The conductometric analysis method is the measurement of electrolytic conductivity to monitor the progress of a chemical reaction. This science is widely used in analytical chemistry, where titration is the standard method of work. What is conductometry? In the usual practice of analytical chemistry, this term is used as a synonym for titration, while it is also used to describe non-titrational applications. What is the use of applying the method of this analysis? It is often used to determine the total conductivity of a solution or to analyze the endpoint of a titration including ions.
History
The measurements began back in the 18th century, when Andreas Baumgartner noticed that salt and mineral waters from Bad Gastein in Austria conduct electricity. Thus, the use of this method to determine the purity of water, which is often used today to test the effectiveness of water treatment systems, began in 1776. And so began the history of the conductometric analysis method.
Friedrich Kohlrausch continued the development of this science in 1860, when he applied alternating current to water, acids and other solutions. Around the same time, Willis Whitney, who studied the interactions of complexes of sulfuric acid and chromium sulfate, found the first conductometric endpoint. These findings culminated in potentiometric titration and the first volumetric analysis tool by Robert Berend in 1883 for titration of chloride and bromide HgNO3. Thus, the modern conductometric analysis method was founded by Berend.
This development made it possible to check the solubility of salts and the concentration of hydrogen ions, as well as acid-base and redox titration. The conductometric analysis method was improved with the development of the glass electrode, which began in 1909.
Titration
Conductometric titration is a measurement in which the electrolytic conductivity of the reaction mixture is continuously monitored by adding one reagent. The equivalence point is the point at which the conductivity suddenly changes. A noticeable increase or decrease in conductivity is associated with a change in the concentration of the two most highly conductive ions - hydrogen and hydroxyl ions. This method can be used to titrate colored solutions or a homogeneous suspension (for example, a suspension of wood pulp) that cannot be used with conventional indicators.
Often, acid-base and redox titrations are carried out, in which common indicators are used to determine the endpoint, for example, methyl orange, phenolphthalein for acid-base titration and starch solutions for the iodometric-type redox process. However, electrical conductivity measurements can also be used as a tool to determine the end point, for example, when observing an HCl solution with a strong NaOH base.
Proton neutralization
As titration progresses, protons are neutralized to form NaOH by forming water. For each amount of NaOH added, an equivalent number of hydrogen ions are removed. In fact, the mobile H + cation is replaced by the less mobile Na + ion, and the conductivity of the titrated solution, as well as the measured cell conductivity, decrease. This continues until an equivalence point is reached at which a sodium chloride NaCl solution can be obtained. If more base is added, an increase is observed as more Na + and OH- ions are added and the neutralization reaction no longer removes a noticeable amount of H +.
Therefore, when titrating a strong acid with a strong base, conductivity has a minimum at the equivalence point. This minimum can be used instead of indicator dye to determine the end point of the titration. The titration curve is a graph of the measured conductivity or conductivity as a function of the volume of the added NaOH solution. The titration curve can be used to graphically determine the equivalence point. The conductometric analysis method (and its use) is extremely relevant in modern chemistry.
Reaction
For the reaction between a weak acid-weak base, the electrical conductivity initially decreases slightly, since fewer available H + ions are used. Then, the conductivity increases slightly to the volume of the equivalence point due to the contribution of the salt cation and anion (this contribution is insignificant in the case of a strong acid-strong base and is not considered there.) After reaching the equivalence point, the conductivity rapidly increases due to an excess of OH ions.
Conductivity detectors (conductometric analysis method) are also used to measure electrolyte concentrations in aqueous solutions. The molar concentration of the analyte, which creates the conductivity of the solution, can be obtained from the measured electrical resistance of the solution.
Conductometric analysis method: principle and formulas
(2.4.13) = Constcell1Λm1Res, where Constcell is a constant value depending on the measuring cell, Res is the electrical resistance measured by the device (according to Ohm's law, Res = I / V, and at a constant voltage V, measuring I intensity allows you to calculate Res) , and Λm is the equivalent conductivity for ionic particles. Although for practical purposes Λm can be considered constant, it depends on concentration in accordance with the law of Kolrausch:
(2.4.14) = Xm Λm0-ΘC, where Θ is the constant and Λm0 is the limiting molar conductivity characteristic of each ion. Molar conductivity in turn depends on temperature.
