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.
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 2 presents a graph of conductance data for hydrochloric acid and acetic acid.
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.
Scheme 1 depicts the situation that ensues when acetic acid is dissolved in water.
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 Keq 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 Keq .
The symbol Ka is called the acidity constant. For acetic acid, the numerical value of Ka 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.
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.
The equilibrium constant, Keq, 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, Ka, 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 10-7 M.
Exercise 3 The Ka value of phenol, C6H5OH in water is 1.3 x 10-10 while that of cyclohexanol C6H12OH is 1 x 10-16. Which compound is the weaker acid? phenol cyclohexanol
Exercise 4 The Ka value of tert-butyl alcohol, (CH3)3COH in water is 1 x 10-18. Write an equation depicting the transfer of a proton from tert-butyl alcohol to a water molecule. Which would contain a higher concentration of hydronium ions, a 0.1M solution of tert-butyl alcohol in water or pure water? tert-butyl alcohol water neither
Exercise 5 Write equations depicting the auto-ionization of a. methanol, CH3OH b. formic acid, HCO2H c. sulfuric acid, H2SO4
Exercise 6 Assume you dissolve 1000 molecules of an acid HA in water. If 20 of HA molecules dissociate and A- ions, how many H3O+ ions are formed? How many A- ions are formed? How many HA molecules are left undissociated? What is the acidity constant of HA?
Topics
