Concentrations as function

We have seen that a kinetic scheme does not have to be very complex before explicit solutions for concentrations as functions of time become difficult or impossible to obtain. Even with those complex schemes for which solutions are possible, the... 

The computation result yield acetaldehyde concentration as function of time. The value of kinetics parameters, ki, ka, k3 were adjusted to minimize the sum of square of error between the predicted and measured concentration using Hooke Jeeve method [3]. 

Figure 8.15. Outlet equilibrium methanol concentration as function of the inlet mo e fraction ofH2, CO, and COa-Notice that the highest methanol concentration is or a mixture of only Ha and CO at a ratio o...

Equation 27 can be numerically integrated along the conversion trajectory to obtain the Initiator concentration as function of time. Therefore, calculation of t, 6 and C together with the values of M, Rp, rw and rn from the equations In Table II allows the estimation of the ratios (ktc/kp1), (kx/kp) and the efficiency as functions of conversion. Figure 3 shows the efficiency as function of conversion. Figure 4 shows the variation of the rate constants and efficiencies normalized to their initial values. The values for the ratio (ktc/kpl)/(ktc/kpl)o reported by Hui (18) are also shown for comparison. From the definition of efficiency it is possible to derive an equation for the instantaneous loading of initiator fragments,... 

The radon emanation and the ventilation rate of a room can be derived from the increase of the radon concentration by the radon exhalation and from the steady state condition between exhalation and air exchange with the free atmosphere. In Fig. 2 the variation of the radon concentration as function of time is shown measured in two houses with different radon emanations and ventilation rates. 

Find concentrations as functions of time. Unsteady material balances,... 

With consecutive—parallel systems in which the reaction steps are not first order, analytical expressions for species concentrations as functions of time (which would apply to batch reactors) are sometimes unobtainable. Numerical procedures can be used. However, analytical procedures can still be used to obtain some indication of relative yields of reaction... 

Figure 2. Average monthly radon concentration as function of stability...

Fig. 13.2 Predicted equilibrium concentrations as function of temperature of selected major and minor species in a typical flue gas from combustion.

The Static Reactor Static reactors are conceptually simple. They consist typically of a spherical vessel that is filled with the reactive mixture. The gas phase reactants are, at least initially, maintained at the desired temperature by an oven or a thermostated bath. The progress of reaction is observed by measuring the change in pressure (reaction takes place at constant volume) or by detecting concentrations as function of time for one or several species. 

IUPAC.-Working Party on "The Relationship of Performance Characteristics to Basic Parameters of Polymers . This sample has been investigated in transdecalin at 160° C. Fig. 3.8 shows the extinction angle curves obtained for the three indicated concentrations as functions of A linear extrapolation at various /Sy.urvalues was possible and led... 

FIGURE 4 Exit concentrations as functions of Da for five reactors. 

Free europium ion concentration as function of the concentration of complexed europium ... 

Figure 1.6 shows the normalized concentrations as functions of time during the batch for different values of the two rate constants kK and kc. The higher the value of kB compared with kc, the more of product B is generated. This is expressed in terms of the selectivity (S) to the desired product, which we preferentially want to be as large as possible ... 

Figure 11-20 shows production rate, cell concentration, and substrate concentration as functions of dilution rate. From Equation 11-74, the maximum production rate can be determined. 

Figure 7.15 Steady-state reactor concentrations as functions of temperature.

Figure 3.1 Concentrate and instantaneous permeate concentration as functions of recovery.

The reader will observe that the discussion of the empirical description of kinetic systems in the preceding section was resolved by a verbal sleight of hand. Whereas the raw kinetic data are usually in the form of concentrations of chemical components at given times (and indeed our aim is to reproduce such data by mathematical equations that represent these concentrations as functions of the time), our very first statement involved an entirely different language, that of the concentration derivatives (the rates of reaction) and their relations to concentrations. 

Consider the combustion reaction between a solid reactant and a gas oxidizer present initially in the constant volume of a porous medium (see Section IV,D,1). In this case, thermodynamic calculations for the silicon-nitrogen system have been made for constant volumes (Skibska et al, 1993b). The calculations yield the adiabatic combustion temperature, as well as pressures and concentration, as functions of the silicon conversion. As shown in Fig. 34a, the reactant gas pressure (curve 3) increases even though conversion increases. This occurs because... 

This is the procedure From the postulated kinetic scheme we write the differential rate equations. Take the Laplace transforms of the differential equations. Solve the resulting set of algebraic equations for the transforms of the concentrations. Then take the inverse transforms to obtain the concentrations as functions of time. 

The differential rate equations of a complex reaction, expressing rates as functions of concentrations, are usually simpler in form than are the corresponding integrated equations, which express concentrations as functions of time moreover, it is always possible to write down the differential rate equations for a postulated kinetic scheme, whereas it may be difficult or impossible to integrate them. Of course, we usually measure concentration as a function of time. If, however, we can measure rates, we may use the differential equations directly. 

Logarithm of Steady-State Radical Concentration as Function of Rate of Light... 

Figure 7 Selected pore-water concentrations as functions of depth in a deeply weathered regolith in the Luquillo Mountains of Puerto Rico. Diagonal solid lines are linear fits to the weathering gradients used by Murphy et al. (1998) to calculate biotite weathering rates (Equation (13)) (after White et al, 1998).

Example 6S Calculating Concentrations as Functions of Position for NH3 Oxidation in a PFR... 

Figure 6. Relative wild-type concentrations as function of error rate 1 - Q g. We show exact solution curve (upper full line) and compare it with result of perturbation theory [Eqn. (III.2) broken line) and exact solution of Eqn. (III.3) with B calculated as in text (lower full line). Following parameters and rate constants applied Ag = 10, = 5, Dq = D, = = and...

Obtain the concentrations as functions of time by substituting these values for the rate constants into the components of the solution vector ... 

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