Reciprocal time

Ap Frictional pressure drop Pa CO Characteristic frequency or reciprocal time scale of flow 1/s... 

Notice that for a first-order reaction the rate constant has the units of reciprocal time, for example, min-1. This suggests a simple physical interpretation of k (at least where k is small) it is the fraction of reactant decomposing in unit time. For a first-order reaction in which... 

HO-oxidation of an individual NMHCj produces H02 radicals with a yield aj, and oxidation of the NMHC oxidation product produces H02 in stoichiometric amount The lumped coefficients or yields a and p need not be integers, and represent the effectiveness of a particular NMHCj in producing RO2. and H02 radicals (lumped together as HO2) that will then oxidize NO. to N02 in processes such as R6 and R13, producing one net ozone molecule each. Alternatively, when the NO. concentration is low, peroxyl radicals may form PAN (as in R22) or hydrogen peroxide (as in R33) which are other oxidant species. In this formulation, transport is expressed by an overall dilution rate of the polluted air mass into unpolluted air with a rate constant (units = reciprocal time dilution lifetime=1// ). This rate constant includes scavenging processes such as precipitation removal as well as mixing with clean air. 

Since S/t has units of moles per volume per time and a has units of moles per volume, the rate constant for a first-order reaction has units of reciprocal time e.g., s. The best example of a truly first-order reaction is radioactive decay for example,... 

Observe that aok has units of reciprocal time so that aokt is dimensionless. The grouping OQkt is the dimensionless rate constant for a second-order reaction, just as kt is the dimensionless rate constant for a first-order reaction. Equivalently, they can be considered as dimensionless reaction times. For reaction rates governed by Equation (1.20),... 

This equation has two parameters t, the mean residence time (z = V/F) with dimensions of time and k, the reaction rate constant with dimensions of reciprocal time, applying for a first-order reaction. The concentration of reactant A in the reactor cannot, under normal circumstances, exceed the inlet feed value, Cao and thus a new dimensionless concentration, Cai, can be defined as... 

Note that since the relaxtion time x has units of time, the rate constant must have units of reciprocal time. Thus the rate constant for a first-order reaction give a measure of the frequency, or periodicity, of reaction (i.e., events per unit time). 

The additional concentration term in Equation (A1.23), compared to Equation (A1.8), requires that the rate constant here, koa, have units of reciprocal time, reciprocal molarity (most commonly M 1 s ) in order for the velocity to be expressed in units of molarity per unit time. Equation (A1.23) can be recast in terms of the initial reactant concentrations ... 

Values of A Ln and B are shown in Table l.74-76 It is worth noting that both ALn and A Ln have dimensions of time, while B has dimensions of reciprocal time and C is dimensionless. It is usual to give A factors the units which correspond to the most convenient units of measuring lifetimes. 

We point out that in enzyme kinetics TON is understood as TOF It is also sometimes called the turnover number, because it is a reciprocal time and defines the number of catalytic cycles (or turnovers ) that the enzyme can undergo in unit time, or the number of molecules of substrate that one molecule of enzyme can convert into products in one unit of time. Quotation from [23]. 

The rate constant has the dimensions of reciprocal time and so k can be replaced by a time constant xm. If we now take the exponential of both sides of this expression and rearrange we can obtain an expression for the stress ... 

The equation is not in dimensionless form. Each term has the dimension of reciprocal time. In order to make the equation completely dimensionless, it is necessary to introduce a time parameter. Equation (7.42) contains two such time parameters ... 

Caution is needed regarding the units of kp. Eq. 3.15 gives kp in units of reciprocal time (e.g., d ). This is a result of expressing Cs on a volume basis. In the case that Cs is expressed on an SPMD mass basis, kp has units of volume per mass per time (e.g., mL g d ). An uptake rate constant given in these units can be converted to kp in d by multiplying with the SPMD density (0.91 g mL ), as further discussed in Appendix A. 

In contrast to a solid boundary, the damping of the turbulence at the liquid-fluid interface can also be affected by the surface tension a of the liquid. In other words, the state of turbulence near that interface is dependent not only on a characteristic velocity u0, on the viscosity r of the liquid and its density p, but also on the surface tension [Pg.82]

This relationship is transformed into an equality by introduction of a proportionality constant, 1, which represents the probability that an atom will decay within a stated period of time. The numerical value of A is unique for each radionuclide and is expressed in units of reciprocal time. Thus, the equation describing the rate of decay of a radionuclide is... 

In this reaction, the rate depends only on the concentration of S. This is called a first-order reaction. The factor A is a proportionality constant that reflects the probability of reaction under a given set of conditions (pH, temperature, and so forth). Here, A is a first-order rate constant and has units of reciprocal time, such as s "1. If a first-order reaction has a rate constant k of 0.03 s-1,... 

The constant kcat is a first-order rate constant and hence has units of reciprocal time. It is also called the... 

Equation (15-11) shows that, if the half-life of a given first-order reaction is known, it is a simple matter to find the corresponding rate constant, and vice versa. Equation 15-11 also emphasizes the fact that the constant are simply reciprocal time sec-1, min-1, hr-1,... 

The units ofk are important. As stated earlier, tlfthdnSSlsQSf Fft rs order reaction are reciprocal time sec-1, min- hr-1,... 

The proportionality constant (the rate constant, k) is diffei t)fcSne MiH6 r tope, and has the units of reciprocal time (sec-1, min-1, yr ... 

An increase of Av to a constant value was observed in the course of vulcanization of polysulphide rubbers in the presence of sodium dichromate. Rates of vulcanization were determined from the time dependence of Av, as the reciprocal time at which Av reaches the maximum constant value. It is found that the rate of vulcanization linearly increases with the oxidizer concentration37. ... 

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