Abstraction made of the time, the geometry is preponderant. In this section, we will discuss a lot about vectors and we define the tangent, the normal and the binormal. The tangent The trajectory is the path a moving object follows through space. Let’s analyse this curve ζ from the geometric point of view. The trajectory […]
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Chapter 3b: the motion, speed and acceleration
There is a motion if the vector changes over time. We can thus note this dependence . The variation of position is thus the motion. Noting the position of the object P1, P2, P3, … at consecutive times t1, t2, t3, … , we can introduce the displacement vector as the vector , and if the objects continues to […]
Chapter 3a: the motion- the position
The first formalism that has to be known in physics is the formalism of the motion. A formalism is associated with a certain rigorous mathematical method, defining symbols and rules that are commonly accepted, in the goal that everybody understands immediately the discussed matter. We will not be interested in the prediction of the motion nor […]
Chapter 10c: The Aluminium-Nickel group
Addition of NH4Cl, NH4OH and (NH4)2S to a solution containing all the cations not precipitated in the preceding groups results in the precipitation of aluminium, chromium and iron(II) as hydroxides, and manganese, nickel, cobalt, iron(II) and zinc as sulphides. Note that we used NH4OH and (NH4)2S in several tests of the preceding groups to separate […]
Chapter 10b: The Copper-Arsenic group
The elements of the copper-arsenic group are Hg2+, Pb2+, Bi3+, Cu2+, Cd2+, As3+, Sb3+ and Sn4+. They form sulphides that are insoluble in dilute HCl. It is not the case for sulphides of the following groups so we can isolate the ions from the copper-arsenic group from the ions of the other groups. Lead and […]
Chapter 10: Qualitative laboratory analyses
In this chapter, we will discuss some procedures used to separate and identify ions/groups of interest in solutions composed of several molecules. We will describe one method for mineral compounds and one for organic compounds. I have no real doubt that nowadays mass spectrometers can probably do the job and with a quantitative result, but […]
Chapter 9c: asymmetric synthesis – formation of optically-pure compounds
There are two ways to obtain such compounds. The first method is called the resolution in which the reactants we are starting with are either racemic or achiral. We separate the enantiomers after the production of both enantiomers. This method is vastly used in industries even if it doubles the volumes. They try to use […]
Chapter 9b: asymmetric synthesis – analytical methods of determination of the enantiomeric excess
A chiral agent is always necessary to differentiate the enantiomers. The most used methods to determine the ee are the GC with a chiral stationnary phase, HPLC with a chiral stationnary phase, NMR with chiral lanthanides. Gazeous chromatography The stationnary phase of the column is chiral and only composed of one enantiomer (for instance the […]
Chapter 9: asymmetric synthesis – stereoisomery
Editor’s note: It is a good exercise to determine the configuration (R or S) of each chiral centre presented in this course. Some molecules have the same composition in terms of atoms but differ by their placement. Those molecules are called conformers (of configuration). Amongst them we distinguish enantiomers and diastereoisomers. The distinction was already […]
Chapter 8: chemical kinetics – enzymatic catalysis
It can be done several ways catalysis by proximity (entropic contribution) electrophile and nucleophile catalyses general basic catalysis Catalysis by proximity We compare here an intramolecular process with an intermolecular process. Intermolecular Imidazole is incorporated into many important biological molecules. One of them is the histidine that is present in many proteins and enzymes. The presented reaction is […]