Titration

Titration (also known as titrimetry^[1] and volumetric analysis) is a common laboratory method of quantitative chemical analysis to determine the concentration of an identified analyte (a substance to be analyzed). A reagent, termed the titrant or titrator,^[2] is prepared as a standard solution of known concentration and volume. The titrant reacts with a solution of analyte (which may also be termed the titrand^[3]) to determine the analyte's concentration. The volume of titrant that reacted with the analyte is termed the titration volume.

History and etymology

The word "titration" descends from the French word titrer (1543), meaning the proportion of gold or silver in coins or in works of gold or silver; i.e., a measure of fineness or purity. Tiltre became titre,^[4] which thus came to mean the "fineness of alloyed gold",^[5] and then the "concentration of a substance in a given sample".^[6] In 1828, the French chemist Joseph Louis Gay-Lussac first used titre as a verb (titrer), meaning "to determine the concentration of a substance in a given sample".^[7]

Volumetric analysis originated in late 18th-century France.

A typical titration begins with a

Many non-acid–base titrations require a constant pH during the reaction. Therefore, a buffer solution may be added to the titration chamber to maintain the pH.^[20]

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 eliminates the effect of the unwanted ion.^[21]

Some reduction-oxidation (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.^[22]

Titration curves

In an acid–base titration, the titration curve represents 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 very irregular. Because of this, no definite indicator may be appropriate and a pH meter is often used to monitor the reaction.^[24]

The type of function that can be used to describe the curve is termed 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

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, representing 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.^[25] 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

The approximate pH during titration can be approximated by three kinds of calculations. Before beginning of titration, the concentration of ${\displaystyle {\ce {[H+]}}}$ is calculated in an aqueous solution of weak acid before adding any base. When the number of moles of bases added equals the number of moles of initial acid or so called equivalence point, one of hydrolysis and the pH is calculated in the same way that the conjugate bases of the acid titrated was calculated. Between starting and end points, ${\displaystyle {\ce {[H+]}}}$ is obtained from the Henderson-Hasselbalch equation and titration mixture is considered as buffer. In Henderson-Hasselbalch equation the [acid] and [base] are said to be the molarities that would have been present even with dissociation or hydrolysis. In a buffer, ${\displaystyle {\ce {[H+]}}}$ can be calculated exactly but the dissociation of HA, the hydrolysis of ${\displaystyle {\ce {A-}}}$ and self-ionization of water must be taken into account.^[28] Four independent equations must be used:^[29]

${\displaystyle [{\ce {H+}}][{\ce {OH-}}]=10^{-14}}$

${\displaystyle [{\ce {H+}}]=K_{a}{\ce {{\frac {[HA]}{[A^{-}]}}}}}$

${\displaystyle [{\ce {HA}}]+[{\ce {A-}}]={\frac {(n_{{\ce {A}}}+n_{{\ce {B}}})}{V}}}$

${\displaystyle [{\ce {H+}}]+{\frac {n_{{\ce {B}}}}{V}}=[{\ce {A-}}]+[{\ce {OH-}}]}$

In the equations, ${\displaystyle n_{{\ce {A}}}}$ and ${\displaystyle n_{{\ce {B}}}}$ are the moles of acid (HA) and salt (XA where X is the cation), respectively, used in the buffer, and the volume of solution is V. The law of mass action is applied to the ionization of water and the dissociation of acid to derived the first and second equations. The mass balance is used in the third equation, where the sum of ${\displaystyle V[{\ce {HA}}]}$ and ${\displaystyle V[{\ce {A-}}]}$ must equal to the number of moles of dissolved acid and base, respectively. Charge balance is used in the fourth equation, where the left hand side represents the total charge of the cations and the right hand side represents the total charge of the anions: ${\displaystyle {\frac {n_{{\ce {B}}}}{V}}}$ is the molarity of the cation (e.g. sodium, if sodium salt of the acid or sodium hydroxide is used in making the buffer).^[30]

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.^[31] 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.^[32]

Some redox titrations do not require an indicator, due to the intense color of the constituents. For instance, in

Gas phase titration

Gas phase titrations are titrations done in the

O₃ + NO → O₂ + NO₂.[34]^[35]

After the reaction is complete, the remaining titrant and product are quantified (e.g., by

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.^[36]

Complexometric titration

Complexometric titrations rely on the formation of a

Zeta potential titrations are titrations in which the completion is monitored by the

An assay is a type of biological titration used to determine the concentration of a

Different methods to determine the endpoint include:^[41]

• Indicator: A substance that changes color in response to a chemical change. An acid–base indicator (e.g., phenolphthalein) changes color depending on the pH. Redox indicators are also used. A drop of indicator solution is added to the titration at the beginning; the endpoint has been reached when the color changes.
• Potentiometer: An instrument that measures the electrode potential of the solution. These are used for redox titrations; the potential of the working electrode will suddenly change as the endpoint is reached.

