Soil Fertility and Nutrient Management

Deptt. Agril. Chemistry and Soil ScienceBidhan Chandra Krishi Viswavidyalaya,

E-mail: pabitramani@gmail.com, Website: www.bckv.edu.in

: 91-33-25822132, 91-9477465968,

Dr. Pabitra Kumar Mani

August 21, 2013

Experiential Learning, NRM Module-1, ACSS-451

Assoc. Professor

The Danish biochemist Soren Sorensen invented the pH scale in 1909.

When applied to the full cell formed from half cells present on inside and outside of glass pH electrode, Nernst equation takes form:

pH inside of the electrode has constant value, thus it can be included in the potential part of the equation:

This form of the equation describes behavior of the glass electrode used for pH measurements

The Ionization of Water Is Expressed by an Equilibrium ConstantThe degree of ionization of water at equilibrium (Eqn 2–1) is small; at 25 °C only about two of every 109 molecules in pure water are ionized at any instant. The equilibrium constant for the reversible ionization of water (Eqn 2–1) is

In pure water at 25°C, the concentration of water is 55.5 M (grams of H2O in 1 L divided by its gram molecular weight: (1,000 g/L)/(18.015 g/mol)) and is essentially constant in relation to the very low concentrations of H and OH, namely, 1X 10-7 M. Accordingly, we can substitute 55.5 M in the equilibrium constant expression (Eqn 2–3) to yield

which, on rearranging, becomes

where Kw designates the product (55.5 M)(Keq), the ion product of water at 25 °C.

The value for Keq, determined by electrical-conductivity measurements of pure water, is 1.8 X 10 -16 M at 25°C. Substituting this value for Keq in Equation gives the value of the ion product of water:

Thus the product [ H+ ][ OH- ] in aqueous solutions at 25°C always equals 1x10 -14 M2. When there are exactly equal concentrations of H+ and OH-, as in pure water, the solution is said to be at neutral pH. At this pH, the concentration of H+ and OH- can be calculated from the ion product of water as follows:

How a pH meter works When one metal is brought in contact with another, a voltage difference occurs due to their differences in electron mobility. When a metal is brought in contact with a solution of salts or acids, a similar electric potential is caused, which has led to the invention of batteries. Similarly, an electric potential develops when one liquid is brought in contact with another one, but a membrane is needed to keep such liquids apart. 

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.

General Principles

Reference electrode | salt bridge | analyte solution | indicator electrode

Eref Ej Eind

Ecell = Eind – Eref + Ej

Reference cell :

a half cell having a known electrode

potential

Indicator electrode:

has a potential that varies in a

known way with variations in

the concentration of an analyte

A cell for potentiometric determinations.

Introduction

1.) Potentiometry Use of Electrodes to Measure Voltages that Provide Chemical Information

- Various electrodes have been designed to respond selectively to specific analytes

Use a Galvanic Cell- Unknown solution becomes a ½-

cell- Add Electrode that

transfers/accepts electrons from unknown analyte

- Connect unknown solution by salt bridge to second ½-cell at fixed composition and potential

Indicator Electrode: electrode that responds to analyte and donates/accepts electrons

Reference Electrode: second ½ cell at a constant potential

Cell voltage is difference between the indicator and reference electrode

Reference Electrodes

1.) Overview Potential change only dependent on one ½ cell

concentrations Reference electrode is fixed or saturated doesn’t change!

