Electroanalytical Chemistry. Gary A. Mabbott

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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.