Analytical Test 3 Short Answer

21-3. You need to choose between determining an analyte by measuring an electrode potential or by performing a titration. Explain which you would choose if you needed to know (a) the absolute amount of the analyte to a few parts per thousand (b) the activity of the analyte

(a) A titration is generally more accurate than measurements of electrode potential. Therefore, if ppt accuracy is needed, a titration should be picked. (b) Electrode potentials are related to the activity of the analyte. Thus, pick potential measurements if activity is the desired quantity.

21-1. Briefly describe or define (c) electrode of the first kind (d) electrode of the second kind

(c) electrode of the first kind - a metal electrode that responds to the activity of its cation in solution (d) electrode of the second kind - a metal electrode that is used to determine the concentration of an anion that forms a precipitate or a stable complex with the cation of the electrode metal

22-4. How does a current in an electrochemical cell affect its potential?

A current in an electrochemical cell always causes the cell potential to become less positive or more negative.

22-10. What is the purpose of a depolarizer?

A depolarizer is a substance that is reduced or oxidized more readily than a potentially interfering species. For example, the codeposition of hydrogen is prevented through the introduction of nitrate ion as a cathodic depolarizer.

21-10. How does a gas-sensing probe differ from other membrane electrodes?

A gas-sensing probe functions by permitting the gas to penetrate a hydrophobic membrane and altering the composition of liquid on the inner side of the membrane. The changes are registered by an indicator/reference electrode pair in contact with the inner solution. Thus, there is no direct contact between the electrodes and the test solution as there is with membrane electrodes.

23-3. Why is a high supporting electrolyte concentration used in most electroanalytical procedures?

A high supporting electrolyte concentration is used in most electroanalytical procedures to minimize the contribution of migration to concentration polarization. The supporting electrolyte also reduces the cell resistance, which decreases the IR drop.

23-9. Suggest how Equation 23-13 could be used to determine the number of electrons in n involved in a reversible reaction at an electrode.

A plot of E_appl versus (see image) should yield a straight line having a slope of -0.0592/n. Thus, n is readily obtained from the slope.

22-12. Why is an auxiliary reagent always required in a coulometric titration?

An auxiliary reagent is generally required in a coulometric titration to permit the analyte to be oxidized or reduced with 100% current efficiency. As a titration proceeds, the potential of the working electrode will inevitably rise as concentration polarization of the analyte begins. Unless an auxiliary reagent is present to terminate this rise by producing a species that reacts with the analyte, some other species will be oxidized or reduced thus lowering the current efficiency and producing erroneous results.

21-8. What experimental factor places a limit on the number of significant figures in the response of a membrane electrode?

Because of variables that cannot be controlled, it is necessary to calibrate the response of the electrode against one or more standards. It must then be assumed that the junction potential associated with the external reference electrode does not change when the standard is replaced by the test solution. The uncertainty associated with this assumption translates into uncertainties in the second decimal place of the measured p-value.

22-6. How do concentration polarization and kinetic polarization resemble one another? How do they differ?

Both kinetic and concentration polarization cause the potential of an electrode to be more negative than the thermodynamic value. Concentration polarization results from the slow rate at which reactants or products are transported to or away from the electrode surfaces. Kinetic polarization arises from the slow rate of electrochemical reaction at the electrode surfaces.

22-3. Describe three mechanisms responsible for the transport of dissolved species to and from an electrode surface.

Diffusion arises from concentration differences between the electrode surface and the bulk of solution. Migration results from electrostatic attraction or repulsion. Convection results from stirring, vibration or temperature differences.

22-8. What is a supporting electrolyte and what is its role in electrochemistry?

High concentration of an inert electrolyte, called the supporting electrolyte, are used to minimize the contribution of migration to concentration polarization. The supporting electrolyte also reduces the cell resistance, which decreases the IR drop.

21-6. Why is it necessary for the glass in the membrane of a pH-sensitive electrode to be appreciably hygroscopic?

In order for a glass membrane to be pH sensitive, it is necessary for the two surfaces to be hydrated so that the equilibria H+Gl- <--> H+ + Gl- can be established.

23-6. Why are stripping methods more sensitive than other voltammetric procedures?

In stripping methods, the electrodeposition step preconcentrates the analyte on the surface of the working electrode. Because of this preconcentration step, stripping methods are more sensitive than ordinary voltammetric methods.

22-7. Describe conditions that favor kinetic polarization in an electrochemical cell.

Kinetic polarization is often encountered when the product of a reaction is a gas, particularly when the electrode is a soft metal such as mercury, zin, or copper. It is likely to occur at low temperatures and high current densities.

