Initiator number

The time required for half of the initial number of a radioactive isotope s atoms to disintegrate (ti/2). 

The ratio of the initial number of A to B groups as defined by the factor r. given by Eq. (5.34). The total number of A groups from both AA and A are included in this application of r. 

As the particles in a coUoidal dispersion diffuse, they coUide with one another. In the simplest case, every coUision between two particles results in the formation of one agglomerated particle,ie, there is no energy barrier to agglomeration. Applying Smoluchowski s theory to this system, the half-life, ie, the time for the number of particles to become halved, is expressed as foUows, where Tj is the viscosity of the medium, k Boltzmann s constant T temperature and A/q is the initial number of particles. 

If the initial number of moles of species i is and if the convention is adopted that = 0 for each reaction in this initial state, then... 

The reqmred values of are determined from the initial numbers of moles, and the values of dji come directly from the chemical formulas of the species. These are shown in the accompanying table. 

This equation was first given by Lord Rayleigh and is called the Rayleigh equation. Integration between the initial number of moles n o in the still with composition over any time yields the following ... 

Integrating Eq. (4.331) and knowing that is the initial number of moles of component i yields... 

A so initial number of seed crystals, /kg solvent c number of crystals, /m ... 

First, calculate the overall compression ratio (R = Pa/Pj). If the compressor ratio is under 5, consider using one stage. If it is not, select an initial number of stages so that R < 5. For initial calculations it can be assumed that ratio per stage is equal for each stage. 

The steady state is obtained by allowing t-+oo. In this manner the initial number i should no longer appear in the result. 

We assume that the initial number of units in the system at time t = 0 is i 2. 

Step 3 Write the chemical equation for the neutralization reaction and use the reaction stoichiometry to find the amount of H. O ions (or OH ions if the analyte is a strong base) that remains in the analyte solution after all the added titrant reacts. Each mole of H30+ ions reacts with 1 mol OH ions therefore, subtract the number of moles of H30+ or OH ions that have reacted from the initial number of moles. 

Radioactive decay is normally discussed in terms of the half-life, tU2, the time needed for half the initial number of nuclei to disintegrate. Just as we did in Section 13.5, we find the relation between tl/2 and k by setting N = N0 and t = tl/2 in Eq. 3 ... 

The apparent reaction rate constant for the first order reaction, k, was calculated from the conversion of CO2. Since the gas-volume reduction rate increased with k, a poor fluidization was induced by high reaction rate. We investigated the effect of the rate of the gas-volume change on the fluidization quality. The rate of the gas-volume change can be defined as rc=EA(dxA/dt), where Sa is the increase in the number of moles when the reactants completely react per the initial number of moles. This parameter is given by 7-1. When the parameter, Ea, is negative, the gas volume decreases as the reaction proceeds. 

Species V Initial number of moles Final number of moles... 

Suppose the initial number of nuclei of a radioactive nuclide is N0, and that the half-life is T. Then the amount of parent nuclei remaining at a time t can be written as Nx = NQ( /2)(tlT>. This relationship is called the radioactive decay equation. What is the number of daughter nuclei present at time t, expressed in terms of N0 and Nx ... 

The first equation gives the rate of gas consumption as moles of gas (n) versus time. This is the only state variable that is measured. The initial number of moles, nO is known. The intrinsic rate constant, K is the only unknown model parameter and it enters the first model equation through the Hatta number y. The Hatta number is given by the following equation... 

The other state variables are the fugacity of dissolved methane in the bulk of the liquid water phase (fb) and the zero, first and second moment of the particle size distribution (p0, Pi, l )- The initial value for the fugacity, fb° is equal to the three phase equilibrium fugacity feq. The initial number of particles, p , or nuclei initially formed was calculated from a mass balance of the amount of gas consumed at the turbidity point. The explanation of the other variables and parameters as well as the initial conditions are described in detail in the reference. The equations are given to illustrate the nature of this parameter estimation problem with five ODEs, one kinetic parameter (K ) and only one measured state variable. 

Assist in Standardization of Nomenclature. The profusion of trade names, initials, numbers, and combinations thereof for pesticides contributes to misuse and errors in the handling of these preparations. The coining of common or generic names for pesticides is a recent and commendable innovation in this field of science. It presents many problems which require the services of many groups. The many years of experience of the Council on Pharmacy and Chemistry in the development of generic names for drugs is at the disposal of the committee in its consideration of nomenclature problems. 

This can be done via Eqs. (29) through (32). From the dissolution data, the coefficient B2 is obtained and through the results from microscopy the moments r2 and p3 can be evaluated. By knowing N, the initial number of particles, and the density of the solid, the average initial volume shape factor for a polydisperse powder can be estimated. 

D) Initial number distribution of Wx Limiting weight ratio of liquid to... 

Assuming p is the conversion ratio equal to the ratio between the actual number of one type of functional group to its initial number... 

Later, Kuppermann and Belford (1962a, b) initiated computer-based numerical solution of (7.1), giving the space-time variation of the species concentrations from these, the survival probability at a given time may be obtained by numerical integration over space. Since then, this method has been vigorously followed by others. John (1952) has discussed the convergence requirement for the discretized form of (7.1), which must be used in computers this turns out to be AT/(Ap)2normalized forms of r and t. Often, Ar/(Ap)2 = 1/6 is used to ensure better convergence. Of course, any procedure requires a reaction scheme, values of diffusion and rate coefficients, and a statement about initial number of species and their distribution in space (vide infra). 

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