ESTUDIO DEL FOSFATO

Key Notes

The conductance of an ionic solution is measured by applying an oscillating voltage between two parallel plate electrodes, which avoids concentration polarization and ensures the current is proportional to the applied voltage. The conductance is the ratio of the current to the voltage. The conductance, L, is used to calculate the conductivity, κ, which is a measure of the charge carrying ability of the ionic solution and is independent of the cell in which the measurement is performed.

The conductivity is proportional to the number of ions in solution. The molar conductivity is κ/c, where c is the salt concentration, and gives a measure of the charge carrying capabilities for the same amount of dissolved salt. This allows comparison of the charge carrying capabilities for the same amount of different dissolved electrolytes. The molar conductivity is an addition of the molar conductivities of the cations and anions.

A strong electrolyte is an electrolyte that completely dissociates into its constituent ions. Its molar conductivity slowly decreases with increasing concentration, due to the increasing importance of ionic interactions.

The limiting molar conductivity of an electrolyte is the molar conductivity as c→0, where there are no ionic interactions. The limiting molar conductivity is a combination of the limiting molar conductivities of the cations and of the anions. The limiting molar conductivity of a particular ion is constant.

Weak electrolytes do not completely separate into their

constituent ions except at high dilution. As c increases, the molar conductivity falls relatively rapidly, as the proportion of undissociated electrolyte increases. Molar conductivity measurements allow the degree of electrolyte dissociation to be calculated at any c.

The transport number of an ion is a measure of the fraction of the total current carried by the ion. The sum of the transport numbers for the ions in solution add up to 1. The transport number for an ion varies with the nature of the counterion(s) and with c.

Related topics Solubility (C5) Thermodynamics of ions in solution

Ions in aqueous solution

(E1) (E2)

Conductance and conductivity

When an electric field is put across an aqueous ionic solution by applying a voltage between two parallel plate electrodes, the cations are attracted towards the negative plate (cathode) and the anions towards the positive plate (anode).

This movement of ions in a field is called migration and the movement of charge results in a current in the electric circuit connecting the electrodes. The field between the plates is initially linear and produces a constant ion velocity at all points. However, if there is no redox reaction, cations and anions will separate and collect at the cathode and anode respectively with time, balancing the electrode charge and there will be fewer ions in the bulk of solution. This is a process known as concentration polarization, which also leads to modification of the original linear potential profile between the two electrodes and a variation of ion velocity between the plates. The observed current will also fall with time (as at infinite time, the ion flow will have stopped as the ions will have reached the plates and the current will have decreased to zero). Concentration polarization is therefore useful when separating ions is desirable, such as in electrophoresis and electro-osmosis, but this is to be avoided when measuring fundamental ion motion.

For these measurements, the field polarity is rapidly switched (at around 1000 times per second) by applying an AC (alternating) voltage to the plates (Fig. 1).

Fig. 1. The effect of an AC voltage on the ion motion as electrode polarity is switched.

The ions then alternately migrate first to one plate and then the other during cycling, so that the ions oscillate around a fixed position, avoiding concentration polarization.

Under these conditions the observed current, i, is always proportional to the applied voltage, V, with i=VL and the constant of proportionality being the conductance, L. L depends on the experimental apparatus; the area, A, of the plate electrodes and the distance, l, between them and for parallel field lines, with two plates exactly opposite

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each other κ=L(l/A), with κ being the conductivity. It is the conductivity that probes the rate of charge transfer in the solution free from variations in apparatus design. In practice it is very difficult to construct experimental conductivity cells which exactly obey this equation, but generally κ=LC, where C is the cell constant which can be determined by calibration. This involves determining L for a solution of known κ, calculating C and using it to determine κ from L for all other solutions.

Molar conductivity

The rate of charge transfer is proportional to the number of ions in the solution between the plates, which itself will vary with the concentration, c, of dissolved electrolyte. The molar conductivity, Λm, is defined as:

and allows for this variation with concentration. Λm values enable comparison of the conductivities (or charge carrying capabilities) of an equivalent number of moles of electrolyte both as the type and the concentration of electrolyte is varied. These measurements allow variation in ion migrational motion in these systems to be studied.

Strong electrolytes

A strong electrolyte completely dissociates into its constituent ions. An example is NaCl. It might be expected that Λm would be independent of concentration for a strong electrolyte, but in reality for dilute solutions

where κ is a constant for a particular electrolyte and c is the electrolyte concentration (Fig. 2a).

Fig. 2. The dependence of molar conductivity on concentration for (a) a strong electrolyte; (b) a weak

electrolyte.

As c increases, the cations and anions migrate more slowly through solution. This is because the anions and cations, moving in opposite directions, are closer together and their electrostatic attraction grows in importance, which progressively slows ion progress.

This is a consequence of the development of an ionic atmosphere around the ions, which explains the dependence of molar conductivity on √I (where I is the ionic strength) and hence √c (see Topics E1 and E2).

Charge is carried in the solution both by cations moving towards the cathode and anions moving in the opposite direction towards the anode, and so the molar conductivity is simply a combination of the molar conductivities of the cation, λ+, and of the anion, λ−:

Λm=n+λ++n−λ−

where n+ and n− are the number of moles of cations and anions per mole of salt, i.e. for an electrolyte with the overall molar formula . The degree of interaction between cation and anion depends on the charge and size of the ions (see Topic E2) and so λ for an ion often varies as the counterion is varied.

Limiting molar conductivity

For non-interacting ions, i.e. when c→0 and the cations and anions are so far apart in solution they do not interact with each other, the molar conductivity is called the limiting molar conductivity, (Fig. 2). This is a combination of the limiting molar conductivities of the cation, λ+0, and the anion, λ−0:

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and under these conditions, λ⁰ values are constant for any ion and do not vary when the counterion is varied. They have been tabulated for many ions, which allows values of

to be calculated for different salts.

Weak electrolytes

For a weak electrolyte, the salt does not completely dissolve into its constituentions and for example the equilibrium:

is present. Dilute concentrations favor the formation of ions and as

because complete dissociation occurs. Increasing the concentration decreases the fraction of dissociated ions (the degree of dissociation, α) in accordance with Le Chatelier’s principle (see Topic C1). Undissociated electrolyte is uncharged and cannot contribute to the conductivity and so the molar conductivity falls much more rapidly with concentration than for a strong electrolyte (Fig. 2b). As this fall is much larger than that due to the electrostatic attraction of ions, the fraction of salt present as ions, α, at any electrolyte concentration c is given by .

Λm is measured at c, and in the example if is measured or calculated, α can be used to determine the concentration of cation and anion (each αc) and undissociated electrolyte (c−αc) and obtain a value for the equilibrium constant, K, for the ion dissociation reaction (see Topic C5). In the example, at low ionic strength (see Topic E2),

Transport numbers

The transport number, t, of an ion is the fraction of the total charge carried by the ion in an electrolyte. For the cation, and the anion, these are given by

t+=n+λ+/Λm and t−=n−λ−/Λm

respectively, and the sum of the transport numbers for the cations and the anions must add up to 1. Since λ and Λm vary with concentration and electrolyte, so does t. The limiting transport number, t⁰, is the value measured when c→0.

E7

MOLECULAR ASPECTS OF IONIC