Full Test Bank Chapter.19 Analytical Voltammetry

Chapter 19

Problem 19.1: Parse the experimental method voltabsorptometry, giving the meas­ured parameter, what that parameter is measured as a function of, and what you believe the controlled parameter would be.

Problem 19.2: Describe a possible chemical system in which an experimenter might find voltabsorbtometry to be helpful. Hint: Consider Chapters 6 and 11.

Problem 19.3: Using skills gained in Chapter 18, write the two half-reactions and the overall redox reaction associated with the Daniell cell (Fig. 19.1). Calculate the Gibbs free energy of the cell and confirm that it is galvanic (i.e., that the reaction is spontaneous).

Problem 19.4: Using skills gained in Chapter 18, write the two half-reactions and overall redox reactions associated with the Downs cell (Figure 19.2). Calculate the Gibbs free energy of the cell and confirm that it is electrolytic (i.e., that the reaction is nonspontaneous).

Problem 19.5: Name and briefly describe three common reference electrodes. Hint: See Chapter 18.

Problem 19.6: Consider Figure 19.2. What can you infer about the density of molten Na compared to that of molten NaCl?

Problem 19.7: Why is it important that the divider that separates the working and counter electrodes (or the two electrodes in Figure 19.2) be porous?

Problem 19.8: Sketch the diffusion layers of oxidized and reduced species (similar to that shown in Figure 19.5) for the application of a positive voltage to an electrode at which a reduced substance is oxidized.

Problem 19.9: For each of Equations 19.2, 19.3, and 19.4, confirm that the units bal­ance out on both sides of the equation.

Problem 19.10: Consider Equation 19.3 and the parameters z, D, T, and C. What is the effect on migration flux density when each is increased? Think about the physical phenomena of flux (motion of particles toward the electrode) and explain the effects you noted with each of the parameters.

Problem 19.11: Define the following terms:

(a) Chronopotentiometry

(b) Voltammetry

(c) Cathode

(d) Diffusion

(e) Capacitive charging

(f) Mass transport

(g) Faradaic current

(h) Galvanic

Problem 19.12: CA with an oxidizing potential was conducted with a 1.13 μM solution of luminol using a 3.0 mm diameter carbon disk electrode. The slope of the i(t) versus t^-½ was 3.7 × 10^-8 A·s^½. Luminol has a diffusion coefficient of 4.6 × 10^-6 cm²/s. Estimate the number of electrons transferred in the oxidation of luminol. (Use Example 19.1 as a guide.)

Problem 19.13: CA is often used with a known standard solution to measure the real electrode area, rather than depending on geometry to estimate the area. If Rh(phen)L₄²⁺ were known to have a diffusion coefficient of 9.25 × 10^-6 cm²/s, what is the actual area of the electrode used in Example 19.1?

Problem 19.14: A second metal complex, M(org)²⁺, is discovered that has a ionic diameter approximately 40% smaller than that of Rh(phen)²⁺ described in Example 19.1. If the same electrode and same concentration were used in a chronoamperometric experiment with M(org)²⁺, would you expect the slope of i(t) versus t^{- ½} to be higher or lower than that seen with Rh(phen)L₄²⁺? Explain your answer. Hint: What part of the Cottrell equation is affected by the size of the particle under study?

Problem 19.15: What is the analytical signal in CA and voltammetry? What are the implications from Ohm’s law (Equation 19.6) with respect to the IR drop?

Problem 19.16: Use Equation 19.11 to show that the units of k_s are cm/s.

Problem 19.17: Confirm that the units in Equation 19.12 are correct.

Problem 19.18: What are the units of the constant (2.687 × 10⁵) in Equations 19.13 and 19.14?

Problem 19.19: The CVs in this figure were obtained on a 1.0 mm diameter plat­inum disk electrode at scan rates of 20, 50, 100, 200, 500, and 1,000 mV/s in a 2.0 mM solution of potassium ferricyanide in aqueous 1 M KNO₃ at 25^oC. Estimate the peak currents and calculate the diffusion coefficient of ferricyanide ion in this solution. Assume that ferricyanide ion undergoes a one-electron reduction to ferrocyanide ion. (Use Example 19.2 as a guide.)

Problem 19.20: In a CV experiment, a solution of water from Lake Mary Nell in Elon, North Carolina, was analyzed for Cr³⁺. A 25.00 mL sample showed an i_p of 31.6 μA. A 25.00 mL sample of standard Cr³⁺ (4.56 × 10^-7 M) exhibited an i_p of 52.4 μA. What is the concentration of Cr³⁺ in Lake Mary Nell?

Problem 19.21: For important measurements taken in the medical field, the experimental parameters needed to consider the elevated temperature of the human body (compared to standard 25°C). Derive a simplified form (as in Equation 19.13) of Equation 19.12 for the scientific medical community, taking into account standard human body temperature of 37°C.

Problem 19.22: At 25°C the Rh(III) complex, Rh(bpca)²⁺, exhibits a reversible two-electron redox peak at –0.82 V versus Ag/AgCl and a diffusion coefficient of 5.8 × 10^-6 cm²/s. A cyclic voltammogram was obtained at a potential sweep rate of 100.0 mV/s using a 3.00 mm diameter glassy carbon disk electrode and the peak height, i_p, was found to be 67.3 μA. What was the millimolar concentration of Rh(bpca)²⁺? (The ligand bpca is the bis(2-pyridylcarbonyl) amide anion, which exhibits a –1 ionic charge.)

