Solutions of electrolytes

Electrolytic solutions are those that are capable of conducting an electric current. A substance that, when added to water, renders it conductive, is known as an electrolyte. A common example of an electrolyte is ordinary salt, sodium chloride. Solid NaCl and pure water are both non-conductive, but a solution of salt in water is readily conductive. A solution of sugar in water, by contrast, is incapable of conducting a current; sugar is therefore a non-electrolyte.

See this video demonstrating electrical conductance of an electrolyte (4 min)

These facts have been known since 1800 when it was discovered that an electric current can decompose the water in an electrolytic solution into its elements (a process known as electrolysis). By mid-century, Michael Faraday had made the first systematic study of electrolytic solutions.

Faraday recognized that in order for a sample of matter to conduct electricity, two requirements must be met:

• The matter must be composed of, or contain, electrically charged particles.
• These particles must be mobile; that is, they must be free to move under the influence of an external applied electric field.

In metallic solids, the charge carriers are electrons rather than ions; their mobility is a consequence of the quantum-mechanical uncertainty principle which promotes the escape of the electrons from the confines of their local atomic environment. (More)

In the case of electrolytic solutions, Faraday called the charge carriers ions (after the Greek word for "wanderer"). His most important finding was that each kind of ion (which he regarded as an electrically-charged atom) carries a definite amount of charge, most commonly in the range of ±1-3 units.

The fact that the smallest charges observed had magnitudes of ±1 unit suggested an "atomic" nature for electricity itself, and led in 1891 to the concept of the "electron" as the unit of electric charge — although the identification of this unit charge with the particle we now know as the electron was not made until 1897.

← An ionic solid such as NaCl is composed of charged particles, but these are held so tightly in the crystal lattice that they are unable to move about, so the second requirement mentioned above is not met and solid salt is not a conductor. If the salt is melted or dissolved in water, the ions can move freely and the molten liquid or the solution becomes a conductor.

Since positively-charged ions are attracted to a negative electrode that is traditionally known as the cathode, these are often referred to as cations. Similarly, negatively-charged ions, being attracted to the positive electrode, or anode, are called anions. (These terms were all coined by Faraday.)

Although we tend to think of the solvent (usually water) as a purely passive medium within which ions drift around, it is important to understand that

• Electrolytic solutions would not exist without the active involvement of the solvent in reducing the strong attractive forces that hold solid salts and molecules such as HCl together;
• Once the ions are released, they are stabilized by interactions with the solvent molecules.

Water is not the only liquid capable of forming electrolytic solutions, but it is by far the most important. It is therefore essential to understand those properties of water that influence the stability of ions in aqueous solution.

According to Coulomb's law, the force between two charged particles is directly proportional to the product of the two charges, and inversely proportional to the square of the distance between them:

The proportionality constant D is the dimensionless dielectric constant. Its value in empty space is unity, but in other media it will be larger. Since D appears in the denominator, this means that the force between two charged particles within a gas or liquid will be less than if the particles were in a vacuum.

Water has one of the highest dielectric constants of any known liquid; the exact value varies with the temperature, but 80 is a good round number to remember. When two oppositely-charged ions are immersed in water, the force acting between them is only 1/80 as great as it would be between the two gaseous ions at the same distance.

It can be shown that in order to separate one mole of Na⁺ and Cl^– ions at their normal distance of 23.6 pm in solid sodium chloride, the work required will be 586 J in a vacuum, but only 7.3 J in water

When an ion is introduced into a solvent, the attractive interactions between the solvent molecules must be disrupted in order to create space for the ion. This costs energy and would by itself tend to inhibit dissolution. But if the solvent has a high permanent dipole moment, the energy cost is more than recouped by the ion-dipole attractions between the ion and the surrounding solvent molecules.

... but it is by far the best. For some purposes, chemists occasionally need to employ non-aqueous solvents when studying electrolytes. Here are a few examples:

Pure water is believed to consist of ever-changing regions of hydrogen-bonded molecules loosely organized into irregular ice-like tetrahedral "clusters", interspersed with more dense regions of jumbled H₂O molecules in which hydrogen bonding still occurs but not to the extent that it controls the local structure. Clusters are estimated to contain 50-200 H₂O molecules at room temperature and to have lifetimes in the range of 10-100 picoseconds.

