Full Lab Manual
Introduction & Goals
Chemistry & Background
In Your Write-up
Deprotonation of a Coordinated Water Molecule
Coordination of a water molecule to a metal center with a high positive charge greatly increases its acidity, compared to free water. For example, your cobalt complex acts as a weak acid in aqueous solution by donating a hydrogen ion to water:
Remember that the Ka for uncoordinated water is only 10-14, so the acidity of the coordinated water in the pentaamminecobalt complex is greatly increased. For comparison, the Ka for acetic acid is 1.8 x 10-5. The Ka value of 2.04 x 10-6 M quoted here is for an infinitely dilute solution, a condition that is not satisfied in this experiment. The presence of a significant concentration of highly charged ions in solution will result in a value which is somewhat smaller than 2.04 x 10-6 . In the following section, we show how a familiar acid-base titration can be used to analyze this acidity of the coordinated H2O.
Addition of the base NaOH to a solution of the [Co(NH3)5(H2O)]3+ brings about the loss of a hydrogen ion from the coordinated water molecule.
The equilibrium constant for this process can be calculated by combining the acid dissociation constant for [Co(NH3)5(H2O)]3+ and the equilibrium constant for the autoionization of water.
Example. A 4.0 mL volume of 0.100 M NaOH is added to 40 mL of 0.025 M [Co(NH3)5(H2O)]3+. What are the resulting concentrations of [Co(NH3)5(H2O)]3+, [Co(NH3)5(OH)]2+, and OH-?
The above considerations assume that the reaction goes to completion, i.e. there is no unreacted OH-. Although K6 is very large, there will be a small concentration of unreacted OH-. When this is taken into account, the following concentrations are obtained:
These data are summarized below:
If it is assumed that the concentration of unreacted OH-, (X), is negligibly small compared to both 1.4 x 10-2 M and 9.1 x 10-3 M, the following expression is obtained from K6:
X = [OH-] = 3.3 x 10-9 M
If the assumption of complete reaction is invoked throughout the titration, a simple expression can be derived for the concentrations of both the aqua and hydroxo complexes as functions of the volume of base added. Let
Before the end point:
The end point will be reached when V2C2 = V1C1, since the moles of base added equals the moles of acid. At, and after, the end point nearly all the cobalt will be present as the hydroxo complex, and its concentration will be given by (9):
Potentiometric End Point Detection
Much ingenuity has gone into devising methods for detecting the end points of analytically useful titrations. Many of them are chemical techniques, generally involving indicators. In recent years, however, there has been increased reliance on the use of physical methods to detect end points. One reason for their popularity is that they often are able to circumvent restrictions which limit the applicability of chemical methods. Phenolphthalein would be unsuitable, for example, in the titration of the aqua complex with base since the indicator color change would be masked by the color of the complex. Another important reason for the increased use of physical methods is that they are intrinsically well-suited to automation. Most of the routine analyses of industrial and clinical importance are now done with some degree of automation. Automatic titrators are one example, and instruments which employ both pH and light absorption monitoring to locate the end point have been developed. In your titration, the pH of the solution will be monitored. The pH meter is a central fixture in research laboratories, whether they be concerned with chemistry, biology, geology, or medicine. Your pH meter will detect the end point by observing the sharp change in pH that accompanies it.
By far the most general method of end point detection for acid-base titrations involves measuring the pH during the titration. One of the main advantages of the pH method is that it is capable of high precision since the pH changes very rapidly near the end point.
The literature value for the acid dissociation constant of [Co(NH3)5(H2O)]3+ was provided in the previous section:
Titration curve for 100 mL of 0.01 M [Co(NH3)5(H2O)][NO3]3 with 0.10 M NaOH.
I. Initial Solution. Since Ka is small, a negligible fraction of the weak acid [Co(NH3)5(H2O)]3+ is assumed to be dissociated. Equal concentrations of [Co(NH3)5(OH)]2+ and H3O+ are produced by this dissociation:
X is assumed to be much smaller than 0.01 M. Thus,
II. Buffer Region. Nearly the entire titration curve before the equivalence point can be treated by the simple assumption that the reaction between the added base and [Co(NH3)5(H2O)]3+ goes stoichiometrically to completion. Let V2 = the volume of base added in milliliters for the net titration reaction
[H3O+] = Ka pH = -log10 (2.04 x 10-6) = 5.69 = pKa
III. The Equivalence Point. Here nearly all the cobalt is present as the conjugate base[Co(NH3)5(OH)]2+. A small concentration of [Co(NH3)5(H2O)]3+ arises from the following equilibrium (known as hydrolysis):
IV. Past Equivalence. All but a negligible fraction of cobalt exists as [Co(NH3)5(OH)]2+. Excess hydroxide is present and the concentration of this excess base determines the pH.
How nearly do the results in I through IV produce a full pH titration curve? The answer depends in general on concentrations and the Ka value involved. For the present rather typical case, the results are excellent, as is shown in Figure 4. The solid curve in Figure 4 represents an exact computer-generated curve for the whole titration. The discrete points have been calculated at 0.5 mL intervals using cases I, II, III, or IV as appropriate. The rapid rise in pH at the equivalence point allows precise determination of the titration end point.
Again it should be stressed that an understanding of the calculations of cases I, II, III and IV is of great importance to building a useful familiarity with the concepts of acid-base equilibrium.
The experimental method is conveniently summarized by rearranging equation (2) above:
Preliminary Kinetics Measurements
In addition to the acid-base titration of your complex, you and your partner will perform preliminary kinetics measurements this week. The mechanism of the ligand exchange reaction between the water ligand of your complex and the nitrite ion, NO2-, will be examined by following the reaction colorimetrically. Details of the reaction kinetics will be further investigated next week. Introductory material and procedural information can be found in the pages for Week 7 Part 2.
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