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For example, sulfuric acid (H 2 SO 4) is a diprotic acid. Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: f eq (H 2 SO 4) = 0.5. If the concentration of a sulfuric acid solution is c(H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be called a "2 normal" solution.
The solution has 1 mole or 1 equiv Na +, 1 mole or 2 equiv Ca 2+, and 3 mole or 3 equiv Cl −. An earlier definition, used especially for chemical elements , holds that an equivalent is the amount of a substance that will react with 1 g (0.035 oz) of hydrogen , 8 g (0.28 oz) of oxygen , or 35.5 g (1.25 oz) of chlorine —or that will displace ...
The word "class" in the term "equivalence class" may generally be considered as a synonym of "set", although some equivalence classes are not sets but proper classes. For example, "being isomorphic " is an equivalence relation on groups , and the equivalence classes, called isomorphism classes , are not sets.
The row and column indices of nonwhite cells are the related elements, while the different colors, other than light gray, indicate the equivalence classes (each light gray cell is its own equivalence class). In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation ...
A canonical form thus provides a classification theorem and more, in that it not only classifies every class, but also gives a distinguished (canonical) representative for each object in the class. Formally, a canonicalization with respect to an equivalence relation R on a set S is a mapping c:S→S such that for all s, s 1, s 2 ∈ S:
The equivalence classes form the stalk at x of the presheaf . This equivalence relation is an abstraction of the germ equivalence described above. Interpreting germs through sheaves also gives a general explanation for the presence of algebraic structures on sets of germs.
In analytical chemistry, a solution of any substance which contains one equivalent per litre is known as a normal solution (abbreviated N), so the example sodium hydroxide solution would be 0.0893 N. [3] [13] The relative uncertainty (u r) in the measured concentration can be estimated by assuming a Gaussian distribution of the measurement ...
The initial definition of a cardinal number is an equivalence class of sets, where two sets are equivalent if there is a bijection between them. The difficulty is that almost every equivalence class of this relation is a proper class , and so the equivalence classes themselves cannot be directly manipulated in set theories, such as Zermelo ...