Individual hydrogen bonds have lifetimes of only a few picoseconds, so even within a cluster, these bonds are continually breaking and re-forming in new configurations. It is believed that when one bond breaks, it initiates a cascade of breaks among nearby bonds as these molecules settle into more stable tetrahedral arrangements.

There is probably a continual migration of individual H₂O molecules between clustered and disordered regions. As the temperature rises, the more disordered regions begin to grow at the expense of the clusters.

When an ion is introduced into water, the relatively strong ion-dipole attractions tend to impose an octahedral-like configuration on the surrounding H₂O molecules, thus disrupting the quasi-tetrahedral structure of the bulk water. This can either increase or decrease the local ordering of water around the ion:

• Small ions such as Li⁺, Mg²⁺, Al⁺³⁺ and F^– have high charge densities which strongly align the surrounding H₂O's. The amount of new ordering thus created tends to outweigh the disorder due to the "hole" in the water structure that the ion creates. Such ions tend to pull H₂O molecules from bulk water into the more compact hydration shell; they are therefore said to be "structure-making" and often exhibit negative entropies of hydration. NO₃^– and ClO₄^– are also believed to fall into this category.
• Larger and less-polarizing ions such as Cs⁺, Br^– and I^–, as well as the polyatomic ions SO₄^2– and PO₄^3– are less effective in aligning the surrounding H₂O molecules, but their larger volumes tend to cause more local disorder. The "structure-breaking" ions commonly have positive hydration entropies.

As was explained in the section on the energetics of salt dissolution, the ability of salts to dissolve in water depends strongly on their stabilization by the solvent molecules. This process is known generally as solvation, and in the case of water, as hydration. All ions dissolved in water are hydrated.

Bear in mind that the attractive forces that are operational here — hydrogen bonding (dipole-dipole) and even the stronger ion-dipole forces that bind the waters in the primary shell to the central ion — are continually subject to disruption by thermal motions. This affects even the waters within the primary shell; residence times of these H₂O molecules are usually less than 10^–4 sec.

The total number of waters bound to the central ion is known as the hydration number of the ion. Unfortunately, what we mean by "attached" is somewhat difficult to define, and experimental estimates seem to depend a lot on the particular methods employed to investigate it. Whatever the value may be at any instant, it is quite certain to be continually changing, so we can only regard hydration numbers as averages. Moreover, these H₂Os are subject to replacement by other ligands that have a similar or greater affinity for the central ion.

In general, there appears to be more agreement on numbers closer to the upper ends of these ranges. This supports the generally-held assumption that the smaller and more highly charged the ion (i.e., the greater its charge density), the more highly hydrated it will be.

Transition-metal complexes

It is generally known that aqua-complexes such as the iron-III example shown above act as acids (for details, see the section on hydrous complexes in another lesson of this series). What is less widely understood is that all cations are acidic.

The "source" of the acidity is the the primary hydration shell. The nearby positive charge on the ion M⁺ encourages the loss of a proton from an attached H₂O according to

M(H₂O)⁺ → M(OH)^– + H⁺

For a more detailed discussion of cation acid strengths, see the article All Positive Ions Give Acid Solutions in Water: Stephen J. Hawkes, J Chem Educ 1996(6) 516-517. The pK_a values shown in the table are taken from this article.

The acid strengths of these ions depend on their charge densities. The effect is negligible in alkali-metal salts, with the exception of those of the very small Li⁺ ion. In the ions of Group 2, 0.1 M L^–1 solutions of the salts will reduce the pH of water by a few tenths of a unit. Ions of Group 3 and beyond can exhibit strengths comparable to that of acetic acid (pK_a 4.75).

Some pK_a values of 0.1 M solutions of typical ions:

Given the above values, it is not surprising that a solution of FeCl₃ is often referred to as an "acid" in industries that use it.

Many of these ions bind water molecules so strongly that they remain hydrated even in their crystalline forms.

Similarly, each Al³⁺ ion in the double hydrate KAl(SO₄)₂·12H₂O is surrounded by six. Some of the water molecules in these crystals are bound to specific ions, while others belong to the crystal structure as a whole.

