Rearrangement of equations

The simplification of equation 33 to equation 34 is possible only if r = 1 that is, foi simple monoatomic and diatomic gases. Foi other systems the design equation can be obtained by a direct rearrangement of equation 33. 

For consistency, clearance here is expressed in cm /s although the more common clinical units, and those used later in this chapter, are ml,/min. Combination and rearrangement of equations 6—8 allows clearance to be estimated from mass-transfer coefficient and vice versa the conditions of countercurrent flow with no dialysate recycling are shown below. 

Rearrangement of equation (1-31) yields the exponential form of the Nemst equation ... 

Use is made of the Francis formula (equation 6.43). where, as in the previous example, n — 0. In the context of this example the height of liquid flowing over the weir is usually designated hmv and the volumetric liquid flow by Q. Rearrangement of equation 6.43 gives ... 

Simplified dimensional equations have been derived for air, water and organic liquids by grouping the fluid properties into a single factor in a rearrangement of equation 9.102 to give ... 

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

The approach taken here is to use the lattice strain model to derive the partition coefficient of a U-series element (such as Ra) from the partition coefficient of its proxy (such as Ba) under the appropriate conditions. Clearly the proxy needs to be an element that forms ions of the same charge and similar ionic radius to the U-series element of interest, so that the pair are not significantly fractionated from each other by changes in phase composition, pressure or temperature. Also the partitioning behavior of the proxy must be reasonably well constrained under the conditions of interest. Having established a suitable partition coefficient for the proxy, the partition coefficient for the U-series element can then be obtained via rearrangement of Equation (2) (Blundy and Wood 1994) ... 

A poly tropic compression is neither adiabatic nor isothermal, but specific to the physical properties of the gas and the design of the compressor. The polytropic coefficient n must therefore be determined experimentally. If the initial and final conditions for a given compression process are known, then n can be determined from a rearrangement of Equation B.23 ... 

In attempting to determine if a given set of experimental data is of the same mathematical form as equation 7.3.29, there are three routes that permit the graphical determination of the parameters Vmax and K. The most frequently used plot is known as a Lineweaver-Burk or reciprocal plot. It is based on rearrangement of equation 7.3.29 into the following form. 

Rearrangement of Equation 9.23 separates isotropic shift from anisotropic shift ... 

Equation (12) is a linear free-energy relationship, since activity coefficients/can be represented as AG° values. The reason for defining the slope parameter as in equation (12) (subscript e for equilibrium) is that a little rearranging of equations (11) and (12) leads to the easy-to-use Bunnett-Olsen equation for equilibria, equation (13) 30... 

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. 

Here it has been shown that the conclusion about is related to the mathematical approximation used in interpreting the data by way of Method I it is easy to show that the second and third conclusions are also dependent on the initial assumptions in Method I. Rearrangement of Equation 28 and substitution of the constant capacitance constraint yields a relationship between i/>q and In a + ... 

Rearrangement of Equation 11.14 and substitution into Equation 11.13 gives ... 

Having obtained we can calculate mean activity coefficients from a rearrangement of Equation (19.34) to the form... 

The boundary layer thickness, 5, is the thickness, z, where u/U = 0.99. From the numerical solution, this occurs at= 4.85. Then, the thickness of the boundary layer, 5, is found from a rearrangement of equation (E4.4.2) and is provided for different distances in equation (E4.4.7) and Table E4.4.1. 

Equation (4.11) is the Langmuir equation for type I isotherms. Rearrangement of equation (4.11) gives... 

The partial molar excess Gibbs free energy of the methylene group can be used as a means of characterizing stationary phases. From rearrangement of Equation 11.46, an expression for the standard partial molar Gibbs free energy can be obtained. 

With particularly simple networks, some rearrangement of equations sometimes can be made to simplify the solution. Example 6.7 is of such a case. 

Note that N is constantly reducing in magnitude as a function of time. Rearrangement of Equation (3.2) to separate the variables gives... 

The difference between the carbocation rearrangement and the rearrangement of Equation 11-5 is that R migrates from boron to oxygen as HO departs in what might be considered an internal SN2 reaction. We can generalize this kind of reaction of boron with a substance, X—Y, as in Equation 11-6 ... 

C6. To account for this Roberts suggested that 6,2- or 6,1-hydride shifts occur in the carbonium ion simultaneously with the rearrangement of Equation 6.39 as shown in Equation 6.40.103... 

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