Relative molecular velocity

If one follows the approach of Landau and Teller [11], who in dealing with vibrational relaxation developed an expression by averaging a transition probability based on the relative molecular velocity over the Maxwellian distribution, one can obtain the following expression for the recombination rate constant [6] ... 

Arrange the following gases, all at standard temperature, in order of increasing relative molecular velocities H2, CH, Rn, Nj, Fj, and He. What is your basis for determining the order ... 

The molecular weight (mean relative molecular mass) was obtained by determination of density but, in order to determine that the gas was monatomic and its atomic and molecular weights identical, it was necessary to measure the velocity of sound in the gas and to derive from this the ratio of its specific heats kinetic theory predicts that Cp/C = 1.67 for a monatomic and 1.40 for a diatomic gas. 

During ultracentrifugation, when the frictional force equals the centrifugal force and the particle achieves maximum velocity, the relative molecular mass... 

Sedimentation velocity. Tire relative molecular mass Mr can also be measured from observation of the velocity of movement of the boundary (or boundaries for multicomponent systems) between solution and solvent from which the macromolecules have sedi-... 

Mt (s) = relative molecular mass from sedimentation velocity measurements Mr (e) = relative molecular mass from sedimentation equilibrium measurements Mt (it) = relative molecular mass from osmotic pressure measurements... 

One of the practical applications of the optical polarization of molecular angular momenta is the investigation of the stereochemical forces in the process of molecule-atom collisions. The most complete information on the dependence of atom-molecule interaction potential on the orientation of the molecule with respect to the relative collision velocity can be obtained by the method of molecular beams, and often in conjunction with inhomogeneous magnetic and electric fields which orient the molecules. Such investigations are undoubtedly very complex, and their realization rather costly. To convince oneself of it one might just peruse the Proceedings of the First Workshop on Dynamic Stereochemistry in Jerusalem in 1986 [66] see also [67, 341],... 

Class Project. The qnenching results can be shared and form the basis for a class project to examine which molecular properties of the quenching molecule are important in causing relaxation of I. According to one simple model proposed by Rossler and discussed by Steinfeld, the quenching cross-section (Tq = dg shonld be proportional to the polarizability uq of the gas molecule and to the duration of the collision. Since the latter is inversely proportional to the relative collision velocity Crei, one predicts... 

The molecular velocity distribution was monitored by averaging over the total number of time steps and all the particles. It was foimd to reproduce the Maxwell distribution relative to the average temperature of the system (the value of (v y/(v ) - was about 0.01). We wish to point out, however, that the thermalization in the one-dimensional case offered some difficulties, in contrast with the two-dimensional case, where it requires usually only a few hundred time steps. This occurred principally at low densities where the collisions between the particles are mainly binary collisions. In this case, with our starting conditions, the distribution was found to be... 

The translational motion of a particular collection of molecules can either be specified by their velocity c relative to a standard frame of reference, or by their velocity relative to a frame moving with a specified velocity. The molecular velocity defined in the frame of reference which moves with the local... 

Sedimentation coefficients—Sjow—representing the velocity of sedimentation in unit gravitational field in water at 20°C, may be used, together with diffusion constants, to calculate the relative molecular masses of purified enzyme preparations. Reported values of S20W for cholinesterase isolated from human or equine serum are given in Table 7. Furthermore, the Sjow value for highly purified butyrylcholine esterase of porcine parotid gland is 9.7 units (T9) and it is 2.5 units for the enzyme from P. polycolor (N2). 

One consequence of the continuum approximation is the necessity to hypothesize two independent mechanisms for heat or momentum transfer one associated with the transport of heat or momentum by means of the continuum or macroscopic velocity field u, and the other described as a molecular mechanism for heat or momentum transfer that will appear as a surface contribution to the macroscopic momentum and energy conservation equations. This split into two independent transport mechanisms is a direct consequence of the coarse resolution that is inherent in the continuum description of the fluid system. If we revert to a microscopic or molecular point of view for a moment, it is clear that there is only a single class of mechanisms available for transport of any quantity, namely, those mechanisms associated with the motions and forces of interaction between the molecules (and particles in the case of suspensions). When we adopt the continuum or macroscopic point of view, however, we effectively spht the molecular motion of the material into two parts a molecular average velocity u = (w) and local fluctuations relative to this average. Because we define u as an instantaneous spatial average, it is evident that the local net volume flux of fluid across any surface in the fluid will be u n, where n is the unit normal to the surface. In particular, the local fluctuations in molecular velocity relative to the average value (w) yield no net flux of mass across any macroscopic surface in the fluid. However, these local random motions will generally lead to a net flux of heat or momentum across the same surface. 

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