It is of course impossible to introduce a single kind of ion into water; bulk matter cannot possess a significant net electric charge, so all ionic solutions contain both anions and cations in the proportions required to ensure electroneutrality. Coulombic interactions between charged particles fall off with separation distance far more slowly than do the weaker ion-dipole forces responsible for water ordering, and are thus operative even in solutions that we would normally regard as quite dilute — down to about 10^–4 M L^–1.

Depending on the sizes and charges of the two kind of ions, they may form relatively stable ion pairs in which the "bonding" is purely electrostatic and independent of the chemical properties of the ions.

As was mentioned in a previous lesson of this unit, neglect of ion-pairing can lead to erroneous assumptions about the concentrations of "free" ions in solutions, and misinterpretation of solubility-product calculations.

• Thus, in addition to forming the sparingly-soluble solid CdI₂, part of the cadmium in a solution in equilibrium with the two ions will exist as the soluble species CdI^–(aq) and CdI₂⁰(aq).
• Similarly, solutions in equilibrium with Ca(OH)₂(s) will also contain CaOH⁺(aq) and Ca(OH)₂⁰(aq).
• The ion-pair CaCO₃⁰(aq) is believed to tie up a significant fraction of the total carbonate when water is in equilibrium with solid calcium carbonate.

You will recall that the conceptual definition of an ideal solution requires that the interactions of solvent-solvent, solvent-solute, and solute-solute molecules are identical — something that is clearly not possible in ionic solutions. As a consequence, the operational criteria of solution ideality — linear dependence of colligative and other properties on nominal concentrations, does not apply.

For the reasons outlined in the preceding section, you cannot realistically expect calculations based on equilibrium constants to reliably predict the compositions of solutions having significant concentrations of ions.

The actual quantity we use to express the summed concentrations of ions of all kinds in a solution is the ionic strength. See this Wikipedia article for a definition and examples.

What "significant" means in this context depends on the charges of the ions, and this includes "spectator" ions that are not directly involved in a reaction. A very crude rule-of-thumb is that ion concentrations in excess of
0.0001 M L^–1 are likely to exhibit non-ideal behavior.

The quantitative treatment of ionic solutions is based on the Debye-Hückel theory which was developed in the 1920s. This theory models the electrostatic interactions between ions and their ionic atmospheres, and can predict mean ionic activity coefficient for solutions whose ionic strengths are not very high. Many extensions to this model have been suggested; all are mathematically complicated and all fail for "really concentrated" solutions.

The practical approach to the problem of non-ideality is to introduce a quantity known as the activity, which can be thought of as the thermodynamically-effective concentration. The relation between activity a and the "analytical" concentration c is given by the activity coefficient γ (gamma):

a = γ c

• An ideal solution has an activity coefficient of unity.
• As ionic concentrations increase, activity constants diminish.
• Activity coefficients approach unity in the limit of zero concentration.

Because solutions containing ions of a single charge species cannot be prepared, all experimental measurements can only yield mean ionic activity coefficients γ_±.

For reliable calculations, it is necessary to replace ordinary concentration-based equilibrium constants K_c with thermodynamically-effective equilibrium constants K_a:

K_a = γ_± K_c

The conduction of electricity through an ionic solution is different from metallic conduction in two fundamental ways:

• The current is associated with the transport of relatively large and massive hydrated ions, rather than by nearly weightless electrons. Electrons move largely unimpeded through the metal. But ions, with their closely-held waters of hydration and more diffuse secondary hydration shell and oppositely-charged counterions, must disrupt the local hydrogen-bonded water structure as they move through the solution.
• Transfer of electric charge into and out of the solution occurs at electrodes, and is accompanied by chemical reactions at these interfaces.

Electrolytic conduction involves the transport of electric charge in the form of hydrated ions. Movement of these ions in response to an electric potential gradient is known as migration.

Electric charge is measured in units of coulombs. A coulomb is an ampere-second; if a current of 1 amp flows for one minute, the quantity of charge transported will be 3600 C.

When charges migrate in an electric field, thermodynamic work is done. One C of charge moving through a potential difference of one volt results in the performance of one joule of work.

