Second order meaning

The refers to a nucleophilic substitution process where some nucleophile attacks an electrophile and substitutes for some part of the electrophile. The E refers to an elimination process where the nucleophile attacks an electrophile and causes the elimination of something. The 1 and 2 refer to the order of the reaction. A 1 (first order) means only one molecule determines the rate of the reaction, whereas a 2 (second order) means that a combination of two molecules determines the rate of the reaction. In many cases, two or more of these mechanisms are competing and more than one product may result. 

Second order means that two atoms or molecules have to collide so that the reaction will happen. Obviously, if the concentration of one or both of the reactants is low, the reaction will be slow. Thus, the rate of the reaction is proportional to the concentration of both reactants times each other, and the proportionality constant is the rate constant k. 

Second harmonic generation, described in this chapter, is an example of a second-order process. What does second-order mean in this context What are examples of a first-order (or linear) process ... 

What do the terms closely coupled and second order mean in terms of spin states ... 

This equation is second order, meaning that the errors decrease proportional to Ax once Ax is small enough. The two equations can also be rearranged by neglecting the second-order terms, to obtain two other approximations for the first derivative ... 

The mean fluorescence lifetime is the second order mean ... 

This proportionality constant is called the rate constant (see Chapter 7, Section 7.9). A large rate constant means that the starting material is rapidly converted to product. For a second-order reaction, the rate constant is determined from a plot of time versus a concentration term that includes both starting materials. Formally, the 2 in an 8 2 reaction indicates that it follows second-order kinetics, but a second-order reaction is usually associated with the collision process of the nucleophile with the electrophilic carbon atom. As a practical matter, the fact that the S 2 reaction is second order means that if the reaction is slow, increasing the concentration of the nucleophile will increase the rate of the reaction (the rate constant remains the same). Similarly, increasing the concentration of the halide will increase the rate. 

Through second order means that the zeroth-, first- and second-order terms are included. 

Comparisons between the second-order mean hyperpolarizabilities (divided by 10 ) of CdS, CdSe, and CdTe clusters computed at the HF/aug-cc-pVDZ-PP level of theory... 

Syimnetrical tricritical points are predicted for fluid mixtures of sulfur or living polymers m certain solvents. Scott (1965) in a mean-field treatment [38] of sulfiir solutions found that a second-order transition Ime (the critical... 

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

This means that the electronic and nuclear wave functions cannot be separated anymore, and therefore the adiabatic approximation cannot be applied beyond the second-order perturbation. 

Hughes and Ingold interpreted second order kinetic behavior to mean that the rate determining step is bimolecular that is that both hydroxide ion and methyl bromide are involved at the transition state The symbol given to the detailed description of the mech anism that they developed is 8 2 standing for substitution nucleophilic bimolecular... 

When B = 0, the solution behaves ideally, at least through second-order effects. This means that deviations from ideality might be observed at still higher concentrations, but that the van t Hoff equation applies at least in dilute solutions for systems with B = 0. 

Some values of mean concentration ratio C/Cq of first- and second-order reactions obtained with Eq. (7-112) are ... 

Equations (3.42) and (3.43) are the standard forms of transfer functions for a second-order system, where K = steady-state gain constant, Wn = undamped natural frequency (rad/s) and ( = damping ratio. The meaning of the parameters Wn and ( are explained in sections 3.6.4 and 3.6.3. 

Another interesting version of the MM model considers a variable excluded-volume interaction between same species particles [92]. In the absence of interactions the system is mapped on the standard MM model which has a first-order IPT between A- and B-saturated phases. On increasing the strength of the interaction the first-order transition line, observed for weak interactions, terminates at a tricritical point where two second-order transitions meet. These transitions, which separate the A-saturated, reactive, and B-saturated phases, belong to the same universality class as directed percolation, as follows from the value of critical exponents calculated by means of time-dependent Monte Carlo simulations and series expansions [92]. 

This improved procedure is an example of the Runge-Kutta method of numerical integration. Because the derivative was evaluated at two points in the interval, this is called a second-order Runge-Kutta process. We chose to evaluate the mean derivative at points Pq and Pi, but because there is an infinite number of points in the interval, an infinite number of choices for the two points could have been made. In calculating the average for such choices appropriate weights must be assigned. 

Another means is available for studying the exchange kinetics of second-order reactions—we can adjust a reactant concentration. This may permit the study of reactions having very large second-order rate constants. Suppose the rate equation is V = A caCb = kobs A = t Ca, soAtcb = t For the experimental measurement let us say that we wish t to be about 10 s. We can achieve this by adjusting Cb so that the product kc 10 s for example, if A = 10 M s , we require Cb = 10 M. This method is possible, because there is no net reaction in the NMR study of chemical exchange. 

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