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. 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. 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. The approximate pH during titration can be approximated by three kinds of calculations. Before beginning of titration, the concentration of [H+] is calculated in 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, [H+] is obtained