Rate constant half-life

For a number of years, computers have been successfully utilized in pharmacokinetics to 1) fit blood-level data to the appropriate model (single, two, or multiple compartments) and to calculate model parameters, such as absorption rate constant, elimination rate constant, half-life, and volume of distribution 2) evaluate... 

Order Rate equation Differentiai form Integrated form Units of rate constant Half-life... 

Current density (A cm" ) Rate constant Half-life tl 2 (h)... 

The pharmacokinetics (elimination rate constant, half-life, AUC) of a single 400-mg dose of erythromycin ethyl succinate were not significantly altered by a single 1-g dose of sucralfate in 6 healthy subjects. It was concluded that the therapeutic effects of erythromycin are unlikely to be affected by concurrent use. ... 

HOW TO DETERMINE RATE CONSTANTS HALF-LIFE OF A FIRST-ORDER REACTION... 

We next look for a constant half-life, indicative of a first-order reaction. The initial concentration of 0.88 M decreases to one half of that value, 0.44 M, during the first 100 s, indicating a 100-s half-life. The concentration halves again to 0.22 M in the second 100 s, another 100-s half-life. Finally, we note that the concentration halves also from 0.62 M at 50 s to 0.31 M at 150 s, yet another 100-s half-life. The rate is established as first-order. 

Amino Acids Amino acids that enter the liver follow several important metabolic routes (Fig. 23-14). (1) They are precursors for protein synthesis, a process discussed in Chapter 27. The liver constantly renews its own proteins, which have a relatively high turnover rate (average half-life of only a few days), and is also the site of biosynthesis of most plasma proteins. (2) Alternatively amino acids pass in the bloodstream to other organs, to be used in the synthesis of tissue proteins. (3) Other amino acids are precursors in the biosynthesis of nucleotides, hormones, and other nitrogenous compounds in the liver and other tissues. 

Two commonly used properties of first-order kinetics are A plot of logarithm of concentration t>. time is a straight line and there is a constant half life. Thus, each time half life is treated as a constant or a straight line is drawn on semilog paper, one is assuming that first-order kinetics apply. The mathematical expressions appropriate to this rate law are given below ... 

C is correct. A first order reaction has a constant half life. In the first 15 minutes, 16 out of 33 white dots (compound X) turned black, so 15 minutes represents approximately one half life. In the next 15 minutes, the second half life, half of the remaining 17 white dots should turn black. This represents choice C where there are 9 white dots left. Once you identify that 15 minutes is the half life, you should be able to eliminate answer A because there is no change and answer choice B and D because there are very few dots left. Even if you didn t know that a first order reaction has a constant half life, you should know that the reaction will be proportional to the concentration of white dots. In choice B and D, the rate of the reaction hasn t changed in the second 15 minutes even though the concentration of white dots has been reduced after the first 15 minutes, so this can t be right. 

The Cpep group, formed from the enol ether, has a rate of hydrolysis that is only 3.73 times slower at pH 3.75 than at pH 0.5. It is more stable than the Fpmp group at pH 0.5 and yet over twice as labile at pH 3.75. It has a nearly constant half-life between pH 0.5 and 2.5. ... 

When there is a constant source of a reacting chemical species in the water column or at its boundaries (e.g., water-air and/or water-sediment interface) then, by a rule of thumb, a steady-state may be attained within a period of time equal to a few half-lives of the species. In detail, a steady-state concentration is attained after infinitely long time. The time required for the concentration to come close to the steady-state value at any point in the water column depends on its distance from the source, transport properties of the medium (i.e., its diffu-sivity and distribution of advective velocities), and the rates of the reactions removing the species from the water. A concentration of 95% of a steady-state value may be arbitrarily taken as sufficiently close to a steady-state and indicating that the transient state has effectively come to an end. The time required to attain this concentration level (i.e., when C = 0.95C ) at some point of a concentration-depth profile will be referred to as the time to steady-state. By way of generalization, a chemical species with a constant half-life would attain a steady-state concentration at any point in the water column sooner when the distance... 

Consider two reactions. Reaction (1) has a constant half-life, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these ohserrations ... 

A quantity that has proved useful for comparing rates of different reactions is the half-life, or half-period. The half-life of a given reactant is the time that it takes for half of it to be consumed during the reaction. The way in which the half-life depends on reactant concentrations varies with the order of the reaction for the special case of a first-order reaction there is no dependence of half-life on reactant concentration. For a reaction of any order the half-life is inversely proportional to the rate constant half-lives are therefore useful in giving an inverse measure of the rate of a reaction and can be used for comparing reactions of different orders. 

The calculated half-life of 1 mol % (1.5 wt %) of pure gaseous ozone diluted with oxygen at 25, 100, and 250°C (based on rate constants from Ref. 19) is 19.3 yr, 5.2 h, and 0.1 s, respectively. Although pure ozone—oxygen mixtures are stable at ordinary temperatures ia the absence of catalysts and light, ozone produced on an iadustrial scale by silent discharge is less stable due to the presence of impurities however, ozone produced from oxygen is more stable than that from air. At 20°C, 1 mol % ozone produced from air is - 30% decomposed ia 12 h. 

The hydration reaction has been extensively studied because it is the mechanistic prototype for many reactions at carbonyl centers that involve more complex molecules. For acetaldehyde, the half-life of the exchange reaction is on the order of one minute under neutral conditions but is considerably faster in acidic or basic media. The second-order rate constant for acid-catalyzed hydration of acetaldehyde is on the order of 500 M s . Acid catalysis involves either protonation or hydrogen bonding at the carbonyl oxygen. 

If the decomposition reaction follows the general rate law, the activation energy, heat of decomposition, rate constant and half-life for any given temperature can be obtained on a few milligrams using the ASTM method. Hazard indicators include heats of decomposition in excess of 0.3 kcal/g, short half-lives, low activation energies and low exotherm onset temperatures, especially if heat of decomposition is considerable. 

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

Suppose that Cy = 0, Cz = 0, as is often the case. Then the final product concentrations are found by setting f = < in Eqs. (3-12) and (3-13) we obtain Cy = ( ki/k and c = c /Ji lk. The half-life for the production of Y is then given by Eq. (3-12), setting Cy = Cyl2 when t = t i. We find ha = In Hk, and the same result is obtained for product Z. Thus, the products are generated in first-order reactions with the same half-life, even though they have different rate constants. 

No hydration could be detected in 1,4,5-triazanaphthalene. However, the cation of the 2-hydroxy derivative had been shown to hydrate in the 3,4-position, and the ratio of the hydrated to the anhydrous forms is 16, The hydrate of the neutral species is unstable but has a half-life of 6 min at pH 7, which permits easy measurement of the ionization and rate constants. ... 

Calculate the rate constant and the half-life for the reaction at 25°C. 

Strategy First (1), calculate the rate constant, knowing that the half-life is 5730 y. Then (2) find t, using the equation In (A0/A) = kt. 

Pharmacokinetics. Figure 1 Main pharmacokinetic processes and parameters Half-life (T1/2), volume (Vd), elimination rate constant (Ke), and clearance (Cl). 

The half-time (or half-life) of the reaction is independent of [A]o. The reciprocal of the rate constant, t = l/k, is referred to as the lifetime or the mean reaction time. In that time [A] falls to l/e of its initial value. The pharmaceutical industry refers to the shelf life or t90, the time at which [A]/[A]o reaches 0.90. Both t and t90 are also independent of [A]o. 

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