Rate constants zero-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. 

Because the general form of the units of rate constants is (time) (concentration)1 , the unit of the rate constant of a zero-order reaction is (time) 1(con-centration)1. The rate of zero-order reaction is independent of the concentration of the reactant, which is often encountered in heterogeneous reactions on the surface such as activated carbon adsorption. 

Keeping the factors such as pH, temperature and enzyme concentration at optimum levels, if the substrate concentration is increased, the velocity of the reaction recorded a rectangular hyperbola. At very low substrate concentration the initial reaction velocity (v) is nearly proportional to the substrate concentration (first order kinetics). However, if the substrate concentration is increased the rate of increase slows down (mixed order kinetics). With a further increase in the subshate concentration the reaction rate approaches a constant (zero order-reaction where velocity is independent of substrate concentration). 

For first-order reactions, the plots were straight lines of slope -kQ /2.303, where is the first-order rate constant. Mixed order reactions gave curves on both the zero and first-order plots. 

When the product of reaction does not prove a barrier to further chemical change, the rate is constant, zero-order, and the weight of producl is proportional to time,... 

Thus, 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 ). 

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. 

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

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. 

The rate of a ZERO-ORDER REACTION does not change as the substrate concentration changes. As a result, a plot of substrate concentration against time is a straight line (the velocity is constant with time). 

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 We first begin by looking for a constant rate, indicative of a zero-order reaction. If the rate is constant, the concentration will decrease by the same quantity during the same time period. If we choose a 25-s time period, we note that the concentration decreases (0.88 M-0.74 M =)0.14 M during the first 25 s, (0.74 M-0.62 M =)0.12 Mduring the... 

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. 

There are two limiting cases of Michaelis-Menten kinetics. Beginning from Eq. (1) at high substrate excesses (or very small Michaelis constants) Eq. (4 a) results. This corresponds to a zero-order reaction with respect to the substrate, the rate of product formation being independent of the substrate concentration. In contrast, very low substrate concentrations [26] (or large Michaelis constants) give the limiting case of first-order reactions with respect to the substrate, Eq. (4b) ... 

If a reaction that must be investigated follows a reaction sequence as in Scheme 10.1, and if the reaction order for the substrate equals unity, it means that (with reference to Eq. (4 b)), the observed rate constant (k0bs) is a complex term. Without further information, a conclusion about the single constants k2 and fCM is not possible. Conversely, from the limiting case of a zero-order reaction, the Michaelis constant cannot be determined for the substrate. For particular questions such as the reliable comparison of activity of various catalytic systems, however, both parameters are necessary. If they are not known, the comparison of catalyst activities for given experimental conditions can produce totally false results. This problem is described in more detail for an example of asymmetric hydrogenation (see below). 

At all temperatures the initial rate R0, was proportional to the first power of the monomer concentration for the zero order reactions this applied to the constant rate which prevails throughout the reaction ... 

The differential rate equations, corresponding integral rate equations and rate constants for various reactions (having order zero to three) under different sets of conditions are summarized in Table 1.1. 

To estimate a value of L, we assume that the sum of and k, both rate constants for the reaction of adsorbed BD, can be approximated by a single surface rate constant. This approximation is justified if we do indeed observe an appreciable amount of N and Q in the product. Using zero-order TST (that is, using Eq. (10) for Step 5 of Table I), we then obtain from Eq. (71)... 

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