Titration

Not to be confused with the mathematical notion of tetration.
This article is about volumetric titration. For other uses, see Titration (disambiguation).
A Winkler titration to determine the concentration of dissolved oxygen in a water sample. The dissolved oxygen has been converted to an equivalent amount of iodine, which is being titrated with thiosulfate using a starch indicator. The blue color in the flask will disappear when all the iodine has been converted to iodide.

Titration, also known as titrimetry,[1] is a common laboratory method of quantitative chemical analysis that is used to determine the unknown concentration of an identified analyte. Since volume measurements play a key role in titration, it is also known as volumetric analysis. A reagent, called the titrant or titrator[2] is prepared as a standard solution. A known concentration and volume of titrant reacts with a solution of analyte or titrand[3] to determine concentration. The volume of titrant reacted is called titration volume.

History and etymology

The word "titration" comes from the Latin word titulus, meaning inscription or title. The French word titre, also from this origin, means rank.

Volumetric analysis originated in late 18th-century France. François-Antoine-Henri Descroizilles (fr) developed the first burette (which was similar to a graduated cylinder) in 1791.[4] Joseph Louis Gay-Lussac developed an improved version of the burette that included a side arm, and coined the terms "pipette" and "burette" in an 1824 paper on the standardization of indigo solutions. A major breakthrough in the methodology and popularization of volumetric analysis was due to Karl Friedrich Mohr, who redesigned the burette by placing a clamp and a tip at the bottom, and wrote the first textbook on the topic, Lehrbuch der chemisch-analytischen Titrirmethode (Textbook of analytical-chemical titration methods), published in 1855.[5]

Procedure

Analysis of soil samples by titration

A typical titration begins with a beaker or Erlenmeyer flask containing a very precise volume of the analyte and a small amount of indicator (such as phenolphthalein) placed underneath a calibrated burette or chemistry pipetting syringe containing the titrant. Small volumes of the titrant are then added to the analyte and indicator until the indicator changes color in reaction to the titrant saturation threshold, reflecting arrival at the endpoint of the titration. Depending on the endpoint desired, single drops or less than a single drop of the titrant can make the difference between a permanent and temporary change in the indicator. When the endpoint of the reaction is reached, the volume of reactant consumed is measured and used to calculate the concentration of analyte by

where Ca is the concentration of the analyte, typically in molarity; Ct is the concentration of the titrant, typically in molarity; Vt is the volume of the titrant used, typically in liters; M is the mole ratio of the analyte and reactant from the balanced chemical equation; and Va is the volume of the analyte used, typically in liters.[6]

Preparation techniques

Typical titrations require titrant and analyte to be in a liquid (solution) form. Though solids are usually dissolved into an aqueous solution, other solvents such as glacial acetic acid or ethanol are used for special purposes (as in petrochemistry).[7] Concentrated analytes are often diluted to improve accuracy.

Many non-acid-base titrations require a constant pH throughout the reaction. Therefore a buffer solution may be added to the titration chamber to maintain the pH.[8]

In instances where two reactants in a sample may react with the titrant and only one is the desired analyte, a separate masking solution may be added to the reaction chamber which masks the unwanted ion.[9]

Some redox reactions may require heating the sample solution and titrating while the solution is still hot to increase the reaction rate. For instance, the oxidation of some oxalate solutions requires heating to 60 °C (140 °F) to maintain a reasonable rate of reaction.[10]

Titration curves

Main article: Titration curve
A typical titration curve of a diprotic acid titrated with a strong base. Shown here is oxalic acid titrated with sodium hydroxide. Both equivalence points are visible.

A titration curve is a curve in the plane whose x-coordinates are the volume of titrant added since the beginning of the titration, and whose y-coordinate is the concentration of the analyte at the corresponding stage of the titration (in an acid-base titration, the y-coordinate is usually the pH of the solution).[11]

In an acid-base titration, the titration curve reflects the strength of the corresponding acid and base. For a strong acid and a strong base, the curve will be relatively smooth and very steep near the equivalence point. Because of this, a small change in titrant volume near the equivalence point results in a large pH change and many indicators would be appropriate (for instance litmus, phenolphthalein or bromothymol blue).

If one reagent is a weak acid or base and the other is a strong acid or base, the titration curve is irregular and the pH shifts less with small additions of titrant near the equivalence point. For example, the titration curve for the titration between oxalic acid (a weak acid) and sodium hydroxide (a strong base) is pictured. The equivalence point occurs between pH 8-10, indicating the solution is basic at the equivalence point and an indicator such as phenolphthalein would be appropriate. Titration curves corresponding to weak bases and strong acids are similarly behaved, with the solution being acidic at the equivalence point and indicators such as methyl orange and bromothymol blue being most appropriate.

