Units of the Rate Constant

rate = k [reactant]2 describes a second order reaction where 

rate = [reactant]0 = k describes a zero order reaction where 

These depend on the order of the reaction and are worked out as follows. First order reaction  

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The units of the rate constant depend upon the overall reaction order. 

We can reach two useful conclusions from the forms of these equations First, the plots of these integrated equations can be made with data on concentration ratios rather than absolute concentrations second, a first-order (or pseudo-first-order) rate constant can be evaluated without knowing any absolute concentration, whereas zero-order and second-order rate constants require for their evaluation knowledge of an absolute concentration at some point in the data treatment process. This second conclusion is obviously related to the units of the rate constants of the several orders. 

This equation is known as the rate law for the reaction. The concentration of a reactant is described by A cL4/df is the rate of change of A. The units of the rate constant, represented by k, depend on the units of the concentrations and on the values of m, n, and p. The parameters m, n, and p represent the order of the reaction with respect to A, B, and C, respectively. The exponents do not have to be integers in an empirical rate law. The order of the overall reaction is the sum of the exponents (m, n, and p) in the rate law. For non-reversible first-order reactions the scale time, tau, which was introduced in Chapter 4, is simply 1 /k. The scale time for second-and third-order reactions is a bit more difficult to assess in general terms because, among other reasons, it depends on what reactant is considered. 

C15-0009. What are the units of the rate constant for the reaction of hydroxide anions with hydronium cations, which proceeds by the single collision shown in Section 15-1 ... 

Experiments show that this reaction is first order in H2 and one-half order in Br2. What is the rate law, what is the overall order of the reaction, and what are the units of the rate constant ... 

The units of the rate constant will vary depending on the overall order of the reaction. These units are those of a rate divided by the mth power of concentration, as is evident from equations 3.0.17 and 3.0.18. 

Flere, As is the mineral s surface area (cm2) and k+ is the intrinsic rate constant for the reaction. The concentrations of certain species Aj, which make up the rate law s promoting and inhibiting species, are denoted m , and P- are those species exponents, the values of which are derived empirically. Qg is the activity product for Reaction 16.1 (Eqn. 3.41). In the absence of promoting and inhibiting species, the units of the rate constant are mol cm-2 s-1, and in any case these are the units of the product of k+ and the n term. 

Assuming that at time zero no C or D is present, obtain the rate law for this reaction, stating the value and units of the rate constant in terms of L, mol, s. 

Notice that the units of the rate constant are determined by your calculation. For a first-order reaction, the units are always s . Show why this is the case. What are the units for a second-order reaction ... 

What is the relationship between the units of the rate constant, k, and the overall reaction order ... 

To sum up, the condensed form of expressing the rate can be ambiguous. To eliminate any possible confusion, write the stoichiometric equation followed by the complete rate expression, and give the units of the rate constant. 

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. 

As mentioned before, the unit of the rate constant is (time) 1(concentra-tion)1-". 

Accordingly, we parameterize the rate constants for the 71 isomerization steps in terms of two kinetic parameters, /ilso,b and lsonb. The units of the rate constants are s... 

The units of the rate constants (e.g., seconds, days) will depend on the units of concentration as well as the exponents. Temperature is another important factor that is critical in affecting rate constants. It is well established that temperature increases chemical reaction rates and biological processes—particularly important in estuarine biogeochemical cycles... 

Regardless of the order of the reactions, the rate of reaction has the units of concentration/time (i.e., mole/L sec). The units of the rate constant are dependent on the overall order of the reaction ... 

It is important that you make a distinction between the reaction rate and the rate constant. The biggest distinction is that the reaction rate depends on the concentrations of each reactant (which you can see from the formula), and it will always have the same units, usually M s-1. The rate constant is not affected by concentrations. It maintains the same value as long as temperature is kept constant. The units of the rate constant will also vary according to the order of the reaction. 

If we were to calculate the value of units of the rate constant in the previous example, we could do so with relative ease. Beginning with the equation and rearranging it to solve for k, we obtain the expression ... 

Example Staring from the full rate equation, determine the units of the rate constant k for (a) a zero-order reaction (b) a first-order reaction (c) a second-order reaction (d) a third-order reaction and (e) a half-order reaction. Assume that concentrations are expressed in molar units and time in seconds. 

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