Potentiometry and Probes Test Bank Ch18

Chapter 18

Problem 18.1: What would the standard electrolytic cell potential be if the reaction in Example 18.1 took place in a neutral solution?

Problem 18.2: What would the standard electrolytic cell potential be if the reaction in Example 18.1 took place in an alkaline solution?

Problem 18.3: Automobile batteries produce electricity by converting PbO₂ to PbSO₄ in the presence of 30% sulfuric acid at one electrode and converting elemental lead to PbSO₄ at the other electrode. Use data from the half-reactions and electrochem­ical potentials given in Table 18.1 potentials to propose the most likely scheme for this galvanic cell.

Problem 18.4: (a) What potential would you expect to measure in the Daniell cell at a temperature of 0.0^oC if [Cu²⁺] = 0.50 M and [Zn²⁺] = 1.25 M?

(b) What would be the Gibbs free energy of the reaction under those conditions?

(c) Mathematically demonstrate how this cell could be used as a probe of copper ion concentration.

(d) Mathematically demonstrate how this cell could be used as a temperature probe.

Problem 18.5: Are there any conditions of temperature or partial pressures of rele­vant gases that would make the conversion of liquid water into elemental oxygen and hydrogen spontaneous? Explain.

Problem 18.6: Use Equations 18.2, 18.6, and 18.7 to write the Nernst equation for the SCE and Ag/AgCl half-reactions.

Problem 18.7: Use Table 18.1 and your answer from Problem 18.6 to estimate the potential of the Ag/AgCl reference electrode presented in Figure 18.3(B).

Problem 18.8: Demonstrate how the slope of 59.1 mV mentioned in the discussion of Equation 18.11 is determined.

Problem 18.9: How would the slope in Problem 18.8 change if you were conducting experiments at body temperature, 37^oC?

Problem 18.10: Why does the glass membrane electrode have a higher affinity for protons than for other metal cations?

Problem 18.11: A pH meter was calibrated using two standard buffer solutions, measuring –234 mV for the pH 4.00 buffer and –403 mV for the pH 7.00 buffer. In an unknown solution, the voltage measured was –478 mV. What would the meter report as the pH of the unknown solution? If this experiment were to be repeated, can you suggest an improvement in methodology?

Problem 18.12: What would the pH meter used in Problem 18.11 have reported as the percent linearity for the calibration step?

Problem 18.13: If the pH_obs of a sample of sea water is measured to be 8.05, what is the actual pH if the concentration of sodium ion is 0.47 M at 25°, given that f_H/Na = 2.5 × 10^-8? What is the percent error in the measurement?

Problem 18.14: Repeat Problem 18.13, but include interferences by K⁺ (0.015 M, f_H/K = 2.0 × 10^‑10) and Ca²⁺ (0.015 M, f_H/Ca = 1.6 × 10^-8).

Problem 18.15: What is the estimated potential measured in a pH 4.00 buffer at 25°C, assuming nonanalytical factors (i.e., k) are negligible? What would the expected error be if the laboratory temperature increased by 5°C during the day?

Problem 18.16: Compare Equations 18.9 and 18.15. What difference(s) do you observe? Why are they different?

Problem 18.17: For a certain nitrate ISE, the nitrate/nitrite selectivity factor is 0.062, that of nitrate/chloride is 4.0 × 10^-3, and that of nitrate/perchlorate is 990. What is the percent error expected for the measurement of 1.5 mM nitrate in the presence of each interfering anion (individually, not all present at once) at a concentration of 0.1 mM?

Problem 18.18: Given the same conditions as presented in Problem 18.17, what is the expected percent error if all three interferences are present?

Problem 18.19: Assuming that k is negligible, calculate the partial pressure of oxygen in the exhaust gas of an automobile if the lambda sensor is reporting a potential of 317 mV. Assume the reference gas is air.

Problem 18.20: What is the E°_Cell for the chloride probe set to measure only HOCl? What is the E°­ for the measurement of OCl^-?

Problem 18.21: You want to replenish the electrolyte in the DO probe shown in Figure 18.6 when the chloride concentration, originally 1.0 M, has dropped by 10%. How long could you operate the probe continuously before refreshing the electrolyte if the inner chamber has a volume of 500 μL, the polytetrafluoroethylene (PTFE) mem­brane is 25 μm thick, and O₂ diffuses through PTFE at a rate of 1.05 × 10^-7 g/s∙cm?

Problem 18.22: Consider the equilibria presented in Equations 18.17 and 18.18. Use Excel to generate a plot of %Cl₂, %HOCl, and %OCl– versus pH (as in Figure 18.9) for water in an area of industrial runoff where the chloride concentration is 112 ppm and the initial Cl₂ concentration is 4.5 ppm. Hint: The TAC involves only active chlorine—that is Cl₂, HOCl, and OCl^-; therefore, assume the chloride (Cl^-) concentration remains constant, and use the K₁ expression to find HOCl and the K₂ expression to find OCl^-.

Problem 18.23: A conductivity cell uses circular electrodes that are 0.50 cm in diameter and are positioned 1.00 cm apart. When placed in a solution, the resistance is found to be 1100 ohms. Calculate the conductivity of the solution.

Problem 18.24: What is the salinity of the water samples described in Example 18.6 and Problem 18.23, assuming the measurements were made at 25°C? It is probably easier to do this calculation using a spreadsheet.

Problem 18.25: Why do you think the porous polymer electrolyte is coated with platinum black rather than just having it in contact with a standard platinum electrode?

Problem 18.26: Calculate the Gibbs free energy (kJ/mol) associated with the net reaction in the alcohol fuel cell sensor. What does that ΔG_rxn tell you about the overall reaction?

EXERCISE 18.1: Write the anode and cathode half-reac­tions for a galvanic (spontaneous) cell constructed using tin and silver electrodes. Also, write the overall cell reaction and find the standard cell potential.

EXERCISE 18.2: Calculate the Gibbs free energy of the redox reaction described in Problem 18.20.

EXERCISE 18.3: Write the expected anode and cathode re­actions for the electrolysis of water conducted in a neutral solution using NaI as the electrolyte.

EXERCISE 18.4: What is the minimum potential you would need to apply to the system described in Problem 18.3 in order to produce either H₂ or O₂ gas?

EXERCISE 18.5: Why are ISEs usually selective, but rarely specific, for the analyte of interest?

EXERCISE 18.6: What is the estimated potential measured for a glass membrane electrode in a pH = 10.00 buffer at 21°C, assuming nonanalytical factors (i.e., k) are negligible? What would the expected error be if the laboratory temperature rose to 25°C by the end of the day with no additional calibrations?

EXERCISE 18.7: Why is the Clark cell usually operated in the amperometric mode, even though the overall reaction is spontaneous?

EXERCISE 18.8: Estimate the actual cell potential for a Clark cell at 22°C if [Cl^-] = 0.91 M, the pH = 10.12, and dissolved oxygen is present at 7.8 ppm.

EXERCISE 18.9: If the pH_obs of a sample of water from the Great Salt Lake in Utah is measured to be 7.65, what is the actual pH if the concentration of sodium ion is 1.56 M and the Mg²⁺ concentration is 1.89 M 25°C, given that f_H/Na = 2.5 × 10^-8 and f_H/Mg = 1.7 × 10^-8? What is the percent error in the measurement, assuming only sodium and magnesium ions are significant enough to affect the measurement?

EXERCISE 18.10: The concentration of salts in seawater is approximately 0.6 M. By what percent would this affect your pH reading if you failed to correct for salinity? Assume the total salt content can be represented by NaCl.