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# examples of . order of rate of reaction

From Wikipedia

Reaction rate constant

In chemical kinetics a reaction rate constantk or \lambda quantifies the speed of a chemical reaction .

For a chemical reaction where substance A and B are reacting to produce C, the reaction rate has the form:

Reaction: A + B â†’ C
\frac{d[C]}{dt} = k(T)[A]^{m}[B]^{n}

k(T) is the reaction rate constant that depends on temperature.

[C] is the concentration of substance C in moles per volume of solution assuming the reaction is taking place throughout the volume of the solution (for a reaction taking place at a boundary it would denote something like moles of C per area).

The exponents m and n are called orders and depend on the reaction mechanism. They can be determined experimentally.

A single-step reaction can also be written as

\frac{d[C]}{dt} = Ae^\frac{-E_a}{RT}[A]^m[B]^n

Eais theactivation energy and R is the Gas constant. Since at temperatureT the molecules have energies according to a Boltzmann distribution, one can expect the proportion of collisions with energy greater than Eato vary with e-Ea/RT. A is thepre-exponential factor or frequency factor.

The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the reaction rate at which a reaction proceeds.

The units of the rate coefficient depend on the global order of reaction:

• For order zero, the rate coefficient has units of molÂ·L-1Â·s-1
• For order one, the rate coefficient has units of s-1
• For order two, the rate coefficient has units of LÂ·mol-1Â·s-1
• For order n, the rate coefficient has units of mol1-nÂ·Ln-1Â·s-1

## Plasma and gases

Calculation of rate constants of the processes of generation and relaxation of electronically and vibrationally excited particles are of great importance. It is used in the computer simulation of processes in plasma chemistry, microelectronics. First-principle based models should be used for such calculation. It can be done with the help of computer simulation software.

Reaction mechanism

In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.

Although only the net chemical change is directly observable for most chemical reactions, experiments can often be designed that suggest the possible sequence of steps in a reaction mechanism. Recently, electrospray ionization mass spectrometry has been used to corroborate the mechanism of several organic reaction proposals.

## Description

A chemical mechanism describes in detail exactly what takes place at each stage of an overall chemical reaction (transformation). It also describes each reaction intermediate, activated complex, and transition state, and which bonds are broken (and in what order), and which bonds are formed (and in what order). A complete mechanism must also account for all reactants used, the function of a catalyst, stereochemistry, all products formed and the amount of each, and what the relative rates of the steps are. Reaction intermediates are chemical species, often unstable and short-lived, which are not reactants or products of the overall chemical reaction, but are temporary products and reactants in the mechanism's reaction steps. Reaction intermediates are often free radicals or ions. Transition states can be unstable intermediate molecular states even in the elementary reactions. Transition states are commonly molecular entities involving an unstable number of bonds and/or unstable geometry which may be at chemical potential maxima.

The electron or arrow pushing method is often used in illustrating a reaction mechanism; for example, see the illustration of the mechanism for benzoin condensation in the following examples section.

A reaction mechanism must also account for the order in which molecules react. Often what appears to be a single step conversion is in fact a multistep reaction.

## Examples

Consider the following reaction:

CO + NO2&rarr; CO2 + NO

In this case, it has been experimentally determined that this reaction takes place according to the rate law R = k[NO_2]^2. Therefore, a possible mechanism by which this reaction takes place is:

2 NO2&rarr; NO3 + NO (slow)
NO3 + CO &rarr; NO2 + CO2 (fast)

Each step is called an elementary step, and each has its own rate law and molecularity. The elementary steps should add up to the original reaction.

When determining the overall rate law for a reaction, the slowest step is the step that determines the reaction rate. Because the first step (in the above reaction) is the slowest step, it is the rate-determining step. Because it involves the collision of two NO2 molecules, it is a bimolecular reaction with a rate law of R = k[NO_2]^2. If we were to cancel out all the molecules that appear on both sides of the reaction, we would be left with the original reaction.

In organic chemistry, one of the first reaction mechanisms proposed was that for the benzoin condensation, put forward in 1903 by A. J. Lapworth.

## Modelling

A correct reaction mechanism is an important part of accurate predictive modelling. For many combustion and plasma systems, detailed mechanisms are not available or require development.

Even when information is available, identifying and assembling the relevant data from a variety of sources, reconciling discrepant values and extrapolating to different conditions can be a difficult process without expert help. Rate constants or thermochemical data are often not available in the literature, so computational chemistry techniques or group-additivity methods must be used to obtain the required parameters.

At the different stages of a reaction mechanism's elaboration, appropriate methods must be used.

## Molecularity

Molecularity in chemistry is the number of colliding molecular entities that are involved in a single reaction step.

• A reaction involving one molecular entity is called unimolecular.
• A reaction involving two molecular entities is called bimolecular.
• A reaction involving three molecular entities is called termolecular.

Question:so its actually a 2nd order reaction that behaves like a first order since the concentration of only of the reactants really contributes to the rate law. now i wanted to know if it is an SN1 reaction or SN2. or would that depends on the molecule?

Answers:well, I'd say SN2. SN1 reactions, the slowest, rate determining step is the dissociation of the molecule. The molecule has to break up into two parts and that process only depends on the concentration of that molecule. SN2 reactions rely on two molecules clashing, so both concentrations will contribute to the rate. pseudo first order just means that one of the two molecules is in incredibly high concentrations compared to the other, so much that its concentration doesn't really seem to change when you look at the second molecule reacting away. this way, the rate of the reaction only seems to depend on the less concentrated molecule.

Question:What will be the units of the rate constant k for an 1. zero order reaction 2. first order reaction 3.second order reaction if the concentration is in mol/litre and time is in seconds

Answers:1. zero order reaction rate or reaction = k rate constant = mol/litre/s (moles per litre per second) 2. first order reaction Rate of reaction = k[A] rate constant = 1/s