Reaction zero order

Such reactions are represented according to eq. (2.22) by the differential equation 

The time in which the starting material has decreased to half of its original concentration is called the half-life t,/2- In the case of a reaction of zero order, therefore 

For convenience new dimensionless coordinates are defined using Greek symbols for concentration, degree of advancement, and time normalised by division by the initial concentration qq (called general coordinates)  

No elementary reaction can proceed with a rate law of zero order, since -mechanistically speaking - at least one type of molecule must be involved in any chemical elementary reaction. 

Furthermore, after a finite time (that means at t = 1) a has to become zero. In consequence an overall reaction can only be called zero order during a certain time range. During that time the degree of advancement has to be characterised by x (by a linear combination of x ), since the reactions considered need not necessarily be elementary reactions. 

Zero order reactions are a common feature in a variety of disciplines. For example the elimination of a certain drug from the metabolism might follow a zero order reaction. Another example is related to (again) a bank account - standing orders with money paid in or withdrawn often can be described by zero order kinetics. 

In this chapter I will show, how we can formulate the typical rate equation for a zero order reaction. Using examples I will develop the equations for this kind of reaction. By the end of this chapter you should be able to recognize a zero order reaction and calculate various components of a zero order equation. 

Zero-order reactions are not very common. However, they provide an excellent place to begin because the mathematics are quite straightforward. In a zero-order reaction, the reaction rate is independent of the concentration of the reactant(s). Mathematically, this means 

The reaction is called a zero-order reaction because the concentration of the reactants can be included in the rate expression with zero-order exponents to explicitly convey that the rate does not depend on their concentration (as shown in the equation above). In a zero-order reaction, increasing the concentration of the reac-tant(s) will not speed up the rate of the reaction. The most common zero-order reactions are endothermic high-temperature thermal decomposition reactions, where a large amount of thermal energy is required to break a chemical species apart. In such cases, as long as the temperature is not too high, the available thermal energy controls the rate rather than the concentration of the reactants. 

An example of a zero-order reaction is the reverse Haber process  

Note that this example further illustrates how the reaction order (and hence the rate equation) cannot be determined from a simple inspection of the reaction stoichiometry  

We ve seen that in a first-order reaction the concentration of a reactant A decreases non- which times during the 

The most common type of zero-order reaction occurs when a gas undergoes decomposition on the surface of a solid. If the surface is completely covered by decomposing molecules, the rate of reaction is constant because the number of reacting surface molecules is constant, so long as there is some gas-phase substance left. 

Improbable as a zero-order reaction may seem on the basis of what has been said thus far, let us consider the possibility of this rate equation  

Integration between the limits of c = c° when r = 0 and c = c when t = t gives the integrated zero-order rate equation. 

a zero-order reaction yields a linear plot of c vs. t, the slope being equal to — k. It is evident that a zero-order rate constant has the units of a rate, for example, moles per liter-second (M s ). 

According to our formulation, a reaction rate is said to bo of zero order if the rate of the reaction is independent of the concentrations of the substances participating in the reaction. In that case the rate of change of the concentrations is a constant  

Tablk II.I. Units of Spkcific Rate (Constants for Reactions OF Different Order 

Units of specific moles sec i liters liters liters  

Note This table is based on the adoption of moles/liter for concentration units. More explicitly, the units should include the species involved. Thus for the reaction H2 -f- I2 — 2III, which is experimentally first-order with respect to H2 and first-order with respect to I2, the proper units of A m are 

Since conventional usage has been to avoid identification of moles with species, this is written simply as litcrs/mole-sec. Such abbreviation can, however, lead to occasional confusion, and the nature of the abbreviation should be borne in mind. 

Even though concentration of reactants has been given as one of the factors on which reaction rates depend, there are also cases of reactions that are independent of reactant concentration. In this case, the differential rate law is constant 

a zero-order reaction gives a linear plot of change in concentration as a function of time, with slope equal to -k. The units of this rate constant are identical to those of the rate (e.g. litres per second). As with other reaction orders, we can determine the half-life, which is given by 

Zero-order reactions appear in heterogeneous systems when the snrface of a solid phase is saturated with a reactant, but are also seen in certain homogeneons systems. 

At which times during the reaction would you have trouble distinguishing a zero-order reaction from a first-order reaction  

The kinetics of zero-order type of reaction have a rate which is independent of the concentration of the reaetant(s). Inereasing the eoneentration of the reaeting species will not speed up the rate of the reaetion. Zero-order reactions are typically found when a material that is required for the reaetion to proceed, sueh as a surface or a catalyst, is saturated by the reactants. Hence, the rate law for a zero-order reaction is 

If this differential equation is integrated it gives an equation which is often called the integrated zero-order rate law. 

For zero-order reaction, concentration data versus time are plotted as a straight line. The slope of this linear trend is the negative of the zero-order rate constant k. The half-life of a zero-order reaction is given by the following relationship  

There are some reactions in which the rate of the reaction is independent of the concentration of the reactants but does depend on some other factor, such as the amount of catalyst present. These reactions are termed zero-order reactions, and rate equations can be derived as follows  

In zero-order reactions the amount of product formed varies with time so that the amount of product formed after 20 minutes will be twice that formed after 10 minutes. Reactions that follow zero-order kinetics are quite rare, but they do occur in solid-phase reactions such as release of drug from a pharmaceutical suspension. 