Electrical resistance, conductance, and conductivity

Ionic migration is always impeded by the drag created by the hydration shell as the ions break their way through the hydrogen-bonded water structure. Electrolytic conduction is therefore always associated with a certain amount of electrical resistance. Electrical resistance is defined by Ohm's law R = V/i in which V is the potential difference (voltage) and i is the current. Resistance is expressed in ohms, whose symbol is Ω (omega).

Resistance is an extensive property because it depends on the thickness and cross-section area of the material through which the current flows. The intensive analog of resistance is the resistivity ρ (rho), defined as the resistance between opposite faces of a 1-cm cube. Resistivity is usually expressed in ohm-cm.

In working with electrolytic solutions, it is more convenient to use the corresponding reciprocal properties:

conductance Λ (lambda) = 1/R

conductivity κ (kappa) = 1/ρ

The SI unit of conductance is the siemens, indicated by the symbol S.

Conductivity, the reciprocal of the resistivity, is frequently expressed in ohm^–1 cm^–1
or S cm^–1, but the SI units are S m^–1.

Conductance measurements

The traditional method of measuring resistance or conductance is by means of a Wheatstone bridge arrangement in which a known resistance is balanced against the unknown resistance. The latter consists of a conductivity cell having electrodes of fixed size and spacing. Nowadays it is more common to employ a digital measuring device.

[link]

In practical measurements of conductivity, no attempt is made to define the precise dimensions of the conductive path. Instead, the conductance cell is first calibrated by filling it with a standardized solution of potassium chloride, for which extensive conductivity data is available.

Because resistances can be measured to very high precision, conductance measurements can be extended to very dilute solutions if impurities are guarded against, of which dissolved atmospheric CO₂ is the most common.

The conductance of a solution depends on 1) the concentration of the ions it contains, 2) on the number of charges carried by each ion, and 3) on the mobilities of these ions. The latter term refers to the ability of the ion to make its way through the solution, either by ordinary thermal diffusion or in response to an electric potential gradient.

The first step in comparing the conductances of different solutes is to reduce them to a common concentration. For this, we define the conductance per unit concentration which is known as the molar conductivity, denoted by the upper-case Greek lambda:

Λ = κ/c

But if c is the concentration in moles per liter, this will still not fairly compare two salts having different stoichiometries, such as AgNO₃ and FeCl₃, for example. If we assume that both salts dissociate completely in solution, each mole of AgNO₃ yields two moles of charges, while FeCl₃ releases six(i.e., one Fe³⁺ ion, and three Cl^– ions.) So if one neglects the [rather small] differences in the ionic mobilities, the molar conductivity of FeCl₃ would be three times that of AgNO₃.

The most obvious way of getting around this is to note that one mole of a 1:1 salt such as AgNO₃ is "equivalent" (in this sense) to 1/3 of a mole of FeCl₃, and of ½ a mole of MgBr₂.

To find the number of equivalents that correspond a given quantity of a salt, just divide the number of moles by the total number of positive charges in the formula unit. (If you like, you can divide by the number of negative charges instead; because these substances are electrically neutral, the numbers will be identical.)

Note that we can refer to equivalent concentrations of individual ions as well as of neutral salts. Also, since acids can be regarded as salts of H⁺, we can apply the concept to them; thus a 1M L^–1 solution of sulfuric acid H₂SO₄ has a concentration of
2 eq L^–1.

Equivalent conductivity

The concept of equivalent concentration allows us to compare the conductances of different salts in a meaningful way. Equivalent conductivity is defined similarly to molar conductivity

Λ = κ/c

except that the concentration term is now expressed in equivalents per liter instead of moles per liter. (In other words, the equivalent conductivity of an electrolyte is the conductance per equivalent per liter.)

These studies revealed that the equivalent conductivities of electrolytes all diminish with concentration (or more accurately, with the square root of the concentration), but they do so in several distinct ways that are distinguished by their behaviors at very small concentrations. This led to the classification of electrolytes as weak, intermediate, and strong.

Strong electrolytes

These well-behaved systems include many simple salts such as NaCl, as well as all strong acids.
The Λ vs. √c plots closely follow the linear relation

Λ = Λ° – b √c

Intermediate electrolytes

These "not-so-strong" salts can't quite conform to the linear equation above, but their conductivities can be extrapolated to infinite dilution.