Reference electrode, [Cl-] is constant

Potential of the cell only depends on

[Fe2+] & [Fe3+]

Pt wire is indicator electrode whose potential responds to [Fe2+]/[Fe3+]

]Cllog[..]Fe[

]Fe[log

..Ecell

0591602220

1

0591607710

3

2

Unknown solution of[Fe2+] & [Fe3+]

Reference Electrodes

2.) Silver-Silver Chloride Reference Electrode

Convenient- Common problem is porous plug becomes clogged

Eo = +0.222 V

Activity of Cl- not 1E(sat,KCl) = +0.197 V

Reduction potential

Reference Electrodes

3.) Saturated Calomel Reference Electrode (S.C.E)

Saturated KCl maintains constant [Cl-] even with some evaporation

Standard hydrogen electrodes are cumbersome

- Requires H2 gas and freshly prepared Pt surface

Eo = +0.268 V

Activity of Cl- not 1E(sat,KCl) = +0.241 V

Indicator Electrodes

1.) Two Broad Classes of Indicator Electrodes Metal Electrodes

- Develop an electric potential in response to a redox reaction at the metal surface

Ion-selective Electrodes- Selectively bind one type of ion to a membrane to

generate an electric potential

Remember an electric potential is generated by a separation of charge

Indicator Electrodes

2.) Metal Electrodes Platinum

- Most common metal indicator electrode- Inert: does not participate in many chemical reactions- Simply used to transmit electrons

Other electrodes include Gold and Carbon Metals (Ag, Cu, Zn, Cd, Hg) can be used to monitor their aqueous ions

- Most metals are not useable- Equilibrium not readily established at the metal surface

E+o = +799 V

E(sat,KCl) = +0.241 V

½ Reaction at Ag indicator electrode:

½ Reaction at Calomel reference electrode:

24101

1

0591607990 .

]Ag[log

..EEEcell

Potential of Ag indicator electrode

Cell voltage changes as a function of [Ag+]

Example:

Cell Potential from Nernst Equation:

Typical electrode system for measuring pH. (a) Glass electrode (indicator) and saturated calomel electrode (reference) immersed in a solution of unknown pH. (b) Combination probe consisting of both an indicator glass electrode and a silver/silver chloride reference. A second silver/silver chloride electrode serves as the internal reference for the glass electrode.

The two electrodes are arranged concentrically with the internal reference in the center and the external reference outside. The reference makes contact with the analyte solution through the glass frit or other suitable porous medium.

Combination probes are the most common configuration of glass electrode and reference for measuring pH.

The majority of pH electrodes available commercially are combination electrodes that have both glass H+ ion sensitive electrode and additional reference electrode conveniently placed in one housing.

• In a chemical reaction such as: aA + bB cC + dD

QRTGaa

aaRTGG o

bB

aA

dD

cCo log3.2

.

.log3.2

Where: Go : Free energy change when all the reactants and

products are in their standard states (unit activity). R : is the gas constant.

T : is the temperature in the absolute temperatureQ : Reaction Quotient

nFEG oo nFEG

When cell is not at standard conditions, use Nernst Equation

Substitute

ba

dco

BA

DCRTnFEnFE

][][

][][ log3.2

ba

dco

BA

DC

nF

RTEE

][][

][][ log

3.2

Where concentrations are substituted for activitiesAt 298 K the equation becomes

At Equilibrium, G = 0, E = 0. Hence

Kn

E o log0591.0

0 Kn

E o log0591.0

bB

aA

dD

cCo

aa

aaRTGG

.

.log3.2

ba

dco

BA

DC

nEE

][][

][][ log

0591.0

K

…… Nernst Equation

Derivation of the EMF equation

For the general rn., Red Ox + ne⇋ -

The chemical potential are given by

µRed = µ0Red+ RTlnaRed

µOx = µ0Ox+ RTlnaOx

µRed - µOx = µ0Red - µ

0Ox + RTln(aRed /aOx)

-ΔG = (µ0Red - µ

0Ox) + RTln(aRed /aOx)

but , considering the electrical work associated with transfer of n no. Of electrons,

ΔG= -nFE

RedaOxa

lnnF

RT-

nFOx0μ

Red0μ

E

When aOx =aRed = 1, then

nFOx

0μRed

0μE0

RedaOxa

lnnF

RT-EE 0

RedaOxa

logn

0.0591-EE, 0so

T=2980KF=96000 Coulomb

In principle it should be possible to determine the H+ ion activity or concn. of a soln by measuring the potential of a Hydrogen electrode inserted in the given soln. The EMF of a cell, free from liquid junction potential, consisting of a Hydrogen electrode and a reference electrode, should be given by,