Not all reactions are exothermic. Thermal cracking is an endothermic reaction. Heat is absorbed. Good thing, too. If thermal cracking of crude oil was exothermic, all the earth s crude would by now have turned to coal and natural gas. Delayed cokers, visbreakers, and fluid catalytic cracking units are processes that are primarily endothermic in nature. A delayed coker operates with a zero order reaction. This means the rate of reaction depends on time in the coke drum and the temperature in the coke drum. The composition of the products of reaction have no effect. 

On the other hand, hydrocracking is exothermic. The consumption of hydrogen liberates heat in the hydrocracking reaction. 

In this type of reaction the decomposition proceeds at a constant rate and is independent of the concentrations of any of the reactants. The rate equation is given hy equation (4.6) as 

A plot of the amount remaining (as ordinate) against time (as abscissa) is linear with a slope of kQ (concentration time ). 

Use the results of Example 20-3 and data from Table 20.3 to establish the value of k in the rate law (20.8). 

We can use data from any one of the three experiments of Table 20.3, together with the values m = 1 and n = 2. 

If the rate data in Table 20.3 were based on the disappearance of HgCl2 instead of 2042 , Rj in this setup would be twice as great and k for the general rate of reaction would be based on —5 X A[HgCl2]/Af. Note the units on the rate constant are M 2 min which are appropriate units for a third-order rate constant. Checking the units in an answer is one way to ensure that we have not made any mistakes. 

PRACTICE EXAMPLE B What is the rate of reaction (20.7) at the point where [HgCl2] = 0.050M and [C2O42 ] = 0.025 M  

The rate of decomposition of gaseous acetaldehyde, CH3CHO, to gaseous methane and carbon monoxide is found to increase by a factor of 2.83 when the initial concentration of acetaldehyde is doubled. What is the order of this reaction  

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Eor a pseudo-zero-order reaction a plot of [A]( versus time should be linear with a slope of -k, and a y-intercept of [A]o (equation 13.8). A plot of the kinetic data is shown in figure 13.7. Linear regression gives an equation of... 

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... 

A third method, or phenomenon, capable of generating a pseudo reaction order is exemplified by a first-order solution reaction of a substance in the presence of its solid phase. Then if the dissolution rate of the solid is greater than the reaction rate of the dissolved solute, the solute concentration is maintained constant by the solubility equilibrium and the first-order reaction becomes a pseudo-zero-order reaction. 

The inetabolism of ethyl alcohol may be considered to occur via a zero-order reaction (i.e., its elimination occurs linearly w ith time.) If a person is able to metabolize appro.ximately 10 inL of the alcohol per hour, how long a time period is required to elimimite 8 pints of beer containing 3.2% alcohol Assume that tlie volume of a pint of beer is 530 mL. 

In a zero-order reaction, all the reactant is consumed in a finite time. 

It can readily be shown (Problem 87) that the concentration-time relation for a zero-order reaction is... 

Zero-order reaction First-order reaction Second-order reaction Rate constant... 

The decomposition of A at 85°C is a zero-order reaction. It takes 35 minutes to decompose 37% of an initial mass of282 mg. 

Zero order reaction A reaction whose rate is independent of reactant concentration, 289,295-298, 317q Zinc, 86-87,550 Zn-Cn2+ voltaic cell, 481-485 Zwitterion Form of an amino acid in which there is a separation of charge between the nitrogen atom of the NH2 group (+) and one of the oxygen atoms of the COOH group (—), 623-624... 

Zero-order reactions arc so called This decomposition is an example of a zero-order reaction, a reaction for which... 

FIGURE 13.9 (a) The concentration of the reactant in a zero-order reaction falls at a constant rate until the reactant is exhausted. 

The integrated rate law for a zero-order reaction is easy to find. Because the rate is constant (at k), the difference in concentration of a reactant from its initial value, [A]0, is proportional to the time for which the reaction is in progress, and we can write... 

Express the units for rate constants when the concentrations are in moles per liter and time is in seconds for (-a) zero-order reactions (b) first-order reactions (c) second-order reactions. 

If the reaction order does not change, reactions with n < 1 wiU go to completion in finite time. This is sometimes observed. Solid rocket propellants or fuses used to detonate explosives can bum at an essentially constant rate (a zero-order reaction) until all reactants are consumed. These are multiphase reactions limited by heat transfer and are discussed in Chapter 11. For single phase systems, a zero-order reaction can be expected to slow and become first or second order in the limit of low concentration. 

As given above, the statements that adjust the exponents m and n have been commented out and the initial values for these exponents are zero. This means that the program will fit the data to. = k. This is the form for a zero-order reaction, but the real purpose of running this case is to calculate the standard deviation of the experimental rate data. The object of the fitting procedure is to add functionality to the rate expression to reduce the standard deviation in a manner that is consistent with physical insight. Results for the zero-order fit are shown as Case 1 in the following data ... 

Finally, although rare, we mention the occurrence of zero-order reactions. The special case of a pseudo-zero order reaction arises if a reactant is present in large excess, and the reaction does not noticeably change the concentration of the reactant. The differential and integral rate equations for a zero-order reaction R —> P are... 

The speed of autoxidation was compared for different carotenoids in an aqueous model system in which the carotenoids were adsorbed onto a C-18 solid phase and exposed to a continnons flow of water saturated with oxygen at 30°C. Major products of P-carotene were identified as (Z)-isomers, 13-(Z), 9-(Z), and a di-(Z) isomer cleavage prodncts were P-apo-13-carotenone and p-apo-14 -carotenal, and also P-carotene 5,8-epoxide and P-carotene 5,8-endoperoxide. The degradation of all the carotenoids followed zero-order reaction kinetics with the following relative rates lycopene > P-cryptoxanthin > (E)-P-carotene > 9-(Z)-p-carotene. 

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