Weak electrolytes

"Less is more" for these oddities which possess the remarkable ability to exhibit infinite equivalent conductivity at infinite dilution. Although Λ° cannot be estimated by extrapolation, there is a clever work-around.

Since ions are the charge carriers, we might expect the conductivity of a solution to be directly proportional to their concentrations in the solution. So if the electrolyte is totally dissociated, the conductivity should be directly proportional to the electrolyte concentration.

But this ideal behavior is never observed; instead, the conductivity of electrolytes of all kinds diminishes as the concentration rises.

The non-ideality of electrolytic solutions is also reflected in their colligative properties, especially freezing-point depression and osmotic pressure.

The primary cause of this is the presence of the ionic atmosphere that was introduced above. To the extent that ions having opposite charge signs are more likely to be closer together, we would expect their charges to partially cancel, reducing their tendency to migrate in response to an applied potential gradient.

A secondary effect arises from the fact that as an ion migrates through the solution, its counter-ion cloud does not keep up with it. Instead, new counter-ions are continually acquired on the leading edge of the motion, while existing ones are left behind on the opposite side. It takes some time for the lost counter-ions to dissipate, so there are always more counter-ions on the trailing edge. The resulting asymmetry of the counter-ion field exerts a retarding effect on the central ion, reducing its rate of migration, and thus its contribution to the conductivity of the solution.

The nearly-linear nature of conductivity-vs.-√c plots for strong electrolytes is largely explained by the effects discussed immediately above. The existence of intermediate electrolytes served as the first indication that many salts are not completely ionized in water; this was soon confirmed by measurements of their colligative properties.

The curvature of the plots for intermediate electrolytes is a simple consequence of the LeChâtelier effect, which predicts that the equilibrium

MX(aq) = M⁺(aq) + X^–(aq)

will shift to the left as the concentration of the "free" ions increases. In more dilute solutions, the actual concentrations of these ions is smaller, but their fractional abundance in relation to the undissociated form is greater. As the solution approaches zero concentration, virtually all of the MX(aq) becomes dissociated, and the conductivity reaches its limiting value.

Weak electrolytes are dissociated only at extremely high dilution

These weak electrolytes, like the intermediate ones, will be totally dissociated at the limit of zero concentration; if the scale of the weak-electrolyte plot (blue) shown above were magnified by many orders of magnitude, the curve would resemble that for the intermediate electrolyte above it, and a value for Λ° could be found by extrapolation. But at such a high dilution, the conductivity would be so minute that it would be masked by that of water itself (that is, by the H⁺ and OH^– ions in equilibrium with the massive 55.6 M L^–1 concentration of water) — making values of Λ in this region virtually unmeasurable.

The conductance of an electrolytic solution results from the movement of the ions it contains as they migrate toward the appropriate electrodes. But the picture we tend to have in our minds of these ions moving in a orderly, direct march toward an electrode is wildly mistaken.

The average thermal energy at temperatures within water's liquid range (given by RT ) is sufficiently large to dominate the movement of ions even in the presence of an applied electric field. This means that the ions, together with the water molecules surrounding them, are engaged in a wild dance as they are buffeted about by thermal motions (which include Brownian motion).

If we now apply an external electric field to the solution, the chaotic motion of each ion is supplemented by an occasional jump in the direction dictated by the interaction between the ionic charge and the field. But this is really a surprisingly tiny effect:

All ionic solutions contain at least two kinds of ions (a cation and an anion), but may contain others as well. In the late 1870's, the physicist Friedrich Kohlrausch noticed that the limiting equivalent conductivities of salts that share a common ion exhibit constant differences.

These differences represent the differences in the conductivities of the ions that are not shared between the two salts. The fact that these differences are identical for two pairs of salts such as KCl/LiCl and KNO₃ /LiNO₃ tells us that the mobilities of the non-common ions K⁺ and LI⁺ are not affected by the accompanying anions.

Kohlrausch's law greatly simplifies estimates of Λ₀

This principle is known as Kohlrausch's law of independent migration, which states that in the limit of infinite dilution,

Each ionic species makes a contribution to the conductivity of the solution that depends only on the nature of that particular ion, and is independent of the other ions present.

