Half zero order reaction

Even when there is a transport disguise, the reaction order remains one for a first-order reaction. But for reactions that are not intrinsically first order, the transport disguise changes the observed reaction order for an intrinsically zero-order reaction, the observed order becomes 1/2 and for an intrinsically second-order reaction it becomes 3/2 when 0 10. For all reaction orders the apparent activation energy is approximately half the intrinsic... 

In the calculation results, shown in Figure 28.4, phenol concentration decreases with time at a constant rate for about the first 30 days of reaction. Over this interval, the concentration is greater than the value of K, the half-saturation constant, so the ratio m/(m + K ) in Equation 28.9 remains approximately constant, giving a zero-order reaction rate. Past this point, however, concentration falls below K and the reaction rate becomes first order. Now, phenol concentration does not decrease linearly, but asymptotically approaches zero. 

A zero-order reaction has a half life that varies proportionally to [A]0, therefore, increasing [A]0 increases the half-life for the reaction. A second-order reaction s half-life varies inversely proportional to [A]0, that is, as [A]0 increases, the half-life decreases. The reason for the difference is that a zero-order reaction has a constant rate of reaction (independent of [A]0). The larger the value of [A]0, the longer it will take to react. In a second-order reaction, the rate of reaction increases as the square of the [A]0, hence, for high [A]0, the rate of reaction is large and for very low [A]0, the rate of reaction is very slow. If we consider a bimolecular elementary reaction, we can easily see that a reaction will not take place unless two molecules of reactants collide. This is more likely when the [A]0 is large than when it is small. 

The half-life period tm of a zero order reaction can be calculated with the help of equation (1.19), taking t = ty2 and x = all as... 

Thus, the half-life period of zero order reaction is directly proportional to the initial concentration of the reactant. For example, on increasing the initial concentration by two fold, the half-life period of the reaction would also be double. 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first-order, whereas a second-order reaction would have an apparent order 3/2 for diffusion-limited conditions. 

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. 

A zero-order reaction thus becomes a half-order reaction, a first-order reaction remains first order, whereas a second-order reaction has an apparent order of 3/2 when strongly influenced by diffusional effects. Because k and n are modified in the diffusion controlled region then, if the rate of the overall process is estimated by multiplying the chemical reaction rate by the effectiveness factor (as in equation 3.8), it is imperative to know the true rate of chemical reaction uninfluenced by diffusion effects. 

Using concentrations expressed in molarity and time in seconds, what are the units of the rate constant, k, for (a) a zero-order reaction (b) a first-order reaction (c) a second-order reaction (d) a third-order reaction (e) a half-order reaction ... 

Important characteristics of zero-order reactions are that (1) a constant amount of drug is eliminated per unit time since the system is saturated (maximized) and (2) the half-life is not constant for zero-order reactions but depends on the concentration. The higher the concentration, the longer the half-life. Therefore, the term zero-order half-life has little practical significance since it can change and (3) zero-order kinetics is also known as nonlinear or dose-dependent. For example, if the body can metabolize ethanol at a rate of 10 ml per hour, then if one consumes 60 ml, it will take 3 hours to metabolize half of it (the half-life under these circumstances). However, if 80 ml is consumed the half-life will now become 4 hours. This is particularly significant regarding ethanol toxicity. 

The half-life (l,lS) and shelf-life (f 9) are defined as the times required for the concentration of the drug to decrease by 50 and 10%, respectively. For zero-order reactions,... 

The half-life of a zero-order reaction is directly proportional to [A]0. Unlike other reaction kinetics, it is possible to determine the time required for 100% of the drug in a formulation to completely decompose. It takes two half-lives for complete degradation for zero-order reactions. 

The degradation of a colorant in a solid dosage form was found to follow a zero-order reaction with a rate constant of 3.1 x lfh4 absorbance units per hour at 37°C. What is the half-life of the preparation with an initial absorbance of 0.56 at 486 nm This dosage form should be discarded when the absorbance is below 0.34. Calculate the predicted life of the dosage form at 37°C. 

A plot of Aj versus would produce a straight line with slope -k in units of mass per unit time (e.g., mol min-1) (Fig. 7.4). In the case of a zero-order reaction, its half-life is l/2ff, where tf represents the total time needed to decompose the original quantity of compound A (A0). Another way to express such reactions is shown in Figure 7.5. The data show A1 release from y-Al203 at different pH values. The data clearly show that the reaction is zero-order with k dependent on pH. 

What is the fundamental difference between the half life of a first-order and a zero-order reaction Why is the distinction important ... 

Pig. The plot of rate versus concentration for a zero-order reaction The reaction rate does not vary with concentration of reactant. Reaction and Half-lifetime... 

The table indicates, for example, that the difference in times between one-half and three-quarters completion divided by the half-life, (tn — will be 0.500 for a zero-order reaction, 1.000 for a first-order... 

The expression for the half-life of a zero-order reaction can be obtained from the integrated rate law. By definition, [A] = [A]0/2 when t = tyj, so... 

Zero-order reaction can be expressed by the equation, dc/dt = -K, where dc/dt is the rate of change of concentration with time and k is the rate constant. In a zero-order reaction, a plot of concentration against time will produce a straight line whose slope is equal to -K and the half-life of the reactant is equal to % Co/K where Co is the initial concentration of the reactant. 

First-Order, Second-Order, and Zero-Order Reactions Reaction Order Reaction Half-Life... 

Thus, if a zero-order reaction begins with a high reactant concentration, it has a longer half-life than if it begins with a low reactant concentration. Table 16.4 summarizes the essential features of zero-, first-, and second-order reactions. 

Why didn t I tell you about half lives in the zero order reaction For a very simple reason Half lives only work with first order reactions. In all other reactions the half life is dependent on the initial amount and therefore is not a constant, like it is in a first order reaction. 

One concludes that a zero-order reaction in a biofilm either becomes a bulk zero-order reaction or a half-order reaction—depending on the characteristics of the biofilm (/cgf, S, D ff) and on the S concentration at the L S interface. The half-order reaction (see Equ. 4.87) with... 

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