E = E ref – RT/F ln aH+ E = E ref + 2.303 RT/F pH R= 8.314 J/mol/°K

pH = ( E- Eref )F/2.303 RT F= faraday constant ,96,485

T= Kelvin scaleSo, by measuring the EMF of the Cell E obtained by combining the H electrode with a reference electrode of known potential, Eref , the pH of the soln. may be evaluated.The electric potential at any point is defined as the work done in bringing a unit charge from infinity to the particular point

Reduced state Oxidised state + n Electron⇋ M = Mn+ + nE E(+) = E0 – (RT/F) ln aM

n+ Nernst Equation

Electrodes and Potentiometry : pH Electrodes

1.) pH Measurement with a Glass Electrode Glass electrode is most common ion-selective electrode Combination electrode incorporates both glass and

reference electrode in one body

Ag(s)|AgCl(s)|Cl-(aq)||H+(aq,outside) H+(aq,inside),Cl-(aq)|AgCl(s)|Ag(s)

Outer referenceelectrode

[H+] outside(analyte solution)

[H+] inside Inner referenceelectrode

Glass membraneSelectively binds H+

Electric potential is generated by [H+] difference across glass membrane

Electrodes and Potentiometry pH Electrodes

2.) Glass Membrane Irregular structure of silicate lattice

Cations (Na+) bind oxygen in SiO4 structure

pH Electrodes

2.) Glass Membrane Two surfaces of glass “swell” as they absorb water

- Surfaces are in contact with [H+]

pH Electrodes

2.) Glass Membrane H+ diffuse into glass membrane and replace Na+ in hydrated gel

region- Ion-exchange equilibrium- Selective for H+ because H+ is only ion that binds

significantly to the hydrated gel layer

H(0.05916)constant pE

Charge is slowly carried by migration of Na+

across glass membrane

Potential is determined by external [H+]

Constant and b are measured when electrode is calibrated with solution of known pH

the operation of a glass electrode is related to the situations existing at the inner and outer surfaces of the glass membrane. Glass electrodes require soaking in water for some hours before use and it is concluded that a hydrated layer is formed on the glass surface, where an ion exchange process can take place. If the glass contains sodium, the exchange process can be represented by the equilibrium

The concn of the soln within the glass bulb is fixed, and hence on the inner side of the bulb an equilibrium condition leading to a constant potential is established. On the outside of the bulb, the potential developed will be dependent upon the hydrogen ion concentration of the soln in which the bulb is immersed. Within the layer of 'dry' glass which exists between the inner and outer hydrated layers, the conductivity is due to the interstitial migration of sodium ions within the silicate lattice.

Most often used pH electrodes are glass electrodes. Typical model is made of glass tube ended with small glass bubble. Inside of the electrode is usually filled with buffered solution of chlorides in which silver wire covered with silver chloride is immersed. pH of internal solution varies - for example it can be 1.0 (0.1M HCl) or 7.0 (different buffers used by different producers).Active part of the electrode is the glass bubble. While tube has strong and thick walls, bubble is made to be as thin as possible. Surface of the glass is protonated by both internal and external solution till equilibrium is achieved. Both sides of the glass are charged by the adsorbed protons, this charge is responsible for potential difference. This potential in turn is described by the Nernst equation and is directly proportional to the pH difference between solutions on both sides of the glass.

pH Electrodes

3.) Calibration A pH electrode should be calibrated with two or

more standard buffers before use. pH of the unknown should lie within the range

of the standard buffers

Measured voltage is correlated with a pH, which is then used to measure an unknown.

For soils containing predominantly negatively charged clays, dilution of the soil solution by distilled water increases the absolute value of the surface potential and changes the distribution of H+ ions between the DDL and the bulk solution. The proportion of H+ ions in the DDL relative to the bulk solution increases so that the measured pH, which is the bulk solution pH, is higher than that of the natural soil. This effect is especially noticeable in saline soils.