Kohlrausch's law can be expressed as

Λ₀ = Σ λ⁰₊ + Σ λ⁰_–

This means that we can assign a limiting equivalent conductivity λ₀ to each kind of ion:

Just as a compact table of thermodynamic data enables us to predict the chemical properties of a very large number of compounds, this compilation of equivalent conductivities of twenty different species yields reliable estimates of the of Λ₀ values for five times that number of salts.

One useful application of Kohlrausch's law is to estimate the limiting equivalent conductivities of weak electrolytes which, as we observed above, cannot be found by extrapolation. Thus for acetic acid CH₃COOH ("HAc"), we combine the λ₀ values for H₃O⁺ and CH₃COO^– given in the above table:

Λ_⁰HAc = λ⁰_H+ + λ⁰_Ac–

Movement of a migrating ion through the solution is brought about by a force exerted by the applied electric field. This force is proportional to the field strength and to the ionic charge.

Calculations of the frictional drag are based on the premise that the ions are spherical (not always true) and the medium is continuous (never true) as opposed to being composed of discrete molecules. Nevertheless, the results generally seem to be realistic enough to be useful.

According to Newton's law, a constant force exerted on a particle will accelerate it, causing it to move faster and faster unless it is restrained by an opposing force. In the case of electrolytic conductance, the opposing force is frictional drag as the ion makes its way through the medium. The magnitude of this force depends on the radius of the ion and its primary hydration shell, and on the viscosity of the solution.

Eventually these two forces come into balance and the ion assumes a constant average velocity which is reflected in the values of λ₀ tabulated in the table above.

The relation between λ₀ and the velocity (known as the ionic mobility μ₀) is easily derived, but we will skip the details here, and simply present the results:

As with the limiting conductivities, the trends in the mobilities can be roughly correlated with the charge and size of the ion. (Recall that negative ions tend to be larger than positive ions.)

Cations and anions carry different fractions of the current

In electrolytic conduction, ions having different charge signs move in opposite directions. Conductivity measurements give only the sum of the positive and negative ionic conductivities according to Kohlrausch's law, but they do not reveal how much of the charge is carried by each kind of ion. Unless their mobilities are the same, cations and anions do not contribute equally to the total electric current flowing through the cell.

Recall that an electric current is defined as a flow of electric charges; the current in amperes is the number of coulombs of charge moving through the cell per second. Because ionic solutions contain equal quantities of positive and negative charges, it follows that the current passing through the cell consists of positive charges moving toward the cathode, and negative charges moving toward the anode. But owing to mobility differences, cations and ions do not usually carry identical fractions of the charge.

Transference numbers are often referred to as transport numbers; either term is acceptable in the context of electrochemistry.

The fraction of charge carried by a given kind of ion is known as the transference number t_±. For a solution of a simple binary salt,

By definition, t₊ + t_– = 1.

To help you visualize the effects of non-identical transference numbers, consider a solution of M⁺ X^– in which t₊ = 0.75 and t_– = 0.25. Let the cell be divided into three [imaginary] sections as we examine the distribution of cations and anions at three different stages of current flow.

	Initially, the concentrations of M+ and X– are the same in all parts of the cell.
	After 4 faradays of charge have passed through the cell, 3 eq of cations and 1 eq of anions have crossed any given plane parallel to the electrodes. Note that 3 anions are discharged at the anode, exactly balancing the number of cations discharged at the cathode.
	In the absence of diffusion, the ratio of the ionic concentrations near the electrodes equals the ratio of their transport numbers.

Transference numbers can be determined experimentally by observing the movement of the boundary between electrolyte solutions having an ion in common, such as LiCl and KCl:

You may have noticed from the tables above that hydrogen- and hydroxide ions have extraordinarily high equivalent conductivities and mobilities. This is a consequence of the fact that unlike other ions which need to bump and nudge their way through the network of hydrogen-bonded water molecules, these ions are participants in this network. By simply changing the H₂O partners they hydrogen-bond with, they can migrate "virtually". In effect, what migrates is the hydrogen-bonds, rather than the physical masses of the ions themselves.

This process is known as the Grothuss Mechanism. The shifting of the hydrogen bonds occurs when the rapid thermal motions of adjacent molecules brings a particular pair into a more favorable configuration for hydrogen bonding within the local molecular network.

