Titration

Titration setup: the titrant drops from the burette into the analyte solution in the flask. An indicator present then changes color permanently at the endpoint.

Titration is a common laboratory method of quantitative chemical analysis that is used to determine the unknown concentration of a known reactant. Because volume measurements play a key role in titration, it is also known as volumetric analysis. A reagent, called the titrant or titrator,^[1] of a known concentration (a standard solution) and volume is used to react with a solution of the analyte or titrand,^[2] whose concentration is not known. Using a calibrated burette or chemistry pipetting syringe to add the titrant, it is possible to determine the exact amount that has been consumed when the endpoint is reached. The endpoint is the point at which the titration is complete, as determined by an indicator (see below). This is ideally the same volume as the equivalence point—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). In the classic strong acid-strong base titration, the endpoint of a titration is the point at which the pH of the reactant is just about equal to 7, and often when the solution takes on a persisting solid color as in the pink of phenolphthalein indicator. There are however many different types of titrations (see below).

Many methods can be used to indicate the endpoint of a reaction; titrations often use visual indicators (the reactant mixture changes color). In simple acid-base titrations a pH indicator may be used, such as phenolphthalein, which becomes pink when a certain pH (about 8.2) is reached or exceeded. Another example is methyl orange, which is red in acids and yellow in alkali solutions.

Not every titration requires an indicator. In some cases, either the reactants or the products are strongly colored and can serve as the "indicator". For example, a redox titration using potassium permanganate (pink/purple) as the titrant does not require an indicator. When the titrant is reduced, it turns colorless. After the equivalence point, there is excess titrant present. The equivalence point is identified from the first faint persisting pink color (due to an excess of permanganate) in the solution being titrated.

Due to the logarithmic nature of the pH curve, the transitions are, in general, extremely sharp; and, thus, a single drop of titrant just before the endpoint can change the pH significantly—leading to an immediate colour change in the indicator. There is a slight difference between the change in indicator color and the actual equivalence point of the titration. This error is referred to as an indicator error, and it is indeterminate.

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. Titration, by definition, is the determination of rank or concentration of a solution with respect to water with a pH of 7 (which is the pH of pure H₂O under standard conditions).

The origins of volumetric analysis are in late-18th-century French chemistry. Francois Antoine Henri Descroizilles developed the first burette (which looked more like a graduated cylinder) in 1791. 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.^[3]

Preparing a sample for titration

In a titration, both titrant and analyte are required to be in a liquid (solution) form. If the sample is not a liquid or solution, the samples must be dissolved. If the analyte is very concentrated in the sample, it might be useful to dilute the sample.

Although the vast majority of titrations are carried out in aqueous solution, other solvents such as glacial acetic acid or ethanol (in petrochemistry) are used for special purposes.

A measured amount of the sample can be given in the flask and then be dissolved or diluted. The mathematical result of the titration can be calculated directly with the measured amount. Sometimes the sample is dissolved or diluted beforehand, and a measured amount of the solution is used for titration. In this case the dissolving or diluting must be done accurately with a known coefficient because the mathematical result of the titration must be multiplied with this factor.

Many titrations require buffering to maintain a certain pH for the reaction. Therefore, buffer solutions are added to the reactant solution in the flask to maintain the pH of the solution.

Some titrations require "masking" of a certain ion. This can be necessary when two reactants in the sample would react with the titrant and only one of them must be analysed, or when the reaction would be disturbed or inhibited by this ion. In this case another solution is added to the sample, which "masks" the unwanted ion (for instance by a weak binding with it or even forming a solid insoluble substance with it).

Some redox reactions may require heating the solution with the sample and titration while the solution is still hot, in order to increase the reaction rate. For instance, the oxidation of certain oxalate solutions requires heating the solution to approximately 60 degrees in order to maintain a reasonable rate of reaction.

Procedure

A typical titration begins with a beaker or Erlenmeyer flask containing a precise volume of the reactant and a small amount of indicator, placed underneath a burette or buretting syringe containing the reagent. By controlling the amount of reagent added to the reactant, it is possible to detect the point at which the indicator changes color. As long as the indicator has been chosen correctly, this should also be the point where the reactant and reagent neutralize each other, and, by reading the scale on the burette, the volume of reagent can be measured.

As the concentration of the reagent is known, the number of moles of reagent can be calculated (since ). Then, from the chemical equation involving the two substances, the number of moles present in the reactant can be found. Finally, by dividing the number of moles of reactant by its volume, the concentration is calculated.