An alternative method is to shake the soil with 0.01 M CaCl2 solution until equilibrium is attained. This solution, containing the most abundant exchangeable cation in many soils, also has an ionic strength I approximating that of the soil solution.

In this soil suspension, both H+ and Ca2+ exchange with other cations in the DDL, but the ratio of H+/√Ca2+ in solution remains relatively constant, even when the ratio of soil to equilibrating liquid changes. Thus, pH measured in 0.01 M CaCl2 is a more accurate reflection of the natural soil pH, as is demonstrated by the comparison between soil pH measured in water, in 0.01 M CaCl2 , and in a soln. that has been shaken with successive samples of soil to achieve equilibrium

The ionic distribution at a negatively charged clay surface.

For soils containing predominantly negatively charged clays, dilution of the soil solution by distilled water increases the absolute value of the surface potential and changes the distribution of H+ ions between the DDL and the bulk solution. The proportion of H+ ions in the DDL relative to the bulk solution increases so that the measured pH, which is the bulk solution pH, is higher than that of the natural soil. This effect is especially noticeable in saline soils.

An alternative method is to shake the soil with 0.01 M CaCl2 solution until equilibrium is attained. This solution, containing the most abundant exchangeable cation in many soils, also has an ionic strength I approximating that of the soil solution.

In this soil suspension, both H+ and Ca2+ exchange with other cations in the DDL, but the ratio of H+/√Ca2+ in solution remains relatively constant, even when the ratio of soil to equilibrating liquid changes. Thus, pH measured in 0.01 M CaCl2 is a more accurate reflection of the natural soil pH, as is demonstrated by the comparison between soil pH measured in water, in 0.01 M CaCl2 , and in a soln. that has been shaken with successive samples of soil to achieve equilibrium

where Ci and zi are the concentration and charge, respectively, of ion i in a mixture of ionic species i = 1 to n. The term ‘concentration’ refers to the mass of an ionic species per unit volume of solution (e.g. mol/L).

An individual ion experiences weak forces due to its interaction with water molecules (the formation of a hydration shell), and stronger electrostatic forces due to its interaction with ions of opposite charge. Effectively, this means that the ability of the ion to engage in chemical reactions is decreased, relative to what is expected when it is present at a particular concentration with no interactions. This effect is accounted for by defining the activity ai of ion i, which is related to its concentration by the equation

where fi is the activity coefficient of the ion. Values of fi range from 0 to 1. In very dilute solutions where the interaction effects are negligible, fi approaches 1, and ai is approximately equal to Ci. There is extensive theory on the calculation of activity coefficients, but all calculations make use of the ionic strength I, such as in the Debye–Huckel limiting law (Atkins, 1982)

I = 0.0127 x Ecw

Griffin and Jurinak, 1973

The difference in pH(ΔpH) between the sediment and supernatant produced during soil pH determination is termed the 'suspension effect′ (McLean 1982). If the soil suspension is allowed to settle, the pH as measured in the suspension liquid is often higher than in the sediment layer.

The suspension effect is influenced by the extent to which electrodes encounter clay and humus particles and the soil CO2 is in equilibrium with atmospheric concentrations, and the magnitude of liquid junction effects (Foth and Ellis 1988).

The suspension effect is minimised by measuring soil pH using 0.01 M CaCl2 or 1 M KCl solutions instead of water (Sumner 1994). In addition, the use of CaCl2 or KCl solutions has the advantages of (i) decreasing the effect of the junction potential of the calomel reference electrode, (ii) equalising the salt content of soils, and (iii) Preventing dispersion of the soil (Tan 1995).

Junction Potential

1.) Occurs Whenever Dissimilar Electrolyte Solutions are in Contact Develops at solution interface (salt bridge) Small potential (few milli volts) Junction potential puts a fundamental limitation on the

accuracy of direct potentiometric measurements

- Don’t know contribution to the measured voltage

Again, an electric potential is generated by a separation of charge

Different ion mobility results in separation in charge

Mobilties of ions in water at 25oC:

Na+ : 5.19 × 10 –8 m2/sV K+ : 7.62 × 10 –8 Cl– : 7.91× 10 –8

General relationship between soil pH and availability of plant nutrients in minimally and moderately weathered soils; the wider the bar, the more availability.

