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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.
A typical titration curve of a diprotic acid, oxalic acid, titrated with a strong base, sodium hydroxide.Both equivalence points are visible. Titrations are often recorded on graphs called titration curves, which generally contain the volume of the titrant as the independent variable and the pH of the solution as the dependent variable (because it changes depending on the composition of the ...
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 reactions may differ in their stoichiometry. For example, the methylation of benzene (C 6 H 6), through a Friedel–Crafts reaction using AlCl 3 as a catalyst, may produce singly methylated (C 6 H 5 CH 3), doubly methylated (C 6 H 4 (CH 3) 2), or still more highly methylated (C 6 H 6−n (CH 3) n) products, as shown in the following example ...
Figure 2 gives an example; in this example, the two x-intercepts differ by about 0.2 mL but this is a small discrepancy, given the large equivalence volume (0.5% error). Similar equations can be written for the titration of a weak base by strong acid (Gran, 1952; Harris, 1998).
A monoprotic acid or base only has one equivalence point on a titration curve. [13] [9] Diprotic acid titration curve. Highlighted pink regions depict equivalence points. A diprotic acid donates two protons and a diprotic base accepts two protons. The titration curve for a diprotic solution has two equivalence points. [13] [9]
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.
Equivalence relations are a ready source of examples or counterexamples. For example, an equivalence relation with exactly two infinite equivalence classes is an easy example of a theory which is ω-categorical, but not categorical for any larger cardinal number.