Titration curves

A typical titration curve of a diprotic acid, oxalic acid, titrated with a strong base, sodium hydroxide. Each of the two equivalence points are visible

A titration curve is a curve in the plane whose x-coordinate is 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 at the corresponding stage). Often it is the case that the titration curve of a titration reflects the nature of the titration quite well; for instance, it reflects the nature of all solutions involved in the titration.

In the case of acid-base titrations, titration curves reflect the strength of the corresponding acid and base. For instance, in a strong acid and strong base titration, the titration curve will be relatively smooth, although very steep for points near the equivalence point of the titration. Since in this case, small changes in the volume of the titrant result in large changes of the pH near the equivalence point, an extensive range of indicators would be appropriate (for instance litmus, phenolphthalein or bromothymol blue).

On the other hand, if one of the constituents of an acid-base titration is either a weak acid or a weak base, and the other is either a strong acid or a strong base, the titration curve is fairly irregular near the equivalence point (and the pH does not change as much due to the addition of small volumes of titrant). For instance, the titration curve for the titration between oxalic acid (a weak acid) and sodium hydroxide (a strong base) is depicted in the image above. Here, the equivalence point occurs at a pH of about 8-10, and thus the analyte is basic at the equivalence point (more precisely, the sodium salt produced by the reaction hydrolyses in water to produce hydroxide ions). An indicator such as phenolphthalein would be appropriate for this particular titration. The titration curve corresponding to a weak base and strong acid titration is similarly behaved. In this case, indicators such as methyl orange or bromothymol blue are regularly used.

On the other hand, titration curves corresponding to acid-base titrations in which the constituents are a weak acid and weak base, are quite irregular in nature. Due to the nature of such titrations, no definite indicator may be appropriate, and thus pH meters are often used.

Types of titrations

There are various sorts of titrations whose goals are different to the others. The most common types of titrations in qualitative work are acid-base titrations and redox titrations.

Acid-base titration

These titrations are based on the neutralization reaction that occurs between an acid and a base, when mixed in solution. The acid (resp. base) is added to a burette which was rinsed with the same acid prior to this addition to prevent contamination or diluting of the acid being measured. The base (resp. acid) is added to a volumetric flask which had been rinsed with distilled water prior to the addition to prevent contamination or dilution of the base/alkali being measured. The solution in the volumetric flask is often a standard solution; one whose concentration is exactly known. The solution in the burette, however, is the solution whose concentration is to be determined by titration. The indicator used for such an acid-base titration often depends on the nature of the constituents as described in the above section. Common indicators, their colours, and the pH range in which they change colour, are given in the table above. When more precise results are required, or when the titration constituents are a weak acid and a weak base, a pH meter or a conductance meter are used.

Redox titration

These titrations are based on a redox reaction between an oxidizing agent and a reducing agent. The oxidizing agent (resp. reducing agent) is added to the burette which was rinsed with the same oxidizing agent. The reducing agent (resp. oxidizing agent) is added to the conical flask, which had been rinsed with distilled water. Like in an acid-base titration, the standard solution is often the one in the conical flask, and the solution whose concentration is to be determined is the one in the burette. The procedure for carrying out redox titrations is similar to that required for carrying out acid-base titrations.

Most commonly, a potentiometer or a redox indicator are used to determine the end point of the titration. For example, when one of constituents of the titration is the oxidizing agent potassium dichromate, the colour change of the solution from orange to green is not definite and thus an indicator such as sodium diphenylamine is used. The analysis of wines for their sulfur dioxide content requires the use of iodine as an oxidizing agent. In this case, starch is used as an indicator; a blue starch-iodine complex is formed once an excess of iodine is present, thus signalling the endpoint of the titration.

On the other hand, some redox titrations do not require an indicator, due to the intense colour of some of the constituents. For instance, in a titration where the oxidizing agent potassium permanganate (permanganometry) is present, a slight faint persisting pink colour signals the endpoint of the titration, and no particular indicator is therefore required.

Complexometric titration

These titrations are based on the formation of a complex between the analyte and the titrant. The chelating agent EDTA is very commonly used to titrate metal ions in solution. These titrations generally require specialized indicators that form weaker complexes with the analyte. A common example is Eriochrome Black T for the titration of calcium and magnesium ions.

Zeta potential titration

These titrations characterize heterogeneous systems, such as colloids. Zeta potential plays role of indicator. One of the purposes is determination of iso-electric point when surface charge becomes 0. This can be achieved by changing pH or adding surfactant. Another purpose is determination of the optimum dose of the chemical for flocculation or stabilization.

