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The equivalence point, or stoichiometric point, of a chemical reaction is the point at which chemically equivalent quantities of reactants have been mixed. For an acid-base reaction the equivalence point is where the moles of acid and the moles of base would neutralize each other according to the chemical reaction.
Martell and Motekaitis (1992) use the most linear regions and exploit the difference in equivalence volumes between acid-side and base-side plots during an acid-base titration to estimate the adventitious CO 2 content in the base solution. This is illustrated in the sample Gran plots of Figure 1.
An indicator capable of producing an unambiguous color change is usually used to detect the end-point of the titration. Complexometric titrations are those reactions where a simple ion is transformed into a complex ion and the equivalence point is determined by using metal indicators or electrometrically. [1]
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 ...
The pH at the end-point or equivalence point in a titration may be calculated as follows. At the end-point the acid is completely neutralized so the analytical hydrogen ion concentration, T H, is zero and the concentration of the conjugate base, A −, is equal to the analytical or formal concentration T A of the acid: [A −] = T A.
Given two topological spaces X and Y, a homotopy equivalence between X and Y is a pair of continuous maps f : X → Y and g : Y → X, such that g ∘ f is homotopic to the identity map id X and f ∘ g is homotopic to id Y. If such a pair exists, then X and Y are said to be homotopy equivalent, or of the same homotopy type.
Expansion of the circle reaches an endpoint and stops when free antigen is depleted and when antigen and antibody reach equivalence. [ 1 ] [ 2 ] [ 5 ] However, the clarity and density of the circle's outer edge may continue to increase after the circle stops expanding.
A large change in potential will occur then once a small addition of the titrating solution is added, as the final amounts of reducing agent are removed and the potential corresponds solely to the oxidizing agent. This large increase in potential difference signifies the endpoint of the reaction. [1]