Bear in mind that what we refer to as "hydrogen ions" H⁺(aq) are really hydronium ions H₃O⁺, most of which are themselves hydrated, forming units such as H₅O₂⁺ and H₉O₄⁺. Some theoretical studies suggest that H₃O⁺(H₂O)₂₀ might be a major structural form of the "hydronium ion".

It is remarkable that this virtual migration process was proposed by Theodor Grotthuss in 1805 — just five years after the discovery of electrolysis, and he didn't even know the correct formula for water; he thought its structure was H–O–O–H.

From the chemist's standpoint, the most important examples of conduction are in connection with electrochemical cells, electrolysis and batteries. These topics are covered in the separate lesson set All About Electrochemistry.

Owing to their high sensitivity, conductance measurements are well adapted to the measurement of equilibrium constants for processes that involve very small ion concentrations. These include

• K_s values for sparingly soluble solids
• Autoprotolysis constants for solvents (such as K_w )
• Acid dissociation constants for weak acids

As long as the ion concentrations are so low, their values can be taken as activities, and limiting equivalent conductivities Λ₀ can be used directly.

The very small conductivity of pure water makes it rather difficult to obtain a precise value for K_w; better values are obtained by measuring the potential of an appropriate galvanic cell. But the principle illustrated here might be applicable to other autoprotolytic solvents such as H₂SO₄.

A chemical reaction in which there is a significant change in the number or mobilities of ionic species can be followed by monitoring the change in conductance. Many acid-base reactions fall into this category. In conductometric titration, conductometry is employed to detect the end-point of a titration.

Consider, for example, the titration of the strong acid HCl by the strong base NaOH. In ionic terms, the process can be represented as

H⁺ + Cl^– + Na⁺ + OH^– → H₂O + Na⁺+ Cl^–

At the end point, only two ionic species remain, compared to the four during the initial stages of the titration, so the conductivity will be at a minimum. Beyond the end point, continued addition of base causes the conductivity to rise again. The very large mobilities of the H⁺and OH^– ions cause the conductivity to rise very sharply on either side of the end point, making it quite easy to locate.

For most ordinary acid-base titrations, conductometry rarely offers any special advantage over regular volumetric analysis or potentiometry. But in some special cases such as those illustrated here, it is the only method capable of yielding useful results.

Most people think of electrolytic conduction as something that takes place mainly in batteries, electrochemical plants and in laboratories, but by far the biggest and most important electrolytic system is the earth itself, or at least the thin veneer of soil sediments that coat much of its surface.

Soils are composed of sand and humic solids within which are embedded pore spaces containing gases (air and microbial respiration products) and water. This water, both that which fills the pores as well as that which is adsorbed to soil solids, contains numerous dissolved ions on which soil conductivity mainly depends. These ions include exchangeable cations present on the surfaces of the clay components of soils. Although these electrolyte channels are small and tortuously connected, they are present in huge numbers and offer an abundance of parallel conduction paths, so the ground itself acts as a surprisingly efficient conductor.

Ground-wave radio propagation

During the daytime, radio transmission at frequencies below about 5 MHz (such as in the old standard AM broadcast band) depends entirely on so-called ground waves that follow the curvature of the earth. This occurs because that portion of the vertically-polarized wave fronts in contact with the earth induce an electrolytic current in the ground, causing their lower portions to travel more slowly, bending their pathways in toward the earth. (See the diagram in this short article on ground-wave propagation.) The U.S Government publishes several ground-conductivity maps that are used to predict the daytime range of AM radio stations in that country.

Agricultural and environmental soils assessment

Conductivity has long been used as a tool to assess the salinity of agricultural soils — a serious problem in irrigated regions, where evaporation of irrigation water over the years can raise salinity to levels that can reduce crop yields. Because other soil characteristics (moisture content, density, and mineralogy, fertilization) also play important roles, some care is required to correctly interpret measurements. Measuring devices that can be drawn behind a tractor and are equipped with GPS receivers allow the production of conductivity maps for entire fields.

Archaeological exploration

Buried artifacts such as stone walls and foundations and large metallic objects can be located by a series of conductivity measurements at archaeological sites.