Zero-order reactions half-life

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 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. 

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. 

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 ... 

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. 

The mechanism and scope of rare-earth metal-catalyzed intramolecular hydrophosphination has been studied in detail by Marks and coworkers [147,178-181]. The hydrophosphination of phosphinoalkenes is believed to proceed through a mechanism analogous to that of hydroamination. The rate-determining alkene insertion into the Ln-P bond is nearly thermoneutral, while the faster protolytic o-bond metathesis step is exothermic (Fig. 22) [179,181]. The experimental observation of a first-order rate dependence on catalyst concentration and zero-order rate dependence on substrate concentration are supportive of this mechanism. A notable feature is a significant product inhibition observed after the first half-life of the reaction. This is apparently caused by a competitive binding of a cyclic phosphine to the metal center that impedes coordination of the phosphinoalkene substrate and, therefore, diminishes catalytic performance [179]. 

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. 

Derive expressions for the half-life of zero-, first-, and second-order reactions using the integrated rate law for each order. How does each half-life depend on concentration If the half-life for a reaction is 20. seconds, what would be the second half-life assuming the reaction is either zero, first, or second order ... 

If the half-life for a reaction is 20. seconds, what would be the second half-life, assuming the reaction is either zero, first, or second order ... 

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. 

CO)7 in the presence of substantial concentrations of CO to yield HCo(CO>4 and Rh4(CO)i2 [91]. Importantly, the hydrogen activation kinetics are zero order in CO - no dissociation step is needed prior to H2 oxidative addition [92]. The typically observed half-life of the reaction in the range of 250-293 K is 1-2 min which corresponds to the mixing time of the reagents used. 

The half-life period 1- /2 for zero-order reaction is... 

The concept of half-Ufe is applied to first-order reactions, because it is related directly to the reaction rate coefficient The half-life of the reaction is the time required for the reagent concentration be reduced to half of its initial value. For a reaction of zero order, ti/2 = [A]o/(2A ) for a first order reaction, h/2 = (In 2)/A and for a reaction of second order, A-tA = C, h/2 = l/(A [A]o). Thus, the half-Ufe of a first-order reaction is independent of the reagent initial concentration. 

Equation (14.8) has the form of a linear equation. As Figure 14.11 shows, a plot of [A], versus t gives a straight line with slope = -k and y intercept = [A]q. To ealculate the half-life of a zero-order reaction, we set [A], = [A]o/2 in Equation (14.8) and obtain... 

Zero-Order Reactions In contrast to the half-life of a second-order reaction, the... 

For zero-order reactions, the half-life is dependent upon the initial concentration of the reactant. However, in contrast to the second-order reaction, as a zero-order reaction proceeds, each half-life gets shorter. 

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