Nitrogen availability is maximum between pH 6 and 8, because this is the most favorable range for the soil microbes that mineralize the nitrogen in organic matter and those organisms that fix nitrogen symbiotically. High phosphorus availability at high pH-above 8.5-is due to sodium phosphates that have high solubility. In calcareous soil, pH 7.5 to 8.3, phosphorus availability is re-duced by the presence of calcium carbonate that represses the dissolution of calcium phosphates.

Maximum phosphorus availablity is in the range 7.5 to 6.5. Below pH 6.5, increasing acidity is associated with increasing iron and aluminum in solution and the formation of relatively insoluble iron and aluminum phosphates.

Note that potassium, calcium, and magnesium are widely available in alkaline soils. As soil acidity increases, these nutrients show less availability as a result of the decreasing CEC and decreased amounts of exchangeable nutrient cations.

Iron and manganese availability increase with increasing acidity because of their increased solubility.These two nutrients are frequently deficient in plants growing in alkaline soils because of the insolubility of their compounds

Boron, copper, and zinc are leachable and can be deficient in leached, acid soils. Conversely, they can become insoluble (fixed) and unavailable in alkaline soils. In acid soils, molybdenum is commonly deficient owing to its reaction with iron to form an insoluble compound. For plant nutrients as a whole, good overall nutrient

availability occurs near pH 6.5. In intensively weathered soils, nutrients such as B and Zn may be deficient at lower pH than for minimally and moderately weathered soils. As a consequence, a desirable pH is 5.5 in intensively weathered soils.

Ohm's Law States that the current I (amperes) flowing in a conductor is directly proportional to the applied electromotive force E (volts) and inversely proportional to the resistance R (ohms) of the conductor

The reciprocal of the resistance is termed the conductance (G): this is measured in reciprocal ohms (or Ω –), for which the name Siemens (S) is used. The resistance of a sample of homogeneous material, length l, and cross-section area a, is given by:

where ρ is a characteristic property of the material termed the resistivity (formerly called specific resistance). In SI units, l and a will be measured respectively in metres and square metres, so that ρ refers to a metre cube of the material, and

The reciprocal of resistivity is the conductivity, κ (formerly specific conductance), which in SI units is the conductance of a one metre cube of substance and has the units Ω – m - , but if ρ is measured in Ωcm, then κ will be measured in Ω - cm - '.

45

Electrical Conduction• Ohm's Law: V = I R

voltage drop (volts = J/C) C = Coulomb

resistance (Ohms)current (amps = C/s)

1

• Conductivity,

• Resistivity, : -- a material property that is independent of sample size and geometry

RA

l

surface area of current flow

current flow path length

46

Electrical Properties• Which will have the greater resistance?

• Analogous to flow of water in a pipe• Resistance depends on sample geometry and size.

D

2D

R1 2

D2

2

8D2

2

R2

2D

2

2D2

R1

8

This is based on the principle that the conductivity, or ease with which an electric current is carried through a solution, is proportional to the quantity of ions (actually, the quantity of ionic charge) in solution.

To measure soil conductivity, the soil is mixed with water until it has a paste like consistency. A pair of electrodes, commonly made of platinum metal, is inserted into this "saturated paste." The electrodes are characterized by their surface area, A cm2 (usually about 1 cm2), and their separation distance of L cm (usually about 1 cm), as illustrated in Figure. An alternating current is then applied to the electrode pair, and the conductance of the paste is measured in units of reciprocal ohms (mho),or Siemens

Two-electrode cell used to measure electrical conductivity of solutions and saturated soil pastes

Electrical Conductivity

Conductivity Probe

• 2 metals in contact with electrolyte solution

• Voltage is applied to electrodes and resulting current that flows btw electrodes is used to determine conductance

