Читать книгу Electroanalytical Chemistry - Gary A. Mabbott - Страница 27

Because accuracy in measuring the voltage in potentiometry and in controlling the applied voltage in voltammetry experiments is so important, it is worth noting at this stage a common mechanism that can introduce errors in the cell potential measurement. Most electrochemical measurements involve the use of salt bridges to isolate reference electrodes from the sample solution. The contact between the sample solution and the salt bridge introduces another opportunity for a separation of charge to develop as shown in Figure 1.13. The mechanism for the build‐up of a potential is driven by a difference in the mobility of the ions. For example, consider a salt bridge that contains 1 M NaCl as an electrolyte contacting a sample solution with 0.1 M NaCl.

Figure 1.13 A salt bridge is a liquid junction between two solutions that allows a small exchange of ions but prevents the two solutions from mixing. A difference in concentration drives ions from the side of high concentration to the low concentration side. Smaller, faster ions move more charge of one sign across the boundary than the other. The result is a net separation of charge at the boundary causing a voltage difference known as a liquid junction potential.

Intuitively, one would expect that a difference in concentration of the ions at the boundary would lead to the movement of ions from the higher concentration toward the medium with the lower concentration. The movement of ions can be modeled mathematically using the Nernst–Planck equation [15]:

(1.32)

where C_A is the concentration of solute A in mol/cm³, D_A is the diffusion coefficient of that solute in cm²/s, and J_A is the flux or moles crossing a plane perpendicular to the direction of movement (here, in the x‐direction) per square centimeters per second, is the potential gradient, F is Faraday's constant, and T is the absolute temperature. (Notice that the flux, in mol/(s cm²) has the same dimensions as the product of a concentration and a velocity, mol/cm³ × cm/s.) Initially, both the sodium and chloride ions have the same concentration gradient, and there is no electric potential gradient (and the second term on the right is zero). The faster ion is the one with the larger diffusion coefficient. The diffusion coefficients in water of Na⁺ and Cl⁻ are 13.3 × 10⁻⁶ and 20.3 × 10⁻⁶ cm²/s, respectively. That suggests that the chloride moves about 50% faster than the sodium ion. Consequently, a negative charge builds up on the lower concentration (sample solution) side and an equal amount of positive charge accumulates on the salt bridge side of the boundary due to the excess of sodium lagging behind. As a result, this process creates a potential energy difference across the boundary. However, the process quickly reaches a steady‐state potential. The potential gradient across the boundary (the second term in Eq. (1.32)) is no longer zero. The potential gradient accelerates the movement of cations and decelerates the movement of anions so that the cation flux and anion flux become equivalent. This mechanism leads to the liquid junction potential. This junction potential is a part of the measured cell potential and it changes with solution conditions.

(1.33)

The junction potential can introduce errors as big as 50 mV or more [16]. A useful equation for calculating the magnitude of this junction potential was presented by Henderson and is discussed in Appendix C.

Figure 1.14 can guide one's thinking about junction potentials in order to determine the effect on the measured cell potential. The reference point is the reference electrode. Going from the potential of the reference electrode through the electrochemical cell to the other side, the path crosses the salt bridge. The argument above indicated that the sample solution will be at a lower potential (more negative) than the reference solution. The path from there, across the indicator electrode interface, starts from this solution potential which appears lower than it would have in the absence of a junction potential. The measured cell potential is indicated as a vector sum for all the transitions in potential between the meter leads. Ideally, the measured voltage is merely a difference between the reference and indicator electrode potentials, but the junction potential must also be included. The diagram indicates that the junction potential would be a negative number in Eq. (1.33). That is, the junction potential leads to an error that makes the measured potential appear more negative (or less positive) in this situation.

Figure 1.14 The measured potential between the indicator and reference electrodes includes all of the transitions in potential in between, represented by vertical arrows in the diagram. If anions are moving across the salt bridge faster than cations in the direction of the reference solution toward the sample solution, then E_junction is negative; the vector for the potential for the junction is downward. (The sample solution potential is lower than that of the reference solution.) In this case, the E_indicator is positive, so it is represented by an upward vector going from the solution potential toward the second meter lead. The cell potential is the value measured between the two voltmeter leads. If the junction potential had the opposite sign, then the vector for the junction would be upward and the measured potential would be larger than shown here. Both situations yield values that are different than the ideal (when E_junction = 0). (a) Ideal case and (b) real case; E_junction ≠ 0.

Of course, one way to avoid this error is to keep the conditions (other than the analyte concentration) of the sample solution and standards as similar as possible. This concern is another reason for using an ionic strength buffer. A further precaution that minimizes the junction potential is to use an electrolyte for both the salt bridge and test solutions in which the cation and anion have very similar diffusion coefficients, such as KCl. Potassium ions have a diffusion coefficient in water of 19.6 × 10⁻⁶ cm²/s which is very similar to that of chloride ions (20.3 × 10⁻⁶ cm²/s).

There is another consideration in setting up a salt bridge. Despite carefully matched diffusion coefficients, another mechanism can give rise to a junction potential. Glass or ceramic material are often used to make porous frits for salt bridges. These materials usually have a net negative charge on their surfaces. For glass with pores on the order of 5–10 nm in diameter, the negative charge can effectively screen anions from crossing the boundary leading to a junction potential on the order of 50 mV even with KCl as a supporting electrolyte (see Figure 1.15). Consequently, salt bridges made from material with larger (micron size) pores are preferable [16]. The trade‐off is a greater leakage of ions from the salt bridge into the sample.

Figure 1.15 Microscopic pores in a glass frit used as a salt bridge. The electric field (shown by dashed lines) from negative charges on the glass surface extends a few nanometers into the surrounding solution. This distance is called the Debye length of the electrostatic field. The Debye length is inversely dependent on the ionic strength. (a) At high ionic strength, the anion can pass through the pore without its field interacting with that of the glass. (b) At low ionic strength, the field of the anion and the charge on the glass repel each other decreasing the migration of anions through the pore.

Source: Adapted with permission from Mousavi et al. [16]. Copyright 2016, American Chemical Society.