First-order reaction half-life

Half-Lives for First-Order Reactions Half-life expression... 

Model concentration of a chemical species constant (CG) at one boundary (z = h). Transport through the water column by eddy diffusion (K), and removal by first order reaction (half-life t). The other boundary of the water column (z = 0) is impermeable to the chemical species. Time to steady-state at the impermeable boundary shown for different values of dimensionless quotient h/ y/ (Kr). Equations 39y 43. 

First-order reactions, half-life (key equations 22.3, 22.4), p. 643 Second-order reactions, half-life (key equations 22.7, 22.8), p. 645... 

Finally, there is a very popular concept connected to first-order reactions half-life. The half-life of a first-order reaction is the amount of time necessary for half of the original amount to react. We can use equation 20.14 to derive a simple expression for the half-life, ti/2. 

First-Order Reaction Half-Life From the deiinilion of half-life, and from the integrated rate law, we can derive an expression for the half-life. For a first-order reaction, the integrated rate law is ... 

For a first-order reaction, half-life is related to the rate constant by the expression ... 

Notice that the first order reaction half-life is unique in having no dependence on the initial concentration, [A]q. These half-life equations highlight a means for determining reaction order. If t is determined for several different initial concentrations, [A]q, then the data can be used to determine if x varies linearly with [A]q as in Equation 6.25 or inversely as in Equation 6.27, or if it is independent as in Equation 6.26. Once the order of the reaction is determined, the measurement of t and [A]q means that the value of the rate constant, k, is known via one of these three equations or by a corresponding equation for a higher order reaction. 

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

PROBABLE FATE photolysis . C-Cl bond photolysis can occur, not important in aquatic organisms, photooxidation half-life in air 9,24-92.4 hrs, reported to photodegrade in water in spite of the lack of a photoreactive center oxidation-, not an important process hydrolysis . very slow, not important, first-order hydrolytic half-life 207 days, reaction with hydroxyl radicals in atmosphere has a half-life of 2.3 days volatilization may be an important process, however, information is contradictory, volatilization half-life from a model river 6 days, half-life from a model pond considering effects of adsorption 500 days, slow volatilization from water is expected with a rate dependent upon the rate of diffusion through air sorption important for transport to anaerobic sediments biological processes biodegradation is important occurs slowly in aerobic conditions, occurs quickly and extensively in anaerobic conditions... 

PROBABLE FATE photolysis-, aqueous photolysis is not expected to be important, reaction with photochemically produced hydroxyl radicals has a half-life of 13.44 hr, direct photolysis is not expected to be important since it should not adsorb wavelengths >290 nm oxidation photooxidation is not expected to be important, photooxidation only in atmosphere, photooxidation half-life in air 9.65 hrs-4.02 days hydrolysis very slow, maybe significant, hydrolysis of carbon-chloride bonds, release to water results in hydrolysis with a half-life of 40 days when released to soil, it may hydrolyze hydrolyzed slowly in aqueous dimethylformamide at pH 7, first-order hydrolytic half-life 22yrs volatilization expected to volatilize if released to water, volatilization half-lives from lakes, rivers, and streams 3.5, 4.4, and 180.5 days respectively sorption not an important process biological processes biodegrades in water after several weeks of acclimation, biodegradation not important under natural conditions, no bioaccumulation noted... 

PROBABLE FATE photolysis could be important, photooxidation half-life in water 54.1-541 days, direct photolysis in the stratosphere may occur, but is insignificant in the troposphere, reaction with photochemically produced hydroxyl radicals yields a half-life of 1.45 yrs oxidation atmospheric photooxidation by hydroxyl radicals to COBT2 is relatively rapid hydrolysis too slow to be important, first-order hydrolytic half-life 687 yrs volatilization volatilization has been demonstrated, could be an important transport process, volatilization from moist soil surfaces expected to occur sorption no information is available biological processes slight potential for bioaccumulation/metabolization is known to occur in some organisms other reactionsAnteractions possibly produced by halogen reaction... 

PROBABLE FATE photolysis could be important in aqueous environment, in the stratosphere, photodissociation occurs to eventually form phosgene as the principal product oxidation no information available, in troposphere it exhibits an extremely slow rate of reaction with hydroxyl radicals, photooxidation half-life in air 1.8-18.3 yrs hydrolysis first-order hydrolytic half-life 7000 yrs based on a rate constant of 4.8xl0 mol s pH 7 and 25°C vola-... 