• Amount of current flowing depends on:– Solution conductivity– Length, surface area,

geometry of electrodes

Conductivity Probe• Apply an AC Voltage to Two Electrodes of Exact Dimensions• Acids, Bases and Salts (NaCl) Dissolve in Solution and Act as

Current Carriers• Current Flow is Directly Proportional to the Total Dissolved

Solids in Solution • Physical Dimensions of a Conductivity Electrode are Referred to

as the Cell Constant• Cell Constant is Length/Area Relationship

– Distance Between Plates = 1.0 cm– Area of Each Plate = 1.0 cm x 1.0 cm– Cell Constant = 1.0 cm-1

Cell Constant

• Cell constant:– Measure of current

response of a sensor conductive solution

– Due to sensor’s dimensions and geometry

– Units: cm-1 (length divided by area)

EC, unlike conductance, is strictly a property of the solution, whereas L/A is a characteristic of the electrode geometry and is called the cell constant. For a saturated paste, an EC value greater than 4 milli Siemens/cm (mS cm-I) is diagnostic of a saline soil.

But this conductance depends on A and L and is therefore a characteristic of the measuring device as well as the solution. It is more useful to define a specific conductance, termed the electrical conductivity or EC, by the equation:

The current-carrying ability of a mole of cation or anion charge in solution is termed the equivalent conductance. This value is measured in very dilute solutions to ensure that the salts are fully dissociated into individual cations and anions. The measured conductance is then assumed to result from the summation of conductances contributed by each of the ions. As a result, each ion can be assigned an equivalent conductance, listed in Table 8.2, that represents its contribution (per mole of charge) to the measured (total) conductivity.

52

Conduction & Electron Transport• Metals (Conductors):

-- for metals empty energy states are adjacent to filled states.

-- two types of band structures for metals

-- thermal energy excites electrons into empty higher energy states.

- partially filled band - empty band that overlaps filled band

filled band

Energy

partly filled band

empty band

GAP

fille

d st

ates

Partially filled band

Energy

filled band

filled band

empty band

fille

d st

ates

Overlapping bands

53

Energy Band Structures: Insulators & Semiconductors

• Insulators: -- wide band gap (> 2 eV) -- few electrons excited across band gap

Energy

filled band

filled valence band

fille

d st

ates

GAP

empty

bandconduction

• Semiconductors: -- narrow band gap (< 2 eV) -- more electrons excited across band gap

Energy

filled band

filled valence band

fille

d st

ates

GAP?

empty

bandconduction

It is apparent that H+ and OH- have anomalously high conductances, while most cations and anions contribute about equally per mole of ionic charge to the conductivity of solutions. This fact allows simple but approximate empirical relationships to be established between the concentration of electrolyte solutions and the conductivity, irrespective of ionic composition.

For strong electrolytes the molar conductivity increases as the dilution is increased, but it appears to approach a limiting value known as the molar conductivity at infinite dilution(Λ∞). The quantity Λ∞ can be determined by graphical extrapolation for dilute solutions of strong electrolytes.

For weak electrolytes the extrapolation method cannot be used for the determination of Λ∞ but it may be calculated from the molar conductivities at infinite dilution of the respective ions, use being made of the 'Law of Independent Migration of Ions‘. At infinite dilution the ions are independent of each other, and each contributes its part of the total conductivity, thus:

THE BASlS OF CONDUCTIMETRIC TlTRATlONS

principle underlying conductimetric titrations, i.e. The substitution of ions of one conductivity by ions of another conductivity.

57

DefinitionsFurther definitions

J = <= another way to state Ohm’s law

J current density

electric field potential = V/

flux a like area surface

current

A

I

Electron flux conductivity voltage gradient

J = (V/ )

58

What is the minimum diameter (D) of the wire so that V < 1.5 V?

