Molar density dimensional analysis

The key to dimensional analysis is knowing the units associated with each quantity or constant. What are the units of (a) molar mass (b) density (c) molarity (d) specific heat (e) mole fraction (f) vapor pressure of water (g) entropy (h) freezing-point lowering constant (i) R, the ideal gas law constant ... 

Dimensional analysis predicts the various dimensionless parameters which are helpful in correlating experimental data. Certain dimensions must be established as fundamental, with all others expressible in terms of these. One of these fundamental dimensions is length, symbolized L. Thus, area and volume may dimensionally be expressed as L2 and L3, respectively. A second fundamental dimension is time, symbolized t. Velocity and acceleration may be expressed as L/t and Lit1, respectively. Another fundamental dimension is mass, symbolized M. The mole is included in M. An example of a quantity whose dimensional expression involves mass is the density (mass or molar), which would be expressed as Mil . 

FUNCTIONAL DEPENDENCE OE THE MOLAR DENSITY OF SPECIES i VIA DIMENSIONAL ANALYSIS... 

Notice that the molar density profiles for these problems are not affected by any dimensionless numbers because either there is only one mass transfer rate process for steady-state analysis, or both rate processes are described by the same dimensional scaling factor. These qualitative trends should be considered before one seeks quantitative information about a particular mass transfer problem. 

If you follow the dimensional analysis techniques you learned in Chapter 1, you can convert between concentration units, as shown in Sample Exercise 13.5. To convert between molality and molarity, the density of the solution will be needed, as in Sample Exercise 13.6. 

A measurement system that is able to quantitatively determine the interactions of receptor and G protein has the potential for more detailed testing of ternary complex models. The soluble receptor systems, ([l AR and FPR) described in Section II, allow for the direct and quantitative evaluation of receptor and G protein interactions (Simons et al, 2003, 2004). Soluble receptors allow access to both the extracellular ligandbinding site and the intracellular G protein-binding site of the receptor. As the site densities on the particles are typically lower than those that support rebinding (Goldstein et al, 1989), simple three-dimensional concentrations are appropriate for the components. Thus, by applying molar units for all the reaction components in the definitions listed in Fig. 2A, the units for the equilibrium dissociation constants are molar, not moles per square meter as for membrane-bound receptor interactions. These assemblies are also suitable for kinetic analysis of ternary complex disassembly. 

A two-dimensional needle-punched carbon fiber (T300-3K of Toray) preforms, with 17.6% fiber volume traction and a bulk density of 0.3 g/cm were used in the study [49] Pyrolytic carbon was coated on the carbon fiber surface as interfacial layer by CVI using 10 kPa propane at 950 °C. The prepared porous C/C composite added with 22.3% (volume traction) pyrolytic carbon exhibited a bulk density of about 0.68 g/cml A commercial polycarbosilane (PCS) with a mean molecular weight of 1380 (in number, Mn) or 2770 (in weight, Mw) with a softening point of 180 °C was used as precursor of SiC, the chemical composition analysis of PCS indicated a C Si molar ratio of 1.38. Pyrolysis of this polymer led to the formation of SiC with some residual carbon (Yajima et al., 1976). 

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