PROBABLE FATE photolysis, sensitized process may be important, reacts in the vapor phase with photochemically produced hydroxyl radicals at an estimated half-life of 6.2 hr, suggesting that this reaction is the predominate chemical removal process oxidation photooxidation half-life in air 5.2-51.7 hrs hydrolysis not an important process, first-order hydrolytic half-life >197,000 yrs volatilization probably an important process, can volatilize significantly from soil surfaces from which it is sprayed, particularly moist soil surfaces, volatilization half-life from a model pond, river, and lake is 18-26,3.6-5.2, and 14.4-20.6 days respectively sorption probably an important process biological processes bioaccumulation is an important process... 

PROBABLE FATE photolysis, could be important, only identifiable transformation process if released to air is reaction with hydroxyl radicals with an estimated half-life of 8.4 months oxidation, has a possibility of occurring, photooxidation half-life in air 42.7 days-1.2 yrs hydroiysis too slow to be important, first-order hydrolytic half-life 275 yrs voiatilization likely to be a significant transport process, if released to water or soil, volatilization will be the dominant environmental fate process, volatilization half-life from rivers and streams 43 min-16.6 days with a typical half-life being 46 hrs sorption adsorption onto activated carbon has been demonstrated bioiogicai processes moderate potential for bioaccumulation, biodegradation occurs in some organisms, in aquatic media where volatilization is not possible, anaerobic degradation may be the major removal process other reactions/interactions may be formed from haloform reaction after chlorination of water if sufficient bromide is present... 

PROBABLE FATE photolysis no direct photolysis, indirect photolysis too slow to be environmentally important, photooxidation half-life in water 2.4-12.2 yrs, photooxidation half-life in air 7.4 hrs-2.5 days oxidation not important, reaction with photochemically produced hydroxyl radicals gives a half-life of 18 hrs hydrolysis hydrolysis (only in surface waters) believed to be too slow to be important, first-order hydrolytic half-life 10 yrs volatilization not expected to be an important transport process sorption sorption onto particulates and com-plexation with organics are dominant transport processes biological processes bioaccumulated in many organisms, biodegraded rapidly in natural soil, some biotransformation, all biological processes are important fates... 

PROBABLE FATE photolysis-, direct photolysis is not significant, photodissociation in stratosphere to chloroacetyl chloride oxidation photooxidation in water expected to be slow primarily removed in air by photooxidation degraded in atmosphere by reaction with hydroxyl radicals, half-life of 1 month and 1.9% loss/12 hr sunlit day products of photooxidation CO and HCl oxidation half-life 1.5 weeks-4 months hydrolysis not significant first-order hydrolytic half-life 1.1 yr volatilization high vapor pressure causes rapid volatilization, major transport process, half-life 30 min 25°C evaporation primary removal from water half-life from 1 ppm solution 25°C, still air, and an avg. depth of 6.5 cm 28 min., evaporation from water 25 °C of 1 ppm solution 50% after 29 min. and 90% after 96 min. 

PROBABLE FATE photolysis, possible, but cannot compete with microbial biodegradation oxidation, any oxidation which occurs is too slow to be important hydrolysis not an important process, first-order hydrolytic half-life 3.4 yrs volatilization not expected to be an important process sorption sorption will not remove significant amounts biological processes rapid microbial degradation is the principal fate of 2,4-DCP other reactions/interactions chlorination of water may produce further chlorination of 2,4-DCP... 

PROBABLE FATE photolysis-, photochemical reactions in aqueous media are probably unimportant, slow decomposition in the troposphere in the presence of nitrogen oxides is possible, appreciable photodissociation may occur in stratosphere, photooxidation half-life in air 19.1-191 days oxidation-, probably unimportant, in troposphere, oxidation by hydroxyl radicals to CO2, CO, and phosgene is important fate mechanism hydrolysis not an important fate process, first-order hydrolytic half-life 704 yrs volatilization due to high vapor pressure, volatilization to the atmosphere is rapid and is a major transport process sorption sorption to inorganic and organic materials is not expected to be an important fate mechanism biological processes bioaccumulation is not expected, biodegradation may be possible but very slow compared with evaporation... 

PROBABLE FATE photolysis-, no data for rate of photolysis in aquatic environment oxidation-, in aquatic systems not expected to be important fate, photooxidation in troposphere is probably the predominant fate hydrolysis expected to be slow, neutral aqueous hydrolysis half-life 25 °C >50 years, first-order hydrolysis half-life 37 years pH 7 volatUiz/ttion primary transport process, volatilization from soil will occur biological processes NA evaporation from water 25 °C of 1 ppm solution is 50% after 21 min and 90% after 102 min release to water primarily through evaporation (half-life days to weeks) rate of evaporation half-life from water 21 min photodegrades slowly by reaction with hydroxyl radicals, half-life 24-50 days in polluted atmosphere to a few days in unpolluted atmospheres will be removed in rain... 