23-5. Why is it necessary to buffer solutions in organic voltammetry?

Most organic electrode processes consume or produce hydrogen ions. Unless buffered solutions are used, marked pH changes can occur at the electrode surface as the reaction proceeds.

22-9. How do electrogravimetric and coulometric methods differ from potentiometric methods? Consider currents, voltages, and instrumentation in your answer.

Potentiometric methods are carried out under zero current conditions and the effect of the measurement on analyte concentration is typically undetectable. In contrast, electrogravimetric and coulometric methods depend on the presence of a net current and a net cell reaction (i.e., the analyte is quantitatively converted to a new oxidation state). Unlike potentiometric methods where the cell potential is simply the difference between two electrode potentials, two additional phenomena, IR drop and polarization, must be considered in electrogravimetric and coulometric methods where current is present. Finally, the final measurement in electrogravimetric and coulometric methods is the mass of the product produced electrolytically, while in potentiometric methods it is the cell potential.

21-13. Give several advantages of a potentiometric titration over a direct potentiometric measurement.

Potentiometric titration offer many advantages over direct potentiometry including (1) yielding equivalence point data that are independent of Ecell and free of uncertainties involving the junction potential (2) electrode fouling and non-Nernstian behavior are not as serious (3) the reference electrode potential does not need to be known (4) the result is analyte concentration even though the electrode responds to activity, thus ionic strengths are not important.

22-13. Determine the number of ions undergoing electron transfer at the surface of an electrode during each second that an electrochemical cell is operated at 0.0175 A at 100% current efficiency and the participating ions are (a) univalent (b) divalent (c) trivalent

See image.

21-14. What is the "operational definition of pH"? Why is it used?

The "operational definition of pH" is based on the direct calibration of the meter with carefully prescribed standard buffers followed by potentiometric determination of the pH of unknown solution. The relationship is (see image), where pHu is the pH of the unknown solution, pHs is the pH of the standard buffer, and Eu and Es are the potentials of the unknown and standard solution, respectively. This relationship has been adopted throughout the world as the operational definition of pH.

23-8. List the advantages and disadvantages of the hanging mercury drop electrode compared with platinum or carbon electrodes.

The advantages of a hanging mercury drop electrode compared with platinum or carbon electrodes include (1) the high overvoltage of hydrogen on mercury, (2) the ability to form fresh electrode surfaces of reproducible area, and (3) the reproducible currents that are achieved on a mercury electrode. The disadvantages include (1) its poor anodic potential range, (2) its relatively large residual current, (3) its inconvenience.

21-9. Describe the alkaline error in the measurement of pH. Under what circumstances is this error appreciable? How are pH data affected by alkaline error?

The alkaline error arises when a a glass electrode is employed to measure the pH of solutions having pH values in the 10 to 12 range or greater. In the presence of alkali ions, the glass surface becomes responsive to not only hydrogen ions but also alkali metal ions. Measured pH values are low as a result.

21-12. How does information supplied by a direct potentiometric measurements of pH differ from that obtained from a potentiometric acid/base titration?

The direct potentiometric measurement of pH provides a measure of the equilibrium activity of hydronium ions in the sample. A potentiometric titration provides information on the amount of reactive protons, both ionized and nonionized, in the sample.

21-5. Describe the source of pH dependence in a glass membrane electrode.

The potential arises from the difference in positions of dissociation equilibria on each of the two surfaces. These equilibria are described by H+Gl- <--> H+ + Gl- (membrane <--> solution + membrane). The surface exposed to the solution having the higher H+ concentration becomes positive with respect to the other surface. This charge difference, or potential, serves as the analytical parameter when the pH of the solution on one side of the membrane is held constant.

23-7. What is the purpose of the electrodeposition step in stripping analysis?

The purpose of the electrodeposition step in stripping analysis is to preconcentrate the analyte on the surface of the working electrode and to separate it from many interfering species.

23-4. Why is the reference electrode placed near the working electrode in a three-electrode cell?

The reference electrode is placed near the working electrode to minimize the IR drop that can distort voltammograms.

22-11. Whys is the working electrode normally isolated in from the counter electrode in a controlled-potential coulometric analysis?

The species produced at the counter electrode are potential interferences by reacting with the products at the working electrode. Isolation of one from the other is ordinarily required.

21-7. List several sources of uncertainty in pH measurements with a glass/calomel electrode system.