Scrit
The development of the conductometric measurement analysis method has led scientists to new discoveries. Scientists determined the critical supersaturation ratio, Scrit, using conductometry in a homogeneous AgCl deposition system in excess of Ag + ions, using hydrolysis of alkyl chloride as a source of CI ions. ” They found Scrit = 1.51, 1.73 and 1.85 at 15, 25 and 35 ° C, respectively, where S = ([Ag +] [Cl-] / Ksp) 1/2 by their definition. If this definition of the coefficient of supersaturation is converted into ours (S = [Ag +] [Cl-] / Ksp), the results correspond to 2.28, 2.99 and 3.42, respectively, in fairly good agreement with the results of this study. However, the temperature dependence of Scrit is opposite to that described in this study. Although the reason for this contradiction is not clear, a decrease in Scrit with increasing temperature can be quite reasonable, since the nucleation rate changes sharply with a small change in ΔGm * / kT, and therefore ΔGm * / kT, which is proportional to T - 3 (lnSm) 2 by the formula (1.4.12), is considered almost constant with a change in temperature in this system. Incidentally, the definition of S should be [Ag +] [Cl -] / Ksp, since the supersaturation ratio in terms of the concentration of the monomer [AgCl] is initially given as S = [AgCl] / [AgCl] (∞) = [Ag +] [Cl -] / Ksp.
Tanaka and Iwasaki
The history of the conductometric analysis method was continued by two iconic Japanese scientists. Tanaka and Iwasaki studied the nucleation of AgCl and AgBr particles using the stopped flow method in combination with a multichannel spectrophotometer, which is useful for studying the fast process of the order of ms. They found that a specific AgXm silver halide complex (m-1), with a rather narrow UV absorption band, formed instantly when an AgC104 solution of the order of 10-4 mol dm-3 was mixed with a KX (X = Cl or Br) solution of the order from 10-2 to 10-1 mol dm-3, followed by its rapid decay of the order of 10 ms during the formation of an intermediate product with wide UV absorption and a much slower change in the spectrum of the intermediate product. They interpreted the intermediate as monodisperse (AgX) n nuclei consisting of n molecules and determined n from the apparent ratio -dC / dt α Cn at t = 0 for various initial C concentrations of the AgXm precursor (m-1) - (n = 7 -10 for AgCl; n = 3-4 for AgBr).
However, since the precursor AgXm (m - 1) decays in a non-stationary manner, the theory of quasistationary nucleation is not applied in this process, and thus, the obtained value of n does not correspond to the n * value of critical nuclei. If the intermediate product contains monodispersed nuclei n formed by the monomer complex, the ratio -dC / dt α C may not be maintained. Unless we assume that clusters smaller than n-measures are in equilibrium, ki - 1, ici - 1c1 = ki, i - 1ci, with each other in the sequential reaction c1 → c2 → c3 → ... → cn - 1 → cn., And only the last step cn - 1 → cn is irreversible; i.e. c1⇌c2⇌c3⇌ ... ⇌cn - 1 → cn.
In addition, it should be assumed that cluster concentrations from 2 to n-1 have negligible equilibrium concentrations. However, there seems to be no reason to justify these assumptions. On the other hand, we tried to calculate the radii of critical nuclei and the supersaturation coefficients S at the end of a fast process using γ = 101 mJ m - 2 for cubic AgCl19 and γ = 109 mJ m - 2 for cubic AgBr20 under the assumption that the values of n , 7-10 for AgCl19 and 3-4 for AgBr20, are equivalent to the size of monodisperse nuclei, n *. The conductometric analysis method, reviews of which range from just approving to admiring, gave a new birth to chemistry as a science.
As a result, scientists discovered the following formula: r * = 0.451 nm and S = 105 for AgCl with n * = 9; r * = 0.358 nm and S = 1230 for AgBr with n * = 4. Since their systems are comparable to the Davis and Jones systems, which received a critical AgCl supersaturation of about 1.7-2.0 at 25 ° C. Using conductometry with direct mixing in equal volumes of diluted aqueous solutions of AgNO3 and KCl, extremely high S values may not reflect the actual supersaturation coefficients in equilibrium with the intermediate nuclei.
Ultraviolet absorption
It seems more reasonable to attribute an intermediate product with wide ultraviolet absorption by nuclei much larger than the average size with a wide size distribution generated by an unsteady sequential reaction. The subsequent slow change in the intermediate nuclei is apparently due to their maturation in Ostwald.
