol H3O aq SO4 aq Strongly exotermic!!! Enthalpy of dissolution dis H  0 Enthalpy of dilution dil H  0 Electric conductivity of electrolytes:

strong electrolyte weak electrolyte Non-electrolyte Electrical conductivity of electrolytes: Physics: l  electrical resistivity [.m] Ohm’s law: U  RI R   l length of conductor [m] S S cross-section [m2] 1 Conductance: G  [S] R 1 Electrical conductivity:   [S.m-1] (specific)  l   G.  G.C C – resistive capacity [m-1] S

Conductivity of the electrolyte i:

  H 2Oi Ridistilled water: 1 H 2O  2  4Sm Water for pharmaceutical use H O  0,3mSm1 (Pharmacopeia): 2  Molar conductivity:  [Sm2mol-1] c [mSm2mol-1]

Molar conductivity of the AB electrolyte:

B  A      

+, - conductivity of ions +, - stoichiometric coefficients

Limiting molar conductivity:0  lim  c0 (molar conductivity at infinite dilution)

Kohlraush’s law of independent migration of ions:

0 B  A    0  0  0  0 Limiting molar conductivities (S.cm2.mol-1):

0 KCl 149,86 0 (KI) 150,38 0 (KClO4 ) 140,04

0 (NaCl) 126,45  (NaI) 126,94 0 0 (NaClO4 ) 116,48

  23,41   23,44   23,56

An example of limiting molar conductivities of selected salts composed of same cations and anions. Note the difference in conductivity (expressed by ) due to cations is higher. Calculation of limiting molar conductivity:

2 1 0 ZnCl2   Zn0Zn  Cl0Cl 10,56  2.7,63  25,82mSm mol

In view of Kohlraush’s law of independent migration of ions, limiting molar conductivities of individual ions can be combined to calculate limiting molar conductivities of electrolytes. Dissociation:

Strong electrolyte:

Weak electrolyte:

Note the difference in dissociation of strong and weak electrolytes Strong electrolyte – at low concentration  depends on c linearly:

Kohlraush’s law   0  k c k – coefficient which depends on the nature of the specific in solution

Weak electrolyte 0: -additive quantity

0 CH3COOH   0 CH3COONa 0 HCl 0 NaCl  2 1  91,0  426,0 126,0  391,0Scm mol 2 -1 0 [Scm mol ]

For strong electrolytes we can determine limiting molar HCl 426,0 conductivity 0 experimentally from the dependence of  = fc. NaCl 126,0 Due to extremal growth of  at very low concentrations of weak electrolytes, the value of 0 is not possible determine from an CH3COONa 91,0 experiment. Frequently are these values calculated, as shown for

CH3COOH. Weak electrolyte – the conductivity depends on the degree of dissociation :  c' c’ – concentration of the dissociated part      c c – total concentration 0

Weak electrolyte e.g. CH3COOH, NH3: a  a    K  H3O A HAaq H 2Ol H3O aq A aq A aHA At the dissociation degree :

  H3O  c A  c HA 1 c

 2c The KA: K A  1 c2 K A  Ostwald’s dilute law: 0 0  

The degree of dissociation of a weak electrolyte depends on its dissociation constant Problem solving:

Concentration of a weak acid HA in is c=0.015 mol/dm3 and at this concentration the found degree of dissociation of the acid  = 0.09.

Calculate dissociation constant KA and pKA of the acid HA, and pH of the solution. Activity and activity coefficients of strong electrolyte K+A- :    0  RT ln a of the solution: i i i ai  ci i + - Electrolyte K A : KA     At standard condition: 0 0 0 KA    

0 0     RT ln a     RT ln a

0 KA  KA  RT ln aa

A mean activity of the electrolyte: a  aa  c c   c   

A mean activity coefficient:        a  c 

a   c   a  c  The activity of ions: K K  A  A  

We do not know to resolve an activity of anions and cations in a solution, respectively. Due to that, a mean activity of electrolyte and a mean activity coefficient were introduced. Debye – Hückel limiting law

log    z z A I

For water, 25 oC: A  0,509

The ionic strength I of a solution is a function of the concentration of all ions present in that solution :

1 2 I  ci zi 2 i Debye, Hückel, 1923

Debye-Huckel limiting law defines a mean activity coefficient. I is the ionic strength of a solution. It characterizes total electrostatic effect of all ions in solution. Problem solving

Solutions of two salts K2SO4 and MgCl2 were mixed together. Final concentration in the solution was 3 found: K2SO4 c=0.001 mol/dm , and MgCl2 c=0.002 mol/dm3. Calculate the ionic strength of the solution. The solubility product Ks .

