Conductivity of Ionic Solutions

In 1869 - 1880 Friedrich Kohlrausch conducted a series of very precise measurements of the conductivities of many compounds at various concentrations and temperatures.  He discovered the constant differences in the conductivities of solutions with a common ion as is illustrated in the Basic Experiment with this simulation (these differences become very precise when the equivalent conductivities are extrapolated to infinite dilution).  This became known as Kohlraush's Law of the Independent Migration of Ions.
It can be illustrated as:

LKCl = LNaCl + LKBr - LNaBr

or as
LKCl = LK+ + LCl-   .

In the Basic Experiment, there were some materials which did not obey these rules, especially those materials which did not completely dissolve.  Kohlraush's Law provides a way to estimate what the conductivity of an insoluble material should be if all of the material would dissolve.  For instance, in the case of Silver Chloride:

LAgCl = LAgNO3 + LNaCl - LNaNO3

The conductivity of a 0.00100 mol/L solution of Silver Chloride should be equal to the sum of the conductivities of 0.00100 mole/L solutions of silver nitrate and sodium chloride minus the conductivity of a 0.00100 mole/L solution of sodium nitrate.  The actual conductivity is much less than this calculated value, indicating that the concentration of silver and chloride ions is much less than 0.00100 moles/Liter.  The actual concentration of the ions can be estimated as:

actual concentration / actual conductivity = 0.00100 / calculated conductivity

A more precise statement of this relationship is:

CAgCl = actual conductivity / LAgCl  .

This principle may be applied to estimate the concentration of ions in a saturated solution of any ionic material, but it works best for materials which are extremely insoluble where the equivalent conductivity values whould be extrapolated to infinite dilution.

The principle can also be applied to solutions of weak electrolytes, which do not completely ionize.  A generic weak acid which we'll call HA comes to equilibrium with its ions:

HA(aq) <=> H+(aq) + A-(aq)      Keq = [H+][A-] / [HA]

The conductivity of the solution depends on the concentration of the ions, since the undissociated molecules (HA) do not conduct electricity.

The conductivity that a 0.00100 M solution of this weak acid should have may be calculated from the conductivities of a strong acid (such as HCl), the sodium salt of this acid, and sodium chloride.  The concentration of the ions is estimated as:

concentration of ions / actual conductivity = 0.00100 / calculated conductivity

The concentration of ions (this is equal to the concentration of hydrogen ions AND to the concentration of the anion) and the concentration of undissociated acid (0.00100 - the concentration of ions) can be used to estimate the equilibrium constant.

Suggested Experiments:

Solubility:

1. Measure the conductivities of 0.00100 M solutions of AgNO3, NaCl, NaNO3, and that of a saturated solution of AgCl.  Estimate the solubility of AgCl.

2. Use these same principles to estimate the solubility of other silver salts, and that of Barium Sulfate.

3. Measure the conductivities of solutions of Calcium Hydroxide, at increasing concentrations until the solubility limit is exceeded.  Estimate the solubility.

Weak Acids and Bases:

1. Measure the conductivities of acetic acid solutions at concentrations up to 1.0 M.  Calculate the ionization constant at each concentration.

2. Measure the conductivities of ammonia solutions at concentrations up to 1.0 M.  Calculate the ionization constant at each concentration.

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