Life methods

The half-life method requires data from several experiments, eaeh at different initial eoneentration. The method shows that the fraetional eonversion in a given time rises with inereased eoneentration for orders greater than one, drops with inereased eoneentration for orders less than one, and is independent of the initial eoneentration for reaetions of first order. This also applies to the reaetion A -i- B —> produets when... 

If the reaetion rate depends on more than one speeies, use the method of exeess eoupled either with the half-life method or the differential method. If the method of exeess is not suitable, an initial rate plot may be eonstrueted by varying the eoneentration of one reaetant while the eoneentrations of the others are held eonstant. This proeess is repeated until the orders of reaetion of eaeh speeies and the speeifie reaetion rate are evaluated. At level 5, the least-squares analysis ean be employed. 

This subject effects designers since many products have the requirement by regulations or otherwise to use recycled plastics. Different methods are used to recycle materials to provide plastics with a continuing life. Method used is influenced by factors such as costs, quantity involved, weight involved, size and shape, complexity of mixed types of plastics, extended of contamination such as metallic particles, continued availability of material, etc. (Recognize that they can also be used as energy sources through incineration that can be combined with production of electricity and/or hot water for example). 

Experimental results O 107ppm A 50ppm 35ppm Calculation results Half-life method... 

Integral Methods for the Analysis of Kinetic Data—Fractional Life Methods. The... 

And here is another variation of the half-life method. 

Fractional Life Method The half-life method can be extended to any fractional life method in which the concentration of reactant drops to any fractional value F = C /Cao in time The derivation is a direct extension of the half-life method giving... 

Guess nth-Order Kinetics. Let s plan to use the fractional life method with F = 80%. Then Eq. 336 becomes... 

Example 3.1c showed how to find a rate equation by using the fractional life method where F = 80%. Take the data from that example and find the rate equation by using the half-life method. As a suggestion, why not take Cao = 10, 6, and 2 ... 

Half-Life Method For a zero-order reaction the half-life (tll2) is proportional to the initial concentration. The half-life for a first-order reaction is independent of the initial concentration while a second-order reaction is proportional to 1/initial concentration. 

An alternative method to determine the reaction order is the half-life method. The half life of a reaction (t /2) is the time it takes for 50% of the reactant(s) to be consumed. At time t /2 the concentration of A must then be [A]o/2. For a first-order reaction, Eq. 13.15 yields... 

We see that the half-life is always inversely proportional to k and that its dependence on [A]o depends on the reaction order. Thereby the method can be used to determine both the rate constant and the reaction order, even for reactions with noninteger reaction order. Similar to the integral method, the half-life method can be used if concentration data for the reactant are available as a function of time, preferably over several half-lives. Alternatively the half-life can be determined for different initial concentrations in several subsequent experiments. 

Half-life method Two different initial concentrations of A are used. The decrease in A over time is measured. The half-life x = tl/2 is defined as the time where c(A) = c(A)0/2. The order can be determined with the following equation (see Figure 4-la, b)... 

There is a second kind of sample, which is hardly ever found in a real-life method development laboratory. That is the sample one knows everything about Even if this might seem to be the case, it is good to be aware of the possibility that unexpected components may be present in the sample. These may include contaminants, side products, degradation products, metabolites, etc.. 

The half-life method (in general, the fractional-life method) is very useful in preliminary estimates of the order of the reaction. A series of experimental runs is carried out with different initial concentrations. If an irreversible reaction is considered ... 

The Half Life Method We have shown above that, provided all reactants are present in the same molar concentrations, the half-life, t1/2, of nth-order reaction is given by Eq. 2.38. 

Fractional-life methods. If a reaction is known to be first order and at constant fluid density, its apparent rate coefficient can be found very quickly. For batch and differential recycle reactors, the relationship between the rate coefficient and the time ty required for all but a fraction y of the reactant to be consumed is... 

Some texts describe fractional-life methods for reactions other than first order and with more than one reactant. However, the effort their application requires is not in proportion to the limited objectives of the evaluation in the present context. 

Fractional life method (7). It follows from either eqn. (18) or (19) that 6 is fixed for a given value of a and (a+b). Therefore, if, in a series of experiments at different values of the initial concentrations of A and B throughout which the ratio... 

Fractional life method (II). If, for some reason, it is not possible to cover a wide range of initial concentration conditions as is clearly necessary for the application of the above method (this could happen when one of the reactants has a limited solubility), essentially the same method can be applied to the data of a single experiment. We select a series of values of a (ao, ai, a2,.... ..) such that... 

The fractional life methods can also be used to determine a. As already indicated, the fractional life method of treating the data of a single experiment has few advantages over the superimposition method and consequently need not be considered further. On the other hand, the measurement of a particular fractional life of the reactant A in a series of experiments in which its initial concentration is varied provides a means by which a can be determined which sometimes offers experimental advantages. The only point to remember is that throughout the series of experiments [BJo must be kept constant at such a value that [BJo/[A]o,i Vb/Va. From the condition that... 

The Half-Life Method The half-life is the batch time required to get 50 percent conversion. For an nth-order reaction,... 

To determine the Cl-nt of compound X, we are able to use the in vitro half-life method, which is simpler than finding all the component Cl nt values. When the substrate concentration is much smaller than Km, the Michaelis-Menten equation simplifies from velocity (V) = Vmax([S])/(Km + [S]), because [S] (substrate concentration) becomes negligible. Furthermore, under these conditions, the in vitro half-life (7) 2 = 0.693/Xel) can be measured, and this, in turn, is related to the Michaelis-Menten equation through the relationship velocity (V) = volume x Kel (where volume is standardized for the volume containing 1 mg of microsomal protein). When both V and Vmax are known, then Km is also found. Although simpler than finding a complicated Cint, one caveat of the in vitro half-life method is that one assumes that the substrate concentration is much smaller than Km. It may be necessary to repeat the half-life determinations at several substrate concentrations, and even model the asymptote of this relationship, because very low substrate concentrations that are beneath biochemical detection may be needed to fulfill the assumptions needed to simplify the Michaelis-Menten equation. 

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