• pH meter: A potentiometer with an electrode whose potential depends on the amount of H⁺ ion present in the solution. (This is an example of an ion-selective electrode.) The pH of the solution is measured throughout the titration, more accurately than with an indicator; at the endpoint there will be a sudden change in the measured pH.
• mobility and ionic strength
  ), predicting the change in conductivity is more difficult than measuring it.
• Color change: In some reactions, the solution changes color without any added indicator. This is often seen in redox titrations when the different oxidation states of the product and reactant produce different colors.
• Precipitation: If a reaction produces a solid, a precipitate will form during the titration. A classic example is the reaction between Ag⁺ and Cl⁻ to form the insoluble salt AgCl. Cloudy precipitates usually make it difficult to determine the endpoint precisely. To compensate, precipitation titrations often have to be done as "back" titrations (see below).
• substrates bind to enzymes
  .
• Thermometric titrimetry
  : Differentiated from calorimetric titrimetry because 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.
• Beer's Law
  .
• Amperometry: Measures the current produced by the titration reaction as a result of the oxidation or reduction of the analyte. The endpoint is 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⁺.

Endpoint and equivalence point

Though the terms equivalence point and endpoint are often 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

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.[43]^{[self-published source?]}

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.^[44]

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,^[45] such as the equiligraph,^[46] have long been used to account for the interaction of coupled equilibria.

Particular uses

Acid–base titrations

• For biodiesel fuel: waste vegetable oil (WVO) must be neutralized before a batch may be processed. A portion of WVO is titrated with a base to determine acidity, so the rest of the batch may be neutralized properly. This removes free fatty acids from the WVO that would normally react to make soap instead of biodiesel fuel.^[47]
• Kjeldahl method: a measure of nitrogen content in a sample. Organic nitrogen is digested into ammonia with sulfuric acid and potassium sulfate. Finally, ammonia is back titrated with boric acid and then sodium carbonate.^[48]
• Acid value: the mass in milligrams of potassium hydroxide (KOH) required to titrate fully an acid in one gram of sample. An example is the determination of free fatty acid content.
• Saponification value: the mass in milligrams of KOH required to saponify a fatty acid in one gram of sample. Saponification is used to determine average chain length of fatty acids in fat.
• Ester value (or ester index): a calculated index. Ester value = Saponification value – Acid value.
• Amine value: the mass in milligrams of KOH equal to the amine content in one gram of sample.
• hydroxyl groups in one gram of sample. The analyte is acetylated using acetic anhydride
  then titrated with KOH.

• Winkler test for dissolved oxygen: Used to determine oxygen concentration in water. Oxygen in water samples is reduced using manganese(II) sulfate, which reacts with potassium iodide to produce iodine. The iodine is released in proportion to the oxygen in the sample, thus the oxygen concentration is determined with a redox titration of iodine with thiosulfate using a starch indicator.^[49]
• Vitamin C: Also known as ascorbic acid, vitamin C is a powerful reducing agent. Its concentration can easily be identified when titrated with the blue dye Dichlorophenolindophenol (DCPIP) which becomes colorless when reduced by the vitamin.^[50]
• Benedict's reagent: Excess glucose in urine may indicate diabetes in a patient. Benedict's method is the conventional method to quantify glucose in urine using a prepared reagent. During this type of titration, glucose reduces cupric ions to cuprous ions which react with potassium thiocyanate to produce a white precipitate, indicating the endpoint.^[51]
• Bromine number: A measure of unsaturation in an analyte, expressed in milligrams of bromine absorbed by 100 grams of sample.
• Iodine number
  : A measure of unsaturation in an analyte, expressed in grams of iodine absorbed by 100 grams of sample.

Miscellaneous

• Karl Fischer titration: A potentiometric method to analyze trace amounts of water in a substance. A sample is dissolved in methanol, and titrated with Karl Fischer reagent (consists of iodine, sulfur dioxide, a base and a solvent, such as alcohol). The reagent contains iodine, which reacts proportionally with water. Thus, the water content can be determined by monitoring the electric potential of excess iodine.^[52]

See also

• Primary standards are compounds with consistent and reliable properties used to prepare standard solutions for titrations.

References

External links

Wikimedia Commons has media related to Titration.

Look up titration in Wiktionary, the free dictionary.

• Wikihow: Perform a Titration
• An interactive guide to titration
• Science Aid: A simple explanation of titrations including calculation examples
• Titration freeware - simulation of any pH vs. volume curve, distribution diagrams and real data analysis
• Graphical method to solve acid-base problems, including titrations
• Graphic and numerical solver for general acid-base problems - Software Program for phone and tablets