PROBABLE FATE photolysis reported in experiments, but environmental significance is unknown, aqueous photolytic half-life 4 days, release to the environment can decrease due to photolysis and reaction with hydroxyl radicals oxidation too slow to be an important process, photooxidation half-life in water 84.5 days, in air 5.1-51.4 days hydrolysis not an important process first-order hydrolytic half-life >8x10 yrs volatilization not an important process, may contribute to losses at the surface of the soil sorption high potential for sorption by organic materials, rate is unknown biological processes biodegradation very important, but exact rate uncertain due to variations between data photomineralization may contribute to losses at the surface of the soil... 

As H O is present in great excess relative to organic compounds, the rates of these reactions are usually considered of pseudo-first order and half-life independent on concentration. 

In a successive reaction, consisting of to irreversible first-order stages, half-life time of an initial reactant equals to the time from the start of the reaction to the moment intermediate s concentration reaches its maximum. What rate constants ratios make such situation possible Initial concentrations of the intermediate and the product are zero. 

Because the reaction is first order, the half-life is given by Equation 13.19. Substitute the value of k into the expression and calculate ty2- 0.693 It... 

First Order Rate Half life Percent reaction ... 

Half-life is constant for first-order reactions but not constant for zero-order or second-order reactions. For a zero-order reaction, half-life decreases with decreasing reactant concentration. For a second-order reaction, half-life increases with decreasing reactant concentration. 

II [Anisole] = 2 x lo mol i" first-order reactions. For the experiment using pure nitric acid the half-life was about i min, but for that using fuming nitric acid reaction was complete in < 30 s. 

Expts. 16, //. Pure nitric acid was used. In expt. 16 the reaction was of the first order in the concentration of the aromatic, and of half-life 1-1-5 minutes (similar to that of toluene under the same conditions). In expt. 17 the sodium nitrate slowed the reaction (half-life c. 60 min). About 2 % of an acetoxylated product was formed (table 5-4). 

The half-life tvi is defined to be the time required for the reactant concentration to decay to one-half its initial value. To find tvi for a first-order reaction we use Eq. (2-6) with the substitutions Ca = c°/2 and t = finding... 

Find a relationship between the half-life tn2 and the lifetime t of a first-order reaction. 

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. 

The analysis of Example 11.3c reveals an important feature of a first-order reaction The time required for one half of a reactant to decompose via a first-order reaction has a fixed value, independent of concentration. This quantity, called the half-life, is given by the expression... 

Sucrose (Ci2H22On) hydrolyzes into glucose and fructose. The hydrolysis is a first-order reaction. The half-life for die hydrolysis of sucrose is 64.2 min at 25°C. How many grams of sucrose in 1.25 L of a 0.389 Af solution are hydrolyzed in 1.73 hours ... 

At high temperatures, the decomposition of cyclobutane is a first-order reaction. Its activation energy is 262kJ/mol. At 477°C, its half-life is 5.00 min. What is its half-life (in seconds) at 527°C ... 

We already know that the higher the value of k, the more rapid the consumption of a reactant. Therefore, we should be able to deduce a relation for a first-order reaction that shows that, the greater the rate constant, the shorter the half-life. 

FIGURE 13.12 Thu ohange in concentration of the reactant in two first-order reactions plotted on the same graph When the first-order rate constant is large, the half-life of the reactant is short, because the exponential decay of the concentration of the reactant is then fast. 

The concentration of the reactant does not appear in Eq. 7 for a first-order reaction, the half-life is independent of the initial concentration of the reactant. That is, it is constant regardless of the initial concentration of reactant, half the reactant will have been consumed in the time given by Eq. 7. It follows that we can take the initial concentration of A to be its concentration at any stage of the reaction if at some stage the concentration of A happens to be A], then after a further time tv2, the concentration of A will have fallen to 2[AJ, after a further tU2 it will have fallen to [A], and so on (Fig. 13.13). In general, the concentration remaining after n half-lives is equal to (t)" A 0. For example, in Example 13.6, because 30 days corresponds to 5 half-lives, after that interval [A ( = (j)5 A]0, or [A]0/32, which evaluates to 3%, the same as the result obtained in the example. 

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