equivalence point

Examples of equivalence point in the following topics:

• Acid-Base Titrations

  • Before you begin the titration, you must choose a suitable pH indicator, preferably one that will experience a color change (known as the "end point") close to the reaction's equivalence point; this is the point at which equivalent amounts of the reactants and products have reacted.
  • Below are some common equivalence point indicators:
  • You can estimate the equivalence point's pH using the following rules:
  • You can determine the pH of a weak acid solution being titrated with a strong base solution at various points; these fall into four different categories: (1) initial pH; (2) pH before the equivalence point; (3) pH at the equivalence point; and (4) pH after the equivalence point.
  • The number of equivalents of acid and base must be equal at the equivalence point.

• Weak Acid-Strong Base Titrations

  • This indicates the formation of a buffer system as the titration approaches the equivalence point.
  • At the equivalence point and beyond, the curve is typical of a titration of, for example, NaOH and HCl.
  • At the equivalence point, all of the weak acid is neutralized and converted to its conjugate base (the number of moles of H+ = added number of moles of OH-).
  • However, the pH at the equivalence point does not equal 7.
  • The endpoint and the equivalence point are not exactly the same: the equivalence point is determined by the stoichiometry of the reaction, while the endpoint is just the color change from the indicator.

• Background and Properties

  • The following table lists some representative derivatives and their boiling points.
  • An aldehyde and ketone of equivalent molecular weight are also listed for comparison.
  • Boiling points are given for 760 torr (atmospheric pressure), and those listed as a range are estimated from values obtained at lower pressures.
  • As noted earlier, the relatively high boiling point of carboxylic acids is due to extensive hydrogen bonded dimerization.
  • The relatively high boiling points of equivalent 3º-amides and nitriles are probably due to the high polarity of these functions.

• Boiling Point and Water Solubility

  • It is instructive to compare the boiling points and water solubility of amines with those of corresponding alcohols and ethers.
  • Corresponding -N-H---N- hydrogen bonding is weaker, as the lower boiling points of similarly sized amines (light green columns) demonstrate.
  • Alkanes provide reference compounds in which hydrogen bonding is not possible, and the increase in boiling point for equivalent 1º-amines is roughly half the increase observed for equivalent alcohols.
  • Indeed, 3º-amines have boiling points similar to equivalent sized ethers; and in all but the smallest compounds, corresponding ethers, 3º-amines and alkanes have similar boiling points.
  • In the examples shown here, it is further demonstrated that chain branching reduces boiling points by 10 to 15 ºC.

• Point-Slope Equations

  • The point-slope equation is another way to represent a line; to use the point-slope equation, only the slope and a single point are needed.
  • To show that these two equations are equivalent, choose a generic point $(x_{1}, y_{1})$.
  • Therefore, the two equations are equivalent and either one can express an equation of a line depending on what information is given in the problem or what type of equation is requested in the problem.
  •  Again, the two forms of the equations are equivalent to each other and produce the same line.  
  • Use point-slope form to find the equation of a line passing through two points and verify that it is equivalent to the slope-intercept form of the equation

• The Knoke bureaucracies information exchange network analyzed by Tabu search

  • At the end of our analysis in the section "Finding equivalence sets" above, we produced a "permuted and blocked" version of our data.
  • In doing this, we used a few rules that, in fact, identify what regular equivalence relations "look like."
  • To repeat the main points: we don't care about the ties among members of a regular class; ties between members of a regular class and another class are either all zero, or such that each member of one class has a tie to at least one member of the other class.
  • Many networks have more than one valid partitoning by regular equivalence, and there is no guarantee that the algorithm will always find the same solution.
  • Four regular equivalence classes for the Knoke information network by optimum search

• Symmetry of Functions

  • It is an equivalence relation.
  • Functions and relations can be symmetric about a point, a line, or an axis.  
  • Yes, the graph is symmetry over the origin or point $(0,0)$.  
  • The points given, $(1,3)$ and $(-1,-3)$ are reflected across the origin.  
  • The curve is split into $2$ equivalent halves.  

• Introduction

  • The whole idea of "equivalence" that we discussed in the last chapter is an effort to understand the pattern of relationships in a graph by creating classes, or groups of actors who are "equivalent" in one sense or another.
  • Third, we will examine the most commonly used approaches for finding structural equivalence classes.
  • These methods (and those for other kinds of "equivalence" in the next two chapters) use the ideas of similarity/distance between actors as their starting point; and, these methods most often use clustering and scaling as a way of visualizing results.

• Defining automorphic equivalence

  • Automorphic equivalence is not as demanding a definition of similarity as structural equivalence, but is more demanding than regular equivalence.
  • There is a hierarchy of the three equivalence concepts: any set of structural equivalences are also automorphic and regular equivalences.
  • Any set of automorphic equivalences are also regular equivalences.
  • Not all regular equivalences are necessarily automorphic or structural; and not all automorphic equivalences are necessarily structural.
  • If the concept is still a bit difficult to grasp at this point, don't worry.

• Acetyl CoA and the Citric Acid Cycle

  • Acetyl-CoA along with two equivalents of water (H2O) are consumed by the citric acid cycle, producing two equivalents of carbon dioxide (CO2) and one equivalent of HS-CoA.
  • In addition, one complete turn of the cycle converts three equivalents of nicotinamide adenine dinucleotide (NAD+) into three equivalents of reduced NAD+ (NADH), one equivalent of ubiquinone (Q) into one equivalent of reduced ubiquinone (QH2), and one equivalent each of guanosine diphosphate (GDP) and inorganic phosphate (Pi) into one equivalent of guanosine triphosphate (GTP).
  • The product of this reaction, acetyl-CoA, is the starting point for the citric acid cycle.