Units zero-order rate constant

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 ). 

Figure 149. Temperature and humidity dependence of the tetrahydrate-to-monohydrate transition kinetics for 5-(4-oxo-phenoxy-4//-quinolizine-3-carboxamidc)-tctrazolatc. Here k refers to the apparent zero-order rate constant for the process (time unit h) and V = k/Ps, where P is water vapor pressure. (Reproduced from Ref. 613 with permission.)...

AH) = heat of reaction, Btu/mole of A converted k = zero order rate constant, moles A/ft -sec k = first order frequency factor, moles A/atm-ft -sec A[ = initial moles of A per unit mass of feed o = total moles of feed per unit mass of feed n, = total moles of reacting system per unit mass of feed xa = moles of A converted per unit mass of feed P = pressure, atm... 

It must be a zero order reaction, because the rate constant k = 24 pM per 12 minutes. The typical unit for a zero order rate constant is concentration per time. 

Fig. 62. pH dependence of zero-order rate constant for hydrolysis of TAMe at 25 (TAMe concentration = 0.01 M). Curve A Seegers citrate thrombin, 10/8 TAMe units per milliliter, in 0.15 M KCl. Curve B Parke, Davis thrombin, 1 TAMe unit per milliliter, in 0.15 M KCl. Curve C Parke, Davis thrombin, 1 TAMe unit per milliliter, in 1 Af NaBr. Points D and E Parke, Davis thrombin, 1 TAMe unit per milliliter, in 0.024 and 0.12 M NaBr, respectively, both being 0.15 Af in KCl (Ehren-preis and Scheraga, 1957). 

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. 

Rate = kPx for a first-order reaction of a gas X. What are the units for the rate constants when partial pressures are expressed in torr and time is expressed in seconds for (a) zero-order reactions (b) first-order reactions (c) second-order reactions ... 

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. 

Using concentrations expressed in molarity and time in seconds, what are 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 (e) a half-order reaction ... 

Thus, the physical significance of the first-order rate constant is that it approximates the fraction of the substrate present that is converted to product per small increment of time. A k that is greater than 1 min means that more than 100% of the substrate present at zero time would be utilized in a minute ifv remained constant for a minute. It may be more meaningful to express k values in units that yield numerical values that are less than unity. 

The level of a particular enzyme is I500units/g tissue in the liver of rats on a natural diet. Studies indicate that the Jirst-order rate constant for the degradation of the enzyme is 0.03 min" , (a) Calculate the zero-order rate of enzyme synthesis, (b) When rats are raised on a completely synthetic diet, the steady-state level of the above enzyme decreases to 848 units/g tissue. If the rate of enzyme synthesis is unaffected by diet, what must the new first-order rate constant for... 

Km measurements, where V,nax has units of mass x time-1. The definition of intrinsic clearance as Vmax x Xm-1 should not be confused with the historically prevalent calculation of ksl (the first-order rate constant of decay of concentration in plasma), calculated from kel = Vmax/Xm, where Vmax is the zero-order rate of plasma concentration decay observed at high concentrations and Xmax is the concentration of plasma at half-maximal rate of plasma level decay. 

Unit of the rate constant (Kb) for zero-order elimination of drug... 

The interpretation follows from the limiting case of Equation 4-8. Consider the limiting case of a high reactant concentration which is so high that the catalytic sites are saturated and [5 ] K - Then, the rate equation reduces to = cat[ ]tot and kcat is recognized as a first-order rate constant. If the rate were written per enzyme molecule rather than per unit volume, then the reaction would be of zero order, and kcat would be the rate at saturation (the maximum number of reactant molecules converted per catalytic site per unit time) this is the definition of the turnover frequency. 

In Eq. (26), we have two new parameters, kt and 5 t. These are the first-order rate constant for hole transfer (units of cm s S see following) and the surface recombination velocity, St- In the combined situation of high Ld. high kt, and very low (or zero) St, Eq. (26) collapses to the Gdrtner limit. 

Many students do not realize that it is easier to derive the units of the rate constants for zero-, firsthand second-order reactions than it is to memorize them. 

Each chemical reaction (first or second order) is described by entering two indexes for the reactants and two for the products. (If the reaction is first order, zero is entered in the space reserved for the second species of a second-order reaction.) First-order rate constants are entered in reciprocal seconds. Second-order rate constants are entered in units of M" s Cnorm. 

Thus, 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... 

We have tacitly assumed that the rate constants depend only on the last unit of the chain. In such a situation, the copolymerization is called a Markov copolymerization of first order. The special case (i), r r- = 1, is a Markov copolymerization of order zero. If reactivity also depends on the penultimate unit of the chain, the polymerization is a Markov copolymerization of second order. 

Rate constant units for zero to third order reactions are summarised in the table on the left. 

The best-known exception to exponential kinetics is the elimination of alcohol (ethanol), which obeys a linear time course (zero-order kinetics), at least at blood concentrations > 0.02 %. It does so because the rate-limiting enzyme, alcohol dehydrogenase, achieves half-saturation at very low substrate concentrations, i.e at about 80 mg/L (0.008 %). Thus, reaction velocity reaches a plateau at blood ethanol concentrations of about 0.02 %, and the amount of drug eliminated per unit of time remains constant at concentrations above this level. 

---