Conductance

We're all familiar with the movement of electrons through a wire and the electrical current associated with that movement, i.e. electricity. Electrons are not the only charged particles that can conduct a current. And a wire is not the only medium through which a current can flow. A solution that contains ions is also capable of conducting a current.

Measuring Conductance

If you put two electrodes into a solution that contains dissolved ions and apply a voltage to the electrodes, the ions will move through the solution: the negative ions (anions) will move toward the positive electrode (the anode); the positive ions (cations) will move toward the negative electrode (the cathode). This simple apparatus is called a conductance cell. Figure 1 uses a schematic diagram of a conductance cell to demonstrate the relationship between the concentration of ions in solution and the amount of current that flows through the solution.

Figure 1

Electrons Aren't The Only Critters That Conduct A Current

Figure 2 presents a graph of conductance data for hydrochloric acid and acetic acid.

Figure 2

All Electrolytes Are Not Created Equal

Two features of this graph are noteworthy. First, the fact that the conductance of acetic acid is much less than that of hydrochloric acid is direct evidence that an aqueous solution of acetic acid contains fewer ions than a solution of hydrochloric acid of comparable concentration. Second, when extrapolated to 0 concentration (dashed line), the conductance of the HCl solution does not equal 0. In other words, pure water has a small, but finite conductance.

Weak Electrolytes

Scheme 1 depicts the situation that ensues when acetic acid is dissolved in water.

Scheme 1

Dissolution and Dissociation of Acetic Acid

The important point here is that the solution contains mostly solvated, but unionized acetic acid molecules with a few hydronium ions and acetate ions that are produced by dissociation of a few acetic acid molecules. The relationship between the numbers of hydronium ions, acetate ions, and undissociated acetic acid in solution is given by the expression

where K_eq stands for the equilibrium constant for the dissociation of acetic acid molecules.

Conductance data of the type shown in Figure 1 allows chemists to calculate the concentrations of the hydronium ions and acetate ions in solution. Once you know that you can determine how much of the acetic acid you started with is still undissociated once the system comes to equilibrium. Then you can calculate K_eq .

Since conductance measurements are generally made with dilute solutions, the concentration of the water is not changed significantly when a few water molecules are converted into hydronium ions. This allows the equilibrium expression for the dissociation of acetic acid to be rewritten as

The symbol K_a is called the acidity constant. For acetic acid, the numerical value of K_a is 1.76 x 10^-5. This is a small number, 0.0000176. Mathematically it means that the numerator of the equilibrium expression is small in comparison to the denominator. Chemically it means that most of the acetic acid in solution is not dissociated. If you were to dissolve 0.1 mole of acetic acid in enough water to make 1 liter of solution, once the solution came to equilibrium, the concentration of hydronium ions would be approximately 0.0013 molar. In other words, approximately 13 out of every 1,000 acetic acid molecules would have dissociated. The concentration of dissolved but undissociated aceti acid would be about 0.1000-0.0013 = 0.0987 molar. Because only a small percentage dissociates when it dissolves, acetic acid is classified as a weak electrolyte. It is also described as a weak acid since it produces a low concentration of hydronium ions.

The Auto-Ionization of Water

We mentioned earlier that a sample of pure water has a small, but finite conductance. This must mean that that water contains some ions. Those ions are produced by a process analogous to the one described in Scheme 1. This process, called the auto-ionization of water, is depicted in Scheme 2.

Scheme 2

The Auto-Ionization of Water

The equilibrium constant, K_eq, for this reaction is 1 x 10^-14, which means that the concentration of hydronium ion in pure water is 1 x 10^-7 moles/liter. In other words, approximately two out of every 10 million water molecules react to form a hydronium ion and a hydroxide ion. The acidity constant, K_a, for water is 1.8 x 10 ^-16. Because of the auto-ionization of water, it is never possible to have an aqueous solution in which the concentration of hydronium ion is less than 1 x 10^-14 M.

For compounds that can be measured in water, acidity constants vary by about 14 powers of 10! Such a wide range of values makes it advantageous to use a logarithmic scale to characterize acidity. The pH scale of acidity is a logarithmic scale. Now we're ready to consider another, related but more general scale, the pK scale.