Titrations between a weak acid and a weak base have titration curves which are highly irregular. Because of this, no definite indicator may be appropriate and a pH meter is often used to monitor the reaction.[12]

The type of function that can be used to describe the curve is called a sigmoid function.

Types of titrations

There are many types of titrations with different procedures and goals. The most common types of qualitative titration are acid-base titrations and redox titrations.

Acid–base titration

Main article: Acid–base titration
Methyl orange
Indicator Color on acidic side Range of color change Color on basic side
Methyl violet Yellow 0.0–1.6 Violet
Bromophenol blue Yellow 3.0–4.6 Blue
Methyl orange Red 3.1–4.4 Yellow
Methyl red Red 4.4–6.3 Yellow
Litmus Red 5.0–8.0 Blue
Bromothymol blue Yellow 6.0–7.6 Blue
Phenolphthalein Colorless 8.3–10.0 Pink
Alizarin yellow Yellow 10.1–12.0 Red

Acid-base titrations depend on the neutralization between an acid and a base when mixed in solution. In addition to the sample, an appropriate pH indicator is added to the titration chamber, reflecting the pH range of the equivalence point. The acid-base indicator indicates the endpoint of the titration by changing color. The endpoint and the equivalence point are not exactly the same because the equivalence point is determined by the stoichiometry of the reaction while the endpoint is just the color change from the indicator. Thus, a careful selection of the indicator will reduce the indicator error. For example, if the equivalence point is at a pH of 8.4, then the Phenolphthalein indicator would be used instead of Alizarin Yellow because phenolphthalein would reduce the indicator error. Common indicators, their colors, and the pH range in which they change color are given in the table above.[13] When more precise results are required, or when the reagents are a weak acid and a weak base, a pH meter or a conductance meter are used.

For very strong bases, such as organolithium reagent, metal amides, and hydrides, water is generally not a suitable solvent and indicators whose pKa are in the range of aqueous pH changes are of little use. Instead, the titrant and indicator used are much weaker acids, and anhydrous solvents such as THF are used.[14][15]

Redox titration

Main article: Redox titration

Redox titrations are based on a reduction-oxidation reaction between an oxidizing agent and a reducing agent. A potentiometer or a redox indicator is usually used to determine the endpoint of the titration, as when one of the constituents is the oxidizing agent potassium dichromate. The color change of the solution from orange to green is not definite, therefore an indicator such as sodium diphenylamine is used.[16] Analysis of wines for sulfur dioxide requires iodine as an oxidizing agent. In this case, starch is used as an indicator; a blue starch-iodine complex is formed in the presence of excess iodine, signalling the endpoint.[17]

Some redox titrations do not require an indicator, due to the intense color of the constituents. For instance, in permanganometry a slight persisting pink color signals the endpoint of the titration because of the color of the excess oxidizing agent potassium permanganate.[18] In iodometry, at sufficiently large concentrations, the disappearance of the deep red-brown triiodide ion can itself be used as an endpoint, though at lower concentrations sensitivity is improved by adding starch indicator, which forms an intensely blue complex with triiodide.

Color of iodometric titration mixture before (left) and after (right) the end point

Gas phase titration

Gas phase titrations are titrations done in the gas phase, specifically as methods for determining reactive species by reaction with an excess of some other gas, acting as the titrant. In one common gas phase titration, gaseous ozone is titrated with nitrogen oxide according to the reaction

O3 + NO → O2 + NO2.[19][20]

After the reaction is complete, the remaining titrant and product are quantified (e.g., by FT-IR); this is used to determine the amount of analyte in the original sample.

Gas phase titration has several advantages over simple spectrophotometry. First, the measurement does not depend on path length, because the same path length is used for the measurement of both the excess titrant and the product. Second, the measurement does not depend on a linear change in absorbance as a function of analyte concentration as defined by the Beer-Lambert law. Third, it is useful for samples containing species which interfere at wavelengths typically used for the analyte.[21]

Complexometric titration

Complexometric titrations rely on the formation of a complex between the analyte and the titrant. In general, they require specialized complexometric indicators that form weak complexes with the analyte. The most common example is the use of starch indicator to increase the sensitivity of iodometric titration, the dark blue complex of starch with iodine and iodide being more visible than iodine alone. Other complexometric indicators are Eriochrome Black T for the titration of calcium and magnesium ions, and the chelating agent EDTA used to titrate metal ions in solution.[22]

