# Definition and Basic principle

## Definition

Coulometry is an electrochemical analysis method developed based on Faraday's law, which calculates the content of substances (i.e., lithium plating, graphite cells) by measuring the amount of electricity consumed when electrolysis is complete.

## Basic principle

Coulometry was developed in the early days of electrochemistry, during the first half of the 19th century.The basic principle of coulometry is to measure the quantity Q of electricity which can be regarded as the integral of current I, and time of passage t.  Figure 1 shows two types of coulometry determination results.

Figure 1The current–time curve obtained by (a) coulometric determination method and (b) the curve of charge quantity–time (License: ACS AuthorChoice license).

The mass W of the product precipitated on the electrode is proportional to the quantity Q of the electrolytic cell.

When electrolyzing Bn+ , for every Faraday of electricity in the electrolyte, the amount of B is 1 mol, which means the amounts of B in the systems were in proportion to the respective chemical equivalents (the molar mass of B divided by the number of electrons it accepts or loses).

$\mathrm{m_B=\dfrac{M_B Q}{F}=\dfrac{M_r It}{nF}}$

mB : The mass of B precipitated on the electrode, g ;

F : Faraday constant，96487 C.mol-1 ;

MB : The mole mass of B, g.mol-1 ;

I : Current, A ;

Q  : Quantization, C ;

t : Time, s ;

Mr : Relative molecular mass of B ;

n : Number of electrons transferred in electrode reaction.

Requirement: Single electrode reaction, 100% current efficiency.

Current efficiency: After a certain amount of electricity flows through the current pool, the ratio of the actual mass of a product to the theoretical mass.

Factors affecting current efficiency:

1. Electrode reaction in solvent;
2. Electrolytic reaction of impurities in solvent;
3. Dissolved oxygen in water;
4. Re-reaction of electrolysis products;
5. Charging capacitor.

# Classification

## Potentiostatic coulometry

Potentiostatic coulometry is to keep the electrode potential constant, electrolyze all substances, and measure the total electricity required for electrolysis.

Figure 2Schematic diagram of coulomb measuring device. (Figure: Ziyue Miao)

Measurement process: When the switch is turned to B, connect to the coulomb counter, record the amount of electricity that flows through, and perform electrolysis until the electrolysis is complete, and calculate the content of the measured substance from the amount of electricity recorded by the coulomb counter.

## Amperostatic coulometry

Amperostatic coulometry is to keep the electrolysis current consistent, use the product of the electrode reaction as a titrant to determine the content of substances to be tested, calculate the amount of electricity consumed.

Figure 3Schematic diagram of coulomb titration device. (Figure: Ziyue Miao)

Measurement process: A large number of substances are added to the test solution to electrolyze the substance to produce a titrant. After the titrant reacts quantitatively with the measured substance, the electrolysis ends immediately, and then calculate the dose of the titrant and the content of the measured substance.

# Applications

## Karl Fischer titration

Karl Fischer titration is a volumetric analysis method for measuring moisture based on the theory of coulomb analysis.Basic principle:

When using iodine to oxidize sulfur dioxide, a certain amount of water is required to participate in the reaction:

$\mathrm{I_2 + SO_2 + 2H_2O\rightarrow 2HI + H_2SO_4}$

When the sulfuric acid concentration reaches 0.05%, the reverse reaction occurs.

When Karl Fischer reagent in the electrolytic cell of the instrument reaches equilibrium, it is injected into the water-containing sample. Water participates in the redox reaction of iodine and sulfur dioxide, pyridine hydroiodic acid and pyridine methyl sulfate are produced in the presence of pyridine and methanol. The iodine produced by the anode electrolysis is consumed, so that the oxidation-reduction reaction continues until the water is completely exhausted. According to Faraday's law, the iodine produced by electrolysis is proportional to the electricity consumed during electrolysis.

The chemical reaction is as follows:

$\mathrm{H_2O + I_2 + SO_2 + 3C_5H_5N\rightarrow 2C_5H_5N\cdot}\mathrm{HI + C_5H_5N\cdot}\mathrm{SO_3}$ $\mathrm{C_5H_5N\cdot}\mathrm{SO_3 + CH_3OH\rightarrow C_5H_5N\cdot}\mathrm{HSO_4CH_3}$

Advantages: It is the most specific and accurate chemical method for measuring the moisture content of substances, and it is also the classic standard analytical method for determining the moisture content worldwide.

Applications: It can quickly determine the water content in liquids, solids and gases, and is suitable for the determination of water content in many inorganic and organic compounds. It is widely used in petroleum, chemical, electric power, medicine, pesticide industries and academic research institutions.When measuring samples that are easily destroyed by heat, not only free water but also bound water can be measured, but it is not suitable for measuring samples containing strong reducing substances such as Vitamin C.

Example: Albino Gallina et al measured the water content in more than 100 honeys of different botanical origin, using KFT determinations, and the particularity was to find the optimal parameters for water determination in honey without any heat treatment of sample or working medium.

## Measurement of Chemical oxygen demand (COD)

The water sample uses potassium dichromate as the oxidant. After reflux oxidation in a sulfuric acid medium, the excess potassium dichromate uses ferrous ionsproduced after electrolysis as a coulometric titrant for coulometric titration.