Uncertainties include (1) the acid error in highly acidic solutions (2) the alkaline error in strongly basic solutions (3) the error that arises when the ionic strength of the calibration standards differs from that of the analyte solution (4) uncertainties in the pH of the standard buffers (5) nonreproducible junction potentials with solutions of low ionic strength (6) dehydration of the working surface

22-5. What experimental variables affect concentration polarization in an electrochemical cell?

Variables that influence concentration polarization include temperature, stirring, reactant concentrations, presence or absence of other electrolytes and electrode surface areas.

22-1. Briefly distinguish between (a) concentration polarization and kinetic polarization (b) a coulomb and an ampere (c) diffusion and migration

(a) In concentration polarization, the current in an electrochemical cell is limited by the rate at which reactants are brought to or removed from the surface of one or both electrodes. In kinetic polarization, the current is limited by the rate at which electrons are transferred between the electrode surfaces and the reactant in solution. For either type, the current is no longer linearly related to cell potential. (b) The coulomb is a unit of electrical charge, whereas the ampere is a unit of current measuring the rate of flow of charge. One ampere is one coulomb/second. (c) Diffusion is the movement of species under the influence of a concentration gradient. Migration is the movement of an ion under the influence of an electrostatic attractive or repulsive force.

23-14. (a) What are the advantages of performing voltammetry with microelectrodes? (b) Is it possible for an electrode to be too small? Explain your answer.

(a) The advantages include reaching steady-state currents rapidly, having very small charging currents which enables rapid potential scanning, having small IR drops, being able to respond to very small volumes and in flowing streams, and having large signal-to- noise ratios.(b) The currents become very small as the electrode size decreases. Problems can also arise if the electrode dimensions become comparable to the double-layer thickness or to molecular dimensions. In some cases for nanoelectrodes, new theories and experimental approaches may be necessary.

21-11. What is the source of (a) the asymmetry potential in a membrane electrode?

(a) The asymmetry potential in a membrane arises from differences in the composition or structure of the inner and outer surfaces. These differences may arise from contamination of one of the surfaces, wear and abrasion and/or strains set up during manufacturing.

23-1. Distinguish between (a) voltammetry and amperometry (b) linear-scan voltammetry and pulse voltammetry (c) differential-pulse voltammetry and square-wave voltammetry

(a) Voltammetry is an analytical technique that is based on measuring the current that develops at a small electrode as the applied potential is varied. Amperometry is a technique in which the limiting current is measured at a constant potential. (b) In linear scan voltammetry, the current in a cell is monitored continuously as the applied potential is changed at a constant rate. In pulse voltammetry, an excitation signal is used that consists of a series of voltage pulses that increase in size linearly as a function of time. (c) Differential pulse and square wave voltammetry differ in the type of pulse sequence used as shown in Figure 23-1b and 23-1c.

21-1. Briefly describe or define (a) indicator electrode (b) reference electrode

(a) indicator electrode - an electrode used in potentiometry that responds to variations in the activity of an analyte ion or molecule (b) reference electrode - an electrode whose potential is known, constant and independent of the type of solution in which it is immersed

21-2. Briefly describe or define (a) liquid-junction potential (b) boundary potential

(a) liquid junction potential - the potential that develops across the interface between two solutions having different electrolyte compositions (b) boundary potential - the potential that develops across an ion-sensitive membrane when the two sides of the membrane are immersed in solutions having different concentrations of the ion to which the membrane is sensitive

22-2. Briefly define (a) ohmic potential (b) overvoltage (c) controlled-potential electrolysis

(a) ohmic potential (IR drop) - the product of the current in the cell in amperes and the electrical resistance of the cell in ohms (b) overvoltage - the amount of extra voltage that must be applied to a cell to overcome the effects of concentration or kinetic polarization. It is the difference between the theoretical cell potential and the actual cell potential at a given current. (c) controlled-potential electrolysis - the potential applied to a cell is continuously adjusted to maintain a constant potential between the working electrode and a reference electrode.

23-2. Define (a) voltammograms (b) hydrodynamic voltammetry (c) Nernst diffusion layer (d) mercury film electrode (e) half-wave potential (f) diffusion current

(a) voltammogram - a plot of current versus applied potential. (b) hydrodynamic voltammetry - current-potential curves are obtained in stirred solution. (c) Nernst diffusion layer - a static layer of solution immediately adjacent to the electrode surface in which mass transport occurs by diffusion alone (d) mercury film electrode - formed by electrodepositing a thin layer of mercury onto a disk electrode (e) half-wave potential - the potential on a voltammetric wave when the current is one-half of the limiting current (f) diffusion current - a limiting current in voltammetry when the analyte is transported to the electrode surface solely by diffusion

21-11. What is the source of (b) the boundary potential in a membrane electrode?

