Number of molecules

LoschmidCs number The number of molecules of an ideal gas in unit volume at stp equal to 2-687 x 10 per cm. ... 

After the primary step in a photochemical reaction, the secondary processes may be quite complicated, e.g. when atoms and free radicals are fcrnied. Consequently the quantum yield, i.e. the number of molecules which are caused to react for a single quantum of light absorbed, is only exceptionally equal to exactly unity. E.g. the quantum yield of the decomposition of methyl iodide by u.v. light is only about 10" because some of the free radicals formed re-combine. The quantum yield of the reaction of H2 -f- CI2 is 10 to 10 (and the mixture may explode) because this is a chain reaction. 

I where n, = the number of molecules of component i having molecular weight Ml. I... 

It is instructive to consider just how mobile the surface atoms of a solid might be expected to be. Following the approach in Section III-2, one may first consider the evaporation-condensation equilibrium. The number of molecules hitting a 1-cm surface per second is from kinetic theory... 

In passing one should note that the metliod of expressing the chemical potential is arbitrary. The amount of matter of species in this article, as in most tliemiodynamics books, is expressed by the number of moles nit can, however, be expressed equally well by the number of molecules N. (convenient in statistical mechanics) or by the mass m- (Gibbs original treatment). 

The microcanonical ensemble is a set of systems each having the same number of molecules N, the same volume V and the same energy U. In such an ensemble of isolated systems, any allowed quantum state is equally probable. In classical thennodynamics at equilibrium at constant n (or equivalently, N), V, and U, it is the entropy S that is a maximum. For the microcanonical ensemble, the entropy is directly related to the number of allowed quantum states C1(N,V,U) ... 

The motion of particles in a fluid is best approached tlirough tire Boltzmaim transport equation, provided that the combination of internal and external perturbations does not substantially disturb the equilibrium. In otlier words, our starting point will be the statistical themiodynamic treatment above, and we will consider the effect of botli the internal and external fields. Let the chemical species in our fluid be distinguished by the Greek subscripts a,(3,.. . and let f (r, c,f)AV A be the number of molecules of type a located m... 

No system is exactly unifomi even a crystal lattice will have fluctuations in density, and even the Ising model must pemiit fluctuations in the configuration of spins around a given spin. Moreover, even the classical treatment allows for fluctuations the statistical mechanics of the grand canonical ensemble yields an exact relation between the isothemial compressibility K j,and the number of molecules Ain volume V ... 

Another example of a teclmique for detecting absorption of laser radiation in gaseous samples is to use multiphoton ionization with mtense pulses of light. Once a molecule has been electronically excited, the excited state may absorb one or more additional photons until it is ionized. The electrons can be measured as a current generated across the cell, or can be counted individually by an electron multiplier this can be a very sensitive technique for detecting a small number of molecules excited. 

In this case, the scattering serves as a means for counting the number of molecules (or particles, or objects) per unit volume (N/V). It is seen that the polarizability, a, will be greater for larger molecules, which will scatter more. If we take the Clausius-Mosotti equation [16] ... 

Let us first consider two identical polymers, one deuterated and the other not, in a melt or a glassy state. The two polymers (degree of polymerization d) differ from each other only by scadermg lengths and b. If the total number of molecules is N, x is the volume fraction of the deuterated species x = N- / N, with Aq -t = A). According to equation (B1.9.116), we obtain... 

Here t. is the intrinsic lifetime of tire excitation residing on molecule (i.e. tire fluorescence lifetime one would observe for tire isolated molecule), is tire pairwise energy transfer rate and F. is tire rate of excitation of tire molecule by the external source (tire photon flux multiplied by tire absorjDtion cross section). The master equation system (C3.4.4) allows one to calculate tire complete dynamics of energy migration between all molecules in an ensemble, but tire computation can become quite complicated if tire number of molecules is large. Moreover, it is commonly tire case that tire ensemble contains molecules of two, tliree or more spectral types, and experimentally it is practically impossible to distinguish tire contributions of individual molecules from each spectral pool. 

On a more rational basis, reactions can be classified according to the overall change in molecularity, the change An in the number of molecules (n) participating in a reaction (Figure 3-3). 

Maxwell obtained equation (4.7) for a single component gas by a momentum transfer argument, which we will now extend essentially unchanged to the case of a multicomponent mixture to obtain a corresponding boundary condition. The flux of gas molecules of species r incident on unit area of a wall bounding a semi-infinite, gas filled region is given by at low pressures, where n is the number of molecules of type r per... 

One of the main advantages of the stochastic dynamics methods is that dramatic tirn savings can he achieved, which enables much longer stimulations to he performed. Fc example, Widmalm and Pastor performed 1 ns molecular dynamics and stochastic dynamic simulations of an ethylene glycol molecule in aqueous solution of the solute and 259 vvatc jnolecules [Widmalm and Pastor 1992]. The molecular dynamics simulation require 300 hours whereas the stochastic dynamics simulation of the solute alone required ju 24 minutes. The dramatic reduction in time for the stochastic dynamics calculation is du not only to the very much smaller number of molecules present hut also to the fact the longer time steps can often he used in stochastic dynamics simulations. 

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