Advantages: This method is simple, fast and use a small amount of reagents, simplifies the steps of calibrating a standard titration solution with a standard solution, shortens the reflux time, and is suitable for industrial wastewater control analysis of industrial and mining enterprises. Besides, coulometry is only decided by the total amount of COD but unrelated to the species of COD. So the amount of the organic compounds can be also determined by coulometry, equivalent to the quantity of COD.

## Measurement of carbon content in steel (Coulomb carbon analyzer)

CO2 produced by the combustion of the steel sample at 1200 degrees Celsius is introduced into a Ba(ClO4)2 solution with a predetermined pH value, and the following reaction occurs:

$\mathrm{Ba(ClO_4)_3 + H_2O + CO_2\rightarrow BaCO_3 + 2HClO_4}$

When using Pt as working electrode for electrolysis:

$\mathrm{2H_2O + 2e^-\rightarrow 2OH^- + H_2}$

OH- produced by electrolysis reacts with HClO4 until the solution returns to its original pH value. According to the amount of electricity consumed and the measurement relationship of the chemical reaction, the carbon content in the steel sample can be calculated. The same method can also be used to test the content of other elements in steel, for example, Takayoshi Yoshimori et al measured 0.0002–0.01 % of boron in several boron steels within 30–50 min by using constant-current coulometry to get accurate results.

## Measurement of atmospheric pollutant hydrogen sulfide content

I2 is continuously produced by the oxidation of the anode, and I2 is reduced to I- at the cathode. If there is no other reaction in the Coulomb cell, the oxidation rate of the anode is equal to the reduction rate of the cathode after the I2 concentration reaches equilibrium. The cathode current is equal to the anode current, and reference electrode has no current output at that time. If the gas entering the electrolytic cell contains H2S, it will react with I2:

$\mathrm{H_2S + I_2\rightarrow 2HI + S}$

The more H2S in the sample, the more I2 is consumed, resulting in a corresponding decrease in the cathode current and a corresponding increase in the current through the reference electrode.

# References

 1 1 Burns, J. C., Stevens, D. A., & Dahn, J. R. (2015). "In-situ detection of lithium plating using high precision coulometry". Journal of the Electrochemical Society, 162(6), A959. https://doi.org/10.1149/2.0621506jes 2 1 Smith, A. J., Burns, J. C., Zhao, X., Xiong, D., & Dahn, J. R. (2011). "A high precision coulometry study of the SEI growth in Li/graphite cells". Journal of The Electrochemical Society, 158(5), A447. https://doi.org/10.1149/1.3557892 3 1 2 3 4 5 6 DeFord, Donald D. (1960). "Electroanalysis and Coulometric Analysis". Analytical Chemistry. 32 (5): 31–37. https://doi.org/10.1021/ac60161a604 4 1 2 3 Stock, J. T. (1992). "A century and a half of silver-based coulometry". Journal of chemical education, 69(12), 949. https://doi.org/10.1021/ed069p949 5 1 2 Mo, H., Chen, Y., Tang, Y., Li, T., Zhuang, S., Wang, L., ... & Wan, P. (2019). "Direct determination of chemical oxygen demand by anodic oxidative degradation of organics at a composite 3-D electrode". Journal of Solid State Electrochemistry, 23(5), 1571-1579. https://doi.org/10.1007/s10008-019-04250-4 6 1 Zhou, M., Myung, N., Chen, X., & Rajeshwar, K. (1995). "Electrochemical deposition and stripping of copper, nickel and copper nickel alloy thin films at a polycrystalline gold surface: a combined voltammetry-coulometry-electrochemical quartz crystal microgravimetry study". Journal of Electroanalytical Chemistry, 398(1-2), 5-12. https://doi.org/10.1016/0022-0728(95)04001-0 7 1 2 3 Bruttel, P., & Schlink, R. (2003). "Water determination by Karl Fischer titration". Metrohm monograph, 8(5003), 2003-09. 8 1 Gallina, A., Stocco, N., & Mutinelli, F. (2010). “Karl Fischer Titration to determine moisture in honey: A new simplified approach”. Food Control, 21(6), 942-944. https://doi.org/10.1016/j.foodcont.2009.11.008 9 1 Lee, K. H., Ishikawa, T., McNiven, S. J., Nomura, Y., Hiratsuka, A., Sasaki, S., ... & Karube, I. (1999). “Evaluation of chemical oxygen demand (COD) based on coulometric determination of electrochemical oxygen demand (EOD) using a surface oxidized copper electrode”. Analytica chimica acta, 398(2-3), 161-171. https://doi.org/10.1016/S0003-2670(99)00417-1 10 1 Ohtaki, H., & Biedermann, G. (1971). Test for validity of constant ionic medium principle. Variation of the activity coefficient of hydrogen ion in various compositions of medium cations with 3 M perchlorate ions. Bulletin of the Chemical Society of Japan, 44(6), 1515-1519. https://doi.org/10.1246/bcsj.44.1515 11 1 Yoshimori, T., Miwa, T., & Takeuchi, T. (1964). “Rapid determination of boron in iron and steel by pyrohydrolysis and constant-current coulometry”. Talanta, 11(7), 993-1001. https://doi.org/10.1016/0039-9140(64)80142-9

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