Zeta potential titration

Zeta potential titrations are titrations in which the completion is monitored by the zeta potential, rather than by an indicator, in order to characterize heterogeneous systems, such as colloids.[23] One of the uses is to determine the iso-electric point when surface charge becomes zero, achieved by changing the pH or adding surfactant. Another use is to determine the optimum dose for flocculation or stabilization.[24]

Assay

Main article: Assay
Main article: Virus quantification

An assay is a form of biological titration used to determine the concentration of a virus or bacterium. Serial dilutions are performed on a sample in a fixed ratio (such as 1:1, 1:2, 1:4, 1:8, etc.) until the last dilution does not give a positive test for the presence of the virus. The positive or negative value may be determined by visually inspecting the infected cells under a microscope or by an immunoenzymetric method such as enzyme-linked immunosorbent assay (ELISA). This value is known as the titer.[25]

Measuring the endpoint of a titration

Main article: Equivalence point

Different methods to determine the endpoint include:[26]

An elementary pH meter that can be used to monitor titration reactions

Endpoint and equivalence point

Though equivalence point and endpoint are used interchangeably, they are different terms. Equivalence point is the theoretical completion of the reaction: the volume of added titrant at which the number of moles of titrant is equal to the number of moles of analyte, or some multiple thereof (as in polyprotic acids). Endpoint is what is actually measured, a physical change in the solution as determined by an indicator or an instrument mentioned above.[27]

There is a slight difference between the endpoint and the equivalence point of the titration. This error is referred to as an indicator error, and it is indeterminate.[28]

Back titration

Back titration is a titration done in reverse; instead of titrating the original sample, a known excess of standard reagent is added to the solution, and the excess is titrated. A back titration is useful if the endpoint of the reverse titration is easier to identify than the endpoint of the normal titration, as with precipitation reactions. Back titrations are also useful if the reaction between the analyte and the titrant is very slow, or when the analyte is in a non-soluble solid.[29]

Graphical methods

The titration process creates solutions with compositions ranging from pure acid to pure base. Identifying the pH associated with any stage in the titration process is relatively simple for monoprotic acids and bases. The presence of more than one acid or base group complicates these computations. Graphical methods,[30] such as the equiligraph,[31] have long been used to account for the interaction of coupled equilibria. These graphical solution methods are simple to implement, however they are infrequently used.

Particular uses

A titration is demonstrated to secondary school students.

