Units third-order rate constant

What are the units of first-order, second-order, and third-order rate constants ... 

We can recognize that because kl and k2 have respectively the units of first-and third-order rate constants, the ratio (k2/k1)112 has the units of concentration. (For the data in Table 2.1 it has the value 2 x 10-5 moldm-3.) This quotient also turns out to be a sensible reference concentration, offering a natural scale on which to measure concentrations in this model. Some concentrations may be judged as being small compared with (k2/kl)u2,... 

We must note that kl is effectively a third-order rate constant, with units of (concentration)-2 (time)-1. Thus multiplying by al and then taking the inverse gives a chemical timescale... 

Energy Levels and Transition Probabilities of Some Atom of Photochemical Interest, 363 Conversion Factors for Absorption Cofficients, 373 Conversion Factors for Second Order Rate Constants, 37 1 Conversion Factors for Third Order Rate Constants, 374 Conversion from Pressure to Concentration Units, 375 Enthalpies of Formation of Atoms at 1 atm and 0°K in 11 . Idea Gas State, 375... 

Note. The units of k2 are those for a third order rate constant, consistent with the contribution from the SO4- catalysis being... 

The dimensions of a third-order rate constant in pressure units are... 

Note All second-order rate constants mentioned in this articie have units of cm molecule s third-order rate constants are in cm molecule- s . Strictly, to correlate with cm> mol s, second-order rate constants should have units cm s > b ause L = 6.02 x I0>>mol however, the expressions more familiar to kineticists have been retained, in I ine with Volume 1. 

If the rate laws are expressed with (a) concentrations in numbers of molecules per cubic meter (molecules m" ) and (b) pressures in kilopascals, what are the units of the second-order and third-order rate constants ... 

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. 

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. 

The constant k in the rate equation is known as the rate constant and the units of the rate constant vary depending on the overall order of the reaction. Suppose that a reaction is third order overall. Its rate equation could take the form rate = k[A] [B] ... 

This is third order, but the quoted observed rate constants are given in terms of a second order rate constant, as indicated by the units, mol-1 dm3 s 1. The standard procedure in reactions of the type being considered is to hold the ligand in excess. That this is the case is confirmed by the question asking what would happen at high and low concentrations of ligand. 

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 ... 

Use times expressed in seconds to give the units of the rate constant for reactions that are overall (a) first order (b) second order (c) third order (d) of order Ij. 

Consider the thermolysis of compound 58 to 59 (equation 6.41). Experimental temperatures and first-order rate constants determined at those temperatures are shown in the first two columns of Table 6.2. Note that the second column is labeled "k x 10 (s )." This means that the experimental rate constants have units of s and that the numerical values were multiplied by 10 for the convenience of listing in the table. Therefore, the observed rate constant at 324.8°C is 1.27 x 10- s . The third column lists the inverse of the reaction temperature in K. As an example, the inverse of (273.15 -I- 324.8) is 0.001672. The fourth column is the natural logarithm of the rate constant. For example. In 0.00127 is -6.669. Plotting the parameters in the second two columns produces Figure 6.18. The slope of the best-fit line through the data points is —23295, which equals —Eg/R. Multiplying the slope by the value of —R therefore gives an Eg of 46,286 cal/mol = 46.3 kcal/mol. The value of In A is 32.3. Traditionally, chemists report values of... 

HzQ = hydroquinone. Third-order rate law incorporating [HO"l term. Value of 13.4 may be obtained depending on mechanistic interpretation. < Units of rate constant are mol 1- s since a term in [H+J is involved. 

The units for the rate constant of a reaction depend on whether the reaction is first, second or third order overall. For example, in a first-order reaction ... 

Note that the units of this rate constant are different from those for the rate constant we calculated for the F2-CIO2 reaction and the bromine reaction. In fact, the units of a rate constant depend on the overall order of the reaction. Table 14.4 compares the units of the rate constant for reactions that are zeroth-, first-, second-, and third-order overall. 

According to the conditions of the problem, time (t) Is In minutes. Therefore, the units of the rate must be Mmin The right-hand side of the rate law contains a product of three concentrations, so it shows third-order behavior overall. This gives concentration units of. This requires units of M min for the rate constant ... 

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

For solution-phase reactions, we use concentration units of mol L, with units for the corresponding rate constants of L mol 1 s 1 (second order) and L2 mol 2 s-1 (third order). 

The simple copolymer model is a first-order Markov chain in which the probability of reaction of a given monomer and a macroradical depends only on the terminal unit in the radical. This involves consideration of four propagation rate constants in binary copolymerizations, Eqs. (7-2)-(7-4). The mechanism can be extended by including a penultimate unit effect in the macroradical. This involves eight rate constants. A third-order case includes antepenultimate units and 16 rate coefficients. A true test of this model is not provided by fitting experimental and predicted copolymer compositions, since a match must be obtained sooner or later if the number of data points is not saturated by the adjustable reactivity ratios. 

For this type of reaction, the rate laws corresponding to a zero-, first-, second-, third-order reaction, together with typical units for the corresponding rate constants, are ... 

For first-order reactions in closed vessels, the half-life is independent of the initial reactant concentration. Defining characteristic times for second- and third-order reactions is somewhat complicated in that concentration units appear in the reaction rate constant k. Integrated expressions are available in standard references (e.g., Capellos and Bielski, 1980 Laidler, 1987 Moore and Pearson, 1981). 

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