(b) The boundary potential for a membrane electrode is a potential that develops when the membrane separates two solutions that have different concentrations of a cation or an anion that the membrane binds selectively. For an aqueous solution, the following equilibria develop when the membrane is positioned between two solutions of A+: A+M- <--> A+ + M- (membrane 1 <--> solution 1 + membrane 1) A+M- <--> A+ + M- (membrane 2 <--> solution 2 + membrane 2) where the subscripts refer to the two sides of the membrane. A potential develops across this membrane if one of these equilibria proceeds further to the right than the other, and this potential is the boundary potential. For example, if the concentration of A+ is greater in solution 1 than in solution 2, the negative charge on side 1 of the membrane will be less than that of side 2 because the equilibrium on side 1 will lie further to the left. Thus, a greater fraction of the negative charge on side 1 will be neutralized by A+.

21-11. What is the source of (c) a junction potential in a glass/calomel electrode system?

(c) The junction potential in a glass/calomel electrode system develops at the interface between the saturated KCl solution in the salt bridge and the sample solution. It is caused by charge separation created by the differences in the rates at which ions migrate across the interface.

21-2. Briefly describe or define (c) asymmetry potential

(c) asymmetry potential - a potential that develops across an ion-sensitive membrane when the concentrations of the ion are the same on either side of the membrane. This potential arises from dissimilarities between the inner and outer surface of the membrane

23-1. Distinguish between (d) a rotating disk electrode and a ring-disk electrode (e) a limiting current and a diffusion current (f) laminar flow and turbulent flow

(d) A rotating disk electrode is a disk electrode rotated rapidly by a motor. The ring- disk-electrode is a modified rotating disk with a second ring-shaped electrode isolated electrically from the center disk. These electrodes are shown in Figure 23-19. (e) In voltammetry, a limiting current is a current that is independent of applied potential. Its magnitude is limited by the rate at which a reactant is brought to the surface of the electrode by migration, convection, and/or diffusion. A diffusion current is a limiting current when analyte transport is solely by diffusion. (f) Laminar flow is a type of liquid flow in which layers of liquid slide by one another in a direction that is parallel to a solid surface. It is characterized by a parabolic flow profile. Turbulent flow is a type of liquid flow that has no regular pattern.

22-1. Briefly distinguish between (d) a working electrode and a reference electrode (e) the electrolysis circuit and the control circuit for controlled-potential methods

(d) The electrode at which an electrochemical oxidation or reduction occurs is the working electrode. The reference electrode is an electrode of constant potential against which the potential of the working electrode is measured. (e) The electrolysis circuit consists of a working electrode and a counter electrode. The control circuit regulates the applied potential such that the potential between the working electrode and a reference electrode in the control circuit is constant and at a desired level.

21-11. What is the source of (d) the potential of a crystalline membrane electrode used to determine the concentration of F-?

(d) The membrane in a solid-state electrode for F- is crystalline LaF3, which when immersed in aqueous solution, dissociates according to the equation (see image). Thus, the boundary potential develops across this membrane when it separates two solutions of F- ion concentration. The source of this potential is the same as described in part (b).

22-2. Briefly define (d) coulometric titration (e) current efficiency (f) galvanostat

(d) coulometric titration - an electroanalytical method in which a constant current of known magnitude generates a reagent that reacts with the analyte; the time required to generate enough reagent to complete the reaction is measured (e) current efficiency - a measure of agreement between the number of faradays of charge and the number of moles of reactant oxidized or reduced at a working electrode (f) galvanostat - an instrument that provides a constant current

23-1. Distinguish between (g) the standard electrode potential and the half-wave potential for a revesible reaction at a working electrode (h) stripping methods and standard voltammetry

(g) The half-wave potential is closely related to the standard potential for a reversible reaction. That is, (see image), where kA and kB are constants that are proportional to the diffusion coefficients of the analyte and product. When these are approximately the same, the half-wave potential and the standard potential are essentially equal. (h) In stripping methods, the analyte is first deposited on a working electrode. The deposited analyte is later stripped from the working electrode and determined by an electroanalytical method, often voltammetry. In standard voltammetry, the electrode current is measured as a function of applied potential.

21-4. What is meant by Nernstian behavior in an indicator electrode?

(see image) The response is Nernstian if a plot of E vs pM is linear with a slope of -0.0592/n.