Problem 19.23: Would you expect to obtain a value for n that is reasonably close to a whole number if the values of both the CA and CV slopes in Example 19.3 were halved? Explain.

Problem 19.24: Confirm your expectation from Problem 19.23 by following through with the calculations following Example 19.3.

Problem 19.25: At 25°C, 2.35 mM solution of potassium ferricyanide, K₃Fe(CN)₆, was used to collect series of CVs at varied sweep rates and a 3.00 mm diameter glassy carbon electrode. A plot of i_P versus ν^½ yielded a slope of 1.59 × 10^-4 amp·s^½/V^½. Using the same system, a plot of i versus t^½ from a CA experiment gave a slope of 3.3 × 10^-5 amp·s^½. Determine the number of electrons (n) transferred in the redox reaction and the diffusion coefficient (D) of the ferricyanide in this solution.

Problem 19.26: Solve Equation 19.15 to demonstrate that ΔE_P is expected to be around 59 mV for a reversible system at 25°C.

Problem 19.27: For a given electrochemical system, at a temperature of 25°C, you measured a ΔE_P of 0.0298 V. What logical explanation(s) can you give for this result?

Problem 19.28: If you conducted a CV of an analyte dissolved in molten NaCl at 900°C, what ΔE_P would you expect to measure, given that it is a one-electron process?

Problem 19.29: Estimate the ΔE_P for the CV shown in Figure 19.10. Would you consider that CV to represent a reversible system? Explain.

Problem 19.30: Estimate E° for the system depicted in Figure 19.10. Do you think that your estimate is reliable? Why or why not?

Problem 19.31: Compare the Cottrell equation (Equation 19.5) with the SWV equation (Equation 19.17). How are they similar? Thinking about what you now know about SWV, explain why you would expect such similarities.

Problem 19.32: To determine the amount of cadmium in a sample of drinking water, a set of calibration solutions were prepared and analyzed with SWV.

The SWV peak height of the drinking water sample was measured to be 1.36 nA. What was the concentration of Cd²⁺ in the drinking water?

Problem 19.33: You want to create a microarray electrode that contains electrodes having a diameter of 1 μm. To avoid having the electrodes interfere with each other, each should be separated from all adjacent electrodes by a distance of at least 10 diameters (10 μm). Given that you have a 1.5 × 1.5 mm square support for the electrodes, how many electrodes can you fit in your array?

Problem 19.34: Consider Table 19.4 and think about the array electrode you designed in Problem 19.33. By what factor do you expect your signal-to-noise ratio to increase compared to a 1 mm diameter electrode? By what factor do you expect the current given by one of your electrodes to decrease compared to the 1 mm elec­trode? What is that current factor when you use your entire array rather than just one electrode?

Exercise 19.1: What values of the standard heterogeneous rate constant, k_s, in units of m/s, would designate electrochemically reversible, quasi-reversible, and irreversible reactions?

Exercise 19.2: What purpose does each electrode in the three-electrode cell serve?

Exercise 19.3: What is the purpose of the porous separator between the counter electrode and the bulk solution in the three-electrode cell?

Exercise 19.4: Explain why the current rises then drops rapidly in a CA experiment. Why does it not drop to zero?

Exercise 19.5: Define the following terms:

(a) Chronoamperometry

(b) Anode

(c) Migration

(d) Convection

(e) Sweep rate

(f) Mechanism

(g) Ultramicro

(h) Electrolytic

Exercise 19.6: A 1.75 × 10^-3 M solution of a metal ion was used to conduct a CV experiment on a square electrode with an edge length of 0.5 cm (only one face of the electrode was exposed to the solution). Using a sweep rate of 50 mV/s, a peak current of 62.9 μA was measured. What is the diffusion coefficient of the metal ion?

Exercise 19.7: A disk electrode of unknown size was used in a CV experiment of a known organic cation with a diffusion coefficient of 7.21 × 10^-10 m²/s. The cation is known to undergo a two-electron reduction. A 2.0 mM solution of the cation was used with a sweep rate of 100 mV/s and a peak current of 78 mV was observed. What was the area of the electrode?

Exercise 19.8: Chronoamperometry with a reducing potential was conducted with a 3.05 × 10^‑3 M solution of a new Rh(phen)L₄²⁺ complex using a 1.0 mm diameter plat­inum disk electrode. The slope of the i_cat versus t^-½ was 3.66 × 10^-6 A·s^½. A literature search reveals that the diffusion coefficient of Ru(phen)L₄²⁺ is known to be 1.1 × 10^-5 cm²/s and the diffusion coefficient of Pd(phen)L₄²⁺ is 7.2 × 10^-6 cm²/s. (Hint: Look at a periodic table.) Give a reasonable estimate of the number of electrons transferred (n) in the chronoamperometric reduction of Rh(phen)L₄²⁺. (The term phen refers to the neutral phenanthroline ligand.)

Exercise 19.9: For a given electrochemical system, you measured a ΔE_P of 0.203 V. What logical explanation(s) can you give for this result? Hint: Consider Figure 19.12 and the accompanying text.

Exercise 19.10: If you conducted a CV of a species in vivo (in the body) at 37°C, what ΔE_P would you expect to measure, assuming that it is a two-electron process?

Exercise 19.11: Estimate the ΔE_P for each of the CVs shown in Figure 19.12. In each case, would you consider that CV to represent a reversible system? Explain.

Exercise 19.12: Estimate E⁰ from each CV depicted in Figure 19.12. What do your results tell you about the re­liability of using Equation 19.16 for systems that are not reversible?