Miscellaneous

A form of titration can also be used to determine the concentration of a virus or bacterium. The original sample is diluted (in some 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. This value, the titre, may be based on TCID50, EID50, ELD50, LD₅₀ or pfu. This procedure is more commonly known as an assay.

Measuring the endpoint of a titration

Different methods to determine the endpoint include:

• pH indicator: This is a substance that changes colour in response to a chemical change. An acid-base indicator (e.g., phenolphthalein) changes colour depending on the pH. Redox indicators are also frequently used. A drop of indicator solution is added to the titration at the start; when the colour changes the endpoint has been reached.
• A potentiometer can also be used. This is an instrument that measures the electrode potential of the solution. These are used for titrations based on a redox reaction; the potential of the working electrode will suddenly change as the endpoint is reached.
• pH meter: This is a potentiometer that uses an electrode whose potential depends on the amount of H⁺ ion present in the solution. (This is an example of an ion-selective electrode.) This allows the pH of the solution to be measured throughout the titration. At the endpoint, there will be a sudden change in the measured pH. It can be more accurate than the indicator method, and is very easily automated.
• Conductance: The conductivity of a solution depends on the ions that are present in it. During many titrations, the conductivity changes significantly. (For instance, during an acid-base titration, the H⁺ and OH^- ions react to form neutral H₂O. This changes the conductivity of the solution.) The total conductance of the solution depends also on the other ions present in the solution (such as counter ions). Not all ions contribute equally to the conductivity; this also depends on the mobility of each ion and on the total concentration of ions (ionic strength). Thus, predicting the change in conductivity is harder than measuring it.
• Colour change: In some reactions, the solution changes colour without any added indicator. This is often seen in redox titrations, for instance, when the different oxidation states of the product and reactant produce different colours.
• Precipitation: If the reaction forms a solid, then a precipitate will form during the titration. A classic example is the reaction between Ag⁺ and Cl^- to form the very insoluble salt AgCl. This usually makes it difficult to determine the endpoint precisely. As a result, precipitation titrations often have to be done as "back" titrations (see below).
• An isothermal titration calorimeter uses the heat produced or consumed by the reaction to determine the endpoint. This is important in biochemical titrations, such as the determination of how substrates bind to enzymes.
• Thermometric titrimetry is an extraordinarily versatile technique. This is differentiated from calorimetric titrimetry by the fact that the heat of the reaction (as indicated by temperature rise or fall) is not used to determine the amount of analyte in the sample solution. Instead, the endpoint is determined by the rate of temperature change.
• Spectroscopy can be used to measure the absorption of light by the solution during the titration, if the spectrum of the reactant, titrant or product is known. The relative amounts of the product and reactant can be used to determine the endpoint.
• Amperometry can be used as a detection technique (amperometric titration). The current due to the oxidation or reduction of either the reactants or products at a working electrode will depend on the concentration of that species in solution. The endpoint can then be detected as a change in the current. This method is most useful when the excess titrant can be reduced, as in the titration of halides with Ag⁺. (This is handy also in that it ignores precipitates.)

Back Titration

The term back titration is used when a titration is done "backwards"; instead of titrating the original analyte, one adds a known excess of a standard reagent to the solution, then titrates the excess. A back titration is useful if the endpoint of the reverse titration is easier to identify than the endpoint of the normal titration. They are also useful if the reaction between the analyte and the titrant is very slow.

Particular uses

• As applied to biodiesel, titration is the act of determining the acidity of a sample of WVO by the dropwise addition of a known base to the sample while testing with pH paper for the desired pH=8.5 reading. By knowing how much base neutralizes an amount of WVO, we discern how much base to add to the entire batch.
• Titrations are a very common procedure held in secondary education, to assess a chemistry student's practical aptitude.
• Titrations in the petrochemical or food industry to define oils, fats or biodiesel and similar substances. An example procedure for all three can be found here: [1].
  • Acid number: an acid-base titration with colour indicator is used to determine the free fatty acid content. See also: pH of fatty acids.
  • Iodine number: a redox titration with colour indication, which indicates the amount of unsaturated fatty acids.
  • Saponification value: an acid-base back titration with colour indicator or potentiometric to get a hint about the average chain length of fatty acids in a fat.
  • Karl Fischer titration: a method to analyse trace amounts of water in a substance.

References

External links

• [2] Wikihow: Do an Acid Base Titration Without Losing Your Mind
• Science aid: Titration An informative yet simple explanation of titration aimed at teens
• Titration - apparatus, technique and calculation
• Titration freeware - simulation of any pH vs. volume curve, distribution diagrams and real data analysis
• Basics of Titration: Free downloadable guide (pdf) from METTLER TOLEDO
• Acid Base Titration