Acid-base titrations

Redox titrations

Miscellaneous

See also

References

  1. ↑ Whitney, W.D.; B.E. Smith (1911). "titrimetry". The Century Dictionary and Cyclopedia. The Century co. p. 6504.
  2. ↑ Compendium for Basal Practice in Biochemistry. Aarhus University. 2008.
  3. ↑ "titrand". Science & Technology Dictionary. McGraw-Hill. Retrieved 30 September 2011.
  4. ↑ Szabadváry, F. (1993). History of Analytical Chemistry. Taylor & Francis. pp. 208–209. ISBN 2-88124-569-2.
  5. ↑ Rosenfeld, L. (1999). Four Centuries of Clinical Chemistry. CRC Press. pp. 72–75. ISBN 90-5699-645-2.
  6. ↑ Harris, D.C. (2007). Quantitative Chemical Analysis (7 ed.). W. H. Freeman and Company. p. 12. ISBN 9780716770411.
  7. ↑ Matar, S.; L.F. Hatch (2001). Chemistry of Petrochemical Processes (2 ed.). Gulf Professional Publishing. ISBN 0-88415-315-0.
  8. ↑ Verma, Dr. N.K.; S.K. Khanna; Dr B. Kapila. Comprehensive Chemistry XI. New Dehli: Laxmi Publications. pp. 642–645. ISBN 81-7008-596-9.
  9. ↑ Patnaik, P. (2004). Dean's Analytical Chemistry Handbook (2 ed.). McGraw-Hill Prof Med/Tech. pp. 2.11–2.16. ISBN 0-07-141060-0.
  10. ↑ Walther, J.V. (2005). Essentials of Geochemistry. Jones & Bartlett Learning. pp. 515–520. ISBN 0-7637-2642-7.
  11. ↑ Reger, D.L.; S.R. Goode; D.W. Ball (2009). Chemistry: Principles and Practice (3 ed.). Cengage Learning. pp. 684–693. ISBN 0-534-42012-5.
  12. ↑ Bewick, S.; J. Edge; T. Forsythe; R. Parsons (2009). CK12 Chemistry. CK-12 Foundation. pp. 794–797.
  13. ↑ "pH measurements with indicators". Retrieved 29 September 2011.
  14. ↑ "Titrating Soluble RM, R2NM and ROM Reagents" (PDF). Retrieved 2014-06-04.
  15. ↑ "Methods for Standardizing Alkyllithium Reagents (literature through 2006)" (PDF). Retrieved 2014-06-04.
  16. ↑ Vogel, A.I.; J. Mendham (2000). Vogel's textbook of quantitative chemical analysis (6 ed.). Prentice Hall. p. 423. ISBN 0-582-22628-7.
  17. ↑ Amerine, M.A.; M.A. Joslyn (1970). Table wines: the technology of their production. 2 (2 ed.). University of California Press. pp. 751–753. ISBN 0-520-01657-2.
  18. ↑ German Chemical Society. Division of Analytical Chemistry (1959). Fresenius' Journal of Analytical Chemistry (in German). 166-167. University of Michigan: J.F. Bergmann. p. 1.
  19. ↑ Hänsch, T.W. (2007). Metrology and Fundamental Constants. IOS Press. p. 568. ISBN 1-58603-784-6.
  20. ↑ "Gas phase titration". Bureau International des Poids et Mesures. Retrieved 29 September 2001.
  21. ↑ DeMore, W.B.; M. Patapoff (September 1976). "Comparison of Ozone Determinations by Ultraviolet Photometry and Gas-Phase Titration". Environmental Science & Technology. 10 (9): 897–899. Bibcode:1976EnST...10..897D. doi:10.1021/es60120a012.
  22. ↑ Khopkar, S.M. (1998). Basic Concepts of Analytical Chemistry (2 ed.). New Age International. pp. 63–76. ISBN 81-224-1159-2.
  23. ↑ Somasundaran, P. (2006). "Calculation of Zeta-Potentials from Electrokinetic Data". Encyclopedia of Surface and Colloid Science (2 ed.). CRC Press. 2: 1097. ISBN 0-8493-9607-7.
  24. ↑ Dukhin, A.S.; P.J. Goetz (2002). Ultrasound for Characterizing Colloids: Particle sizing, Zeta potential, Rheology. Studies in Interface Science. 15. Elsevier. pp. 256–263. ISBN 0-444-51164-4.
  25. ↑ Decker, J.M. (2000). Introduction to immunology. Eleventh Hour (3 ed.). Wiley-Blackwell. pp. 18–20. ISBN 0-632-04415-2.
  26. ↑ "Titration". Science & Technology Encyclopedia. McGraw-Hill. Retrieved 30 September 2011.
  27. ↑ Harris, D.C. (2003). Quantitative Chemical Analysis (6 ed.). Macmillan. p. 129. ISBN 0-7167-4464-3.
  28. ↑ Hannan, H.J. (2007). Technician's Formulation Handbook for Industrial and Household Cleaning Products. Lulu.com. p. 103. ISBN 0-615-15601-0.
  29. ↑ Kenkel, J. (2003). Analytical Chemistry for Technicians. 1 (3 ed.). CRC Press. pp. 108–109.
  30. ↑ "The Equligraph: Revisiting an old tool". Retrieved 4 October 2015.
  31. ↑ Freiser, H. (1963). Ionic Equilibria in Analytical Chemistry. Kreiger. ISBN 0-88275-955-8.
  32. ↑ Purcella, G. (2007). Do It Yourself Guide to Biodiesel: Your Alternative Fuel Solution for Saving Money, Reducing Oil Dependency, Helping the Planet. Ulysses Press. pp. 81–96. ISBN 1-56975-624-4.
  33. ↑ Remington: the science and practice of pharmacy. 1 (21 ed.). Lippincott Williams & Wilkins. 2005. p. 501. ISBN 0-7817-4673-6.
  34. ↑ Spellman, F.R. (2009). Handbook of Water and Wastewater Treatment Plant Operations (2 ed.). CRC Press. p. 545. ISBN 1-4200-7530-6.
  35. ↑ Biology. 3. London: Taylor & Francis. 1967. p. 52.
  36. ↑ Nigam (2007). Lab Manual Of Biochemistry. Tata McGraw-Hill Education. p. 149. ISBN 0-07-061767-8.
  37. ↑ Jackson, M.L.; P. Barak (2005). Soil Chemical Analysis: Advanced Course. UW-Madison Libraries Parallel Press. pp. 305–309. ISBN 1-893311-47-3.
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