Simple Rearrangement

Integrating Equation 4-116 assuming incompressible drilling fluid flow (p is constant) and after simple rearrangements yields the pressure loss across the bit Apj (psi) which is... 

Bimolecular processes are reactions in which two reactant molecules collide to form two or more product molecules. In most cases the reaction involves a rather simple rearrangement of bonds in the two molecules ... 

Note that equations 13 and 14 are simple rearrangements of equations 8 and 9. 

Some simple rearrangement of Equation 3.1 leads to the concepts of transmission T = Io/1 and absorbance A = — log T, with the quantity s c l called the optical density. The choice of units here for the extinction coefficient (M-1 cm-1) is appropriate for measurement of the absorbance of a solution in the laboratory but not so appropriate for a distance Z of astronomical proportions. The two terms and c are contracted to form the absorption per centimetre, a, or, more conveniently (confusingly) in astronomy, per parsec. The intrinsic ability of a molecule or atom to absorb light is described by the extinction coefficient s, and this can be calculated directly from the wavefunction using quantum mechanics, although the calculation is hard. 

An elementary step must necessarily be simple. The reactants are together with sufficient energy for a very short time, and only simple rearrangements can be accomplished. In addition, complex rearrangements tend to require more energy. Thus, almost all elementary steps break and/or make one or two bonds. In the combustion of methane, the following steps (among many others) occur as elementary reactions ... 

These two steps are simple rearrangements. The overall reaction... 

Isomerization polymerizations yield high-molecular-weight products when reaction proceeds through relatively simple rearrangement routes involving stable carbocations. Thus... 

This seemingly simple rearrangement has been subjected to extensive theoretical... 

The simple rearrangement of Eq. 7 leads to the relation for the time-de-pendent scavenging distance along DNA double strands, D t) ... 

By a simple rearrangement, these can be recast as a set of linear equations. Thus,... 

On the other hand, during their sojourn on the surface the adsorbed molecules may undergo chemical change, consisting either in simple rearrangement or decomposition, or in interaction with adjacent molecules. 

After elimination of V the following equation is obtained for x by simple rearrangement ... 

Ring opening by photolysis also occurs in the oxadiazoline ring. Srivastava and Clapp109 noted that a simple rearrangement [Eq. (44)] of 4-/3-ethoxyethyl-3-methyl-5-p-nitrophenyl-l,2,4-oxadiazoline to a substituted amidine (50) took place on a bench top in ordinary daylight or... 

Equation (6.125) is applicable for all the potential pulses of the whole sequence. Thus, from Eqs. (6.125) and (6.126), it is possible to obtain the analytical expression of r Q by substituting p 2 and inserting the expression of /) (Eq. (6.114)) in (6.125). Once ro is known, by carrying out this process p times and after a simple rearrangement, the general analytical explicit expression of is deduced [46] ... 

One of the laboratory procedures that you are expected to know involves the determination of molar mass from gas density. In the sample calculation that follows, you will solve for the density of a gas, but understand that a simple rearrangement of the equation allows you to solve for the molar mass. 

A simple rearrangement of this expression gives the solution resistance for a reference electrode placed a distance d r rt away from the inner cylinder with the outer cylinder at infinity (6). 

As may be recalled from our discussion of the law of definite proportion, isomers are molecules that have been built from the same number and type of atoms but arranged in a different order. We cited, as examples, fulminic acid, cyanic acid, and isocyanic acid HONC, HOCN, and HCNO, respectively. We saw that this simple rearrangement of elements made the first explosive, the second a poison, and the third a pacific participant in several, more constructive, organic syntheses. Isomers that differ only by being mirror images of each other are termed chiral isomers (pronounced kiral, with a hard c sound, the way chemist is pronounced kemisf). 

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