CONCEPT DIAGRAM Zero membrane

current, bulk neutrality Several permeant ions Steady state Single permeant ion Nernst equilibrium System evolves e.g. most living cells No impermeant ions. Concentrations equalise Donnan equilibrium Impermeant ions give Donnan potential Active ion transport e.g. metabolism Concentration difference

Net ion diffusion generates potential difference

Semipermeable membrane

E4: Ion Diffusion 42

PRE-LECTURE!

4-1 CONCENTRATION AND pH Amount of substance

Mass is a common way of specifying how much material you have, but for some purposes it is much more pertinent to think in term of how many particles you have. Since the atoms or molecules of different substances have different masses, equal masses of different substances contain different numbers of particles. It is useful to define a new quantity, amount of substance, such that equal amounts of two different substances have the same number of elementary entities - atoms, molecules or whatever you consider the basic unit of each substance to be. The concept of amount is useful whenever you are studying something that depends on the number of particles present rather than on their masses. The SI unit of amount is called the mole (symbol mol) and is defined to be the amount of substance containing the same number of elementary entities as there are atoms in exactly 12 g of the pure isotope carbon-12. It turns out that there are 6.022 ¥ 102 3 particles per mole. The conversion factor is known as the Avogadro constant N₀ = 6.022 ¥ 102 3 mol-1. (The term Avogadro's number, meaning the pure number 6.022 ¥ 102 3, is regarded as obsolete, since its value depends on a particular system of units, whereas the Avogadro constant is a constant of nature whose value is independent of human invention.)

You can imagine an amount of any discrete entity you like; a mole of water molecules, a mole of electrons, a micromole of sand grains or even a nanomole of bacteria. However the concept of amount is most useful when we are dealing different kinds of particles whose numbers must conform to simple integer ratios, such as atoms in pure chemical compounds. To take a simple example used in this chapter, any amount the chemical compound potassium chloride (KCl) contains exactly the same number of potassium (K) atoms and chlorine (Cl) atoms. So KCl is formed from equal amounts of potassium and chlorine (not equal masses).

Concentration

There are several possible ways of defining or specifying the concentration of a solution. We could for example, specify the mass of solute per mass of solvent, or amount of solute per volume of solution. For the understanding of electrical conduction and other electrical processes at the atomic scale we use the following concepts of number density and concentration.

Number density (n) means number of particles per volume:

n = number!of!particles!in!solution_{volume!of!solution} . This idea has already been used to describe conduction by charge carriers in chapter E3.

Amount of substance per volume, called concentration, is an alternative concept for dealing with phenomena that depend on number densities of particles.

C = amount!of!ion!species_{volume!of!solution}

Concentrations specified in this way are often referred to as molar concentrations. Note that the SI unit of concentration is the mole per cubic metre. A more practical unit (but non-SI) is the mole per litre (mol.L-1). A solution with a concentration of 1 mole per litre is often referred to as a molar solution; a concentration of 1.00!¥!10-3 mole per litre would be called millimolar (mM).

Number density and concentration are connected by the Avogadro constant : n = N₀C .

E4: Ion Diffusion 43

The pH of a solution

The pH of an aqueous solution is a pure number which expresses its acidity (or alkalinity) in a convenient form widely used in the life sciences. (The pH of a solution is literally its ‘hydrogen power’.) It is a measure of the hydrogen ion concentration expressed on a logarithmic scale.

The pH of a solution is defined to be - log₁₀ ËÊC_H+/(mol.L-1) . Note that the value of pH is¯ˆ linked to the chosen unit of concentration, mole per litre.

Example Pure water is partly dissociated into H+ and OH- ions according to the chemical equation:

H₂O Æ_¨ H+ + OH- . (The ions actually attach themselves to water molecules, but in terms of counting charged particles that makes no difference.)

If the concentration of H+ is increased by adding an acid to pure water the equilibrium is disturbed; the additional H+ ions cause some of the OH- ions to recombine, thus decreasing the concentration of OH- ions. Similarly the addition of an alkali causes a reduction in the concentration of H+ ions.

For an aqueous solution in equilibrium, the rate of dissociation of H₂O must be equal to the rate of recombination of H+ and OH-, which is proportional to the product of the concentrations of H+ and OH-. By equating these two rates it is easily shown that

C

H+ ¥COH- = K ( a constant)

Thus by measuring the concentration of hydrogen ions we can determine the acidity (or alkalinity) of a solution.

For pure water C

H+ = COH- = 1.0 ¥ 10

-7 _mol.L-1_,

so the constant in the equation is K = (1.0 ¥ 10-7mol.L-1) ¥ (1.0 ¥ 10-7 mol.L-1) = 1.0 ¥ 10-14 mol2.L-2.

Thus in terms of pH we have C

H+ = 1.0 ¥ 10

-pH _mol.L-1

and C_OH- = 1.0 ¥ 10(pH-14) mol.L-1.

Values of pH

• pH < 7 corresponds to an acid solution, i.e. one in which C_H+ > C_OH- .

• pH = 7 corresponds to a neutral solution, i.e. one in which C_H+ = C_OH- .

• pH > 7 corresponds to an alkaline solution, i.e. one in which C_H+ < C_OH- .

In practice pH occurs in the range 0 < pH < 14; a much narrower range (around 7) is encountered in living systems.

!LECTURE