Example: Conductivity Problem

Cu wire I = 2.5 A- +

V

Solve to get D > 1.87 mm

< 1.5 V

2.5 A

6.07 x 107 (Ohm-m)-1

100 m

I

V

AR

4

2D

100 m

Filling of electronic band structure in various types of material at thermodynamicEquilibrium. In metals and semimetals the Fermi level EF lies inside atleast one band. In insulator (electricity)insulators and semiconductors the Fermilevel is inside a band gap, however in semiconductors the bands are near enough tothe Fermi level to be Fermi-Dirac statistics thermally populated with electrons orElectron holes.

The calomel reference electrode consists of a glass tube with a potassium chloride (KCl) electrolyte which is in intimate contact with a mercuric chloride element at the end of a KCL element. It is a fragile construction, joined by a liquid junction tip made of porous ceramic or similar material. This kind of electrode is not easily 'poisoned' by heavy metals and sodium.

The glass electrode consists of a sturdy glass tube with a thin glass bulb welded to it. Inside is a known solution of potassium chloride (KCl) buffered at a pH of 7.0. A silver electrode with a silver chloride tip makes contact with the inside solution. To minimise electronic interference, the probe is shielded by a foil shield, often found inside the glass electrode.

Most modern pH meters also have a thermistor temperature probe which allows for automatic temperature correction, since pH varies somewhat with temperature

The conductance of an electrolytic solution at any temperature depends only on the ions present, and their concentration. When a solution of an electrolyte is diluted, the conductance will decrease, since fewer ions are present per millilitre of solution to

carry the current. If all the solution be placed between two electrodes 1 cm apart and large enough to contain the whole of the solution, the conductance will increase as the solution is diluted. This is due largely to a decrease in inter-ionic effects for strong electrolytes and to an increase in the degree of dissociation for weak electrolytes.The molar conductivity (Λ) of an electrolyte is defined as the conductivity due to one mole and is given by:

Electrons in solids• In a solid, there are so many electrons with energies very near each

other that ‘bands’ of states develop.

Isolated atoms

SolidAll we draw is the “band diagram”

63

• Room temperature values (Ohm-m)-1 = ( - m)-1

Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 8e.

Conductivity: Comparison

Silver 6.8 x 107

Copper 6.0 x 107

Iron 1.0 x 107

METALS conductors

Silicon 4 x 10-4

Germanium 2 x 10 0

GaAs 10-6

SEMICONDUCTORS

semiconductors

Polystyrene <10-14

Polyethylene 10-15-10-17

Soda-lime glass 10

Concrete 10-9

Aluminum oxide <10-13

CERAMICS

POLYMERS

insulators

-10-10-11

Electrons in atoms

H1s

He1s

B

1s

1p

Electrons in an atom have particular energies (quantized energy states) depending on which orbital they are in.

Energy

Pauli exclusion principle

65

Band Structure Representation

Adapted from Fig. 18.3, Callister & Rethwisch 8e.

• In a solid, there are so many electrons with energies very near each other that ‘bands’ of states develop.

66

Electron Energy Band Structures

Adapted from Fig. 18.2, Callister & Rethwisch 8e.

Definition of Conductivity

• The free-est electron (the electron with the highest energy) defines the position of the “Fermi level.”

– Above Ef, all available electron states in the energy bands are empty

– Below Ef, they are all filled.

• If there is no gap between filled and empty states, the material is conductive.

• If there is a gap, the material is a semiconductor or insulator.

Energy

Metal (Cu)

partially filled 4s

(conduction)

Empty 4p (conduction)

Band gap

Band gap

Filled (valence)

Ef, Fermi level

Energy band structures for various metals

• Partially filled or empty bands are called ‘conduction bands.’

• Any band that is totally filled is considered to be a “valence band.”– We usually ignore ‘deep’

valence bands.

Energy

Metal (Cu)

partially filled 4s

(conduction)

filled 3d, 3p, 3s, 2p, 2s, 1p, 1s (valence)

Empty 4p (conduction)

Band gap

Band gap

Filled 3d (valence)

Deep valence-only an issue for optical properties