- solubility of a slightly soluble salt AgCl, CaF2,... MX s M  aq X  aq T, p  konst.

a  a  M X K  aMX s 1 aMX (pure solid)

The solubility product Ks   K a  .a  M X s  M X      2 K s  M X   In water solution, an equilibrium between a solid (not-dissolved) salt MX and its ions (M+ and X-)

will be created. Note, aMX in the denominator of the fraction of (K) is an activity of pure solid. aMX = 1 for pure solid under standard conditions. Numerator, aM . aX is the + - solubility product, Ks. [M ], [X ] express concentrations of the ions, respectively. The solubility product Ks of selected salts:

  AgCl : AgCls Ag aqCl aq

  2 K s  aAg .aCl  Ag .Cl . 

BaSO sBa2 aq SO 2 aq BaSO4 : 4 4 2 2 2 Ks aBa.aSO Ba .SO4 . 4

2  CaF 2: CaF2 sCa aq 2F aq

2 2  2 3 Ks  aCa .aF  Ca .F  .  The solubility product Ks – the solubility of AgCl: AgCls Ag aqCl aq

  2 K s  aAg .aCl  Ag .Cl . 

a) In water (  1) The solubility s : s  Ag   Cl  

s  K s

b) For a solution in which no common ions are present

(e.g. AgCl in KNO3 solution)

2 2 Ks log   z z A I Ks  s   s       c) For a solution in which are present common ions e.g. AgCl in a solution of NaCl at concentration c:

  cNaCl  sAgCl s  Ag  Cl  cNaCl

  2 2 K s  aAg .aCl  Ag .Cl .   s.cNaCl . 

1 K s I  c z 2 s  log   z z A I  i i 2    2 i cNaCl  The solubility of AgCl in water is s(AgCl) =1,33.10-5 moldm-3 (at 25 oC). Calculate a) The solubility product of AgCl -3 b) The solubility of AgCl in KNO3 at concentration 0,001 moldm c) The solubility of AgCl in KCl solution at concentration 0,0001 moldm-3 (A= 0,511 mol-1/2dm3/2)

  2 K  a .a  Ag . Cl . (  1) a) s Ag Cl     2 10 2 6 Ks  s 1,769.10 mol dm

K 1,769.1010 b) s  s  1,38.105 mol.dm3   0,963

1 2 1 2 2 1 2 2 3 I  c z I  c  z   c  z   0,001.1  0,001. 1  0,001moldm  i i K K NO3 NO3 2 i 2 2 log    z z A I

0,01616   10  0,963 log    1.1.0,511. 0,001  0,01616 c) The solubility of AgCl in KCl solution at concentration 0,0001 moldm-3

10 Ks 1,769.10 6 3 s  2  2 1,812.10 mol.dm cNaCl  0,0001.0,988

1 2 3 I  ci zi  0,0001moldm 2 i

log    z z A I  0,511.1. 0,0001  0,00511

0,00511   10  0,988 Summary Characterize strong and weak electrolytes! (write an example) Express the degree of dissociation of a solution at concentration c when c’ is the dissociated part of the substance. Write the expression for electrical conductivity! Write the expression for molar conductivity! Write the expression for independent migration of ions (Kohlraush’s law)! How depends molar conductivity of strong electrolyte on its concentration? Write the expression for the ionic strength of a solution! Write the equation for the calculation of activity coefficients usig Debye-Huckl limiting law! Express the solubility product of a slightly soluble substance MX! Express the solubility s of a slightly soluble salt with the solubility product Ks in water!