In the above context, the American chemist Nielsen also obtained a similar n * of about 12 and a corresponding S greater than 103 for the nucleation of barium sulfate particles from turbidity measurements as a function of supersaturation using n * = dlogJ / dlogC in a Becher-Dering theory similar to the formula. (1.3.37), but giving (n * + 1) instead of n *. Since solutions of barium ions and sulfate ions were directly mixed in this experiment, rapid unsteady nucleation should have ended immediately after mixing, and what was measured could be the speed of the slow subsequent maturation of Ostwald and / or fusion of the generated nuclei. Apparently, this is the reason for the unreasonably small n * value and extremely high supersaturation. Therefore, we must once again note that a certain reservoir of monomeric species that releases them in response to their consumption is always necessary to achieve quasistationary nucleation in a closed system. All classical nucleation theories, including the Becher-Dering theory, implicitly assume this condition. The definition of the conductometric analysis method was given in the sections of the article above.
Other scientists investigated the process of unsteady nucleation of silver halides by pulsed radiolysis of water containing methylene halide and silver ions, during which methylene halide was decomposed to separate halide ions by hydrated electrons generated by pulsed radiation in the range from 4 ns to 3 μs. Product spectra were recorded using a photomultiplier and a streak camera, and it was found that monomeric precursors of silver halides are formed over a time of the order of microseconds followed by a nucleation process similar to that observed by Tanaka and Iwasaki. Their results clearly show that the process of nucleation of silver halides by direct mixing of the reagents consists of two elementary stages; that is, the formation of a monomeric precursor of the order of μs and the subsequent transition to nuclei of the order of 10 ms. It should be noted that the average size of the nuclei is about 10 nm.
Supersaturation
Regarding the supersaturation coefficients for nucleation of AgCl particles in open systems in which high concentrations of reagents such as AgNO3 and KCl are continuously introduced into the gelatin solution throughout the deposition, Strong and Wey31 reported 1.029 (80 ° C) - 1.260 (40 ° C) and Leubner32 reported 1,024 at 60 ° C, which is estimated from measuring the growth rate of the particles of AgCl seed at critical supersaturation. This is the essence of the conductometric method of quantitative analysis.
On the other hand, for open systems of AgBr particles, some estimated values of the critical supersaturation coefficient, Scrit: Scrit ~ 1.5 at 70 ° C according to Wey and Strong33, were reported, depending on the size of the maximum growth rate, determined by finding the renucleation threshold at various rates adding an AgNO3 solution to a KBr solution in the presence of seed particles by a double jet method; Scrit = 1.2-1.5 at 25 ° C according to Jagannathan and Wey34 as the maximum supersaturation coefficient determined on the basis of the Gibbs-Thomson equation with their data on the minimum average size of nuclei observed by electron microscopy during the nucleation stage of the two-jet AgBr precipitation . This is very effective when applying the conductometric method of quantitative analysis.
In calculating these Scrit values, they assumed γ = 140 mJ m - 2. Since nucleation in open systems corresponds to the survival of nucleating nuclei created in the local zone of extremely high supersaturation near the reagent outlets, critical supersaturation corresponds to the concentration of the solute in equilibrium with the nuclei of maximum size, if we use Sugimoto35 data on the maximum radius of AgBr nuclei in open systems (.3 8.3 nm) with theoretical γ for cubic AgBr (= 109 mJ m - 2) 3, then the coefficient nt critical supersaturation, Scrit, is calculated to be 1.36 at 25 ° C (if γ is assumed to be 140 mJ / m 2, then Scrit = 1.48).
Therefore, in any case, critical supersaturations in open systems of silver halide particles are usually much lower than maximum supersaturations (probably close to critical supersaturations) in closed systems. This is due to the fact that the average radius of the nuclei generated in the local zone of the open system is much larger than rm * in the closed system, probably due to the instant fusion of highly concentrated primary nuclei in the local zone of the open system with a high local concentration of electrolyte.
Application
The use of the conductometric titration method for continuous recording during enzymatic processes has been thoroughly studied and analyzed. Almost all electrochemical analytical methods are based on electrochemical reactions (potentiometry, voltammetry, amperometry, coulometry).
The conductometric analysis method is a method in which either there are no electrochemical reactions at all on the electrodes, or there are secondary reactions that can be neglected. Therefore, in this method, the most important property of the electrolyte solution in the boundary layer is its electrical conductivity, which varies in accordance with a fairly wide range of biological reactions.
Benefits
Conductivity biosensors also have some advantages over other types of transducers. First, they can be manufactured using inexpensive thin-film standard technology. This, along with the use of an optimized method of immobilization of biological material, leads to a significant reduction in both the initial cost of devices and the total cost of analyzes. For built-in microbiosensors, it is easy to perform a differential measurement mode, which compensates for external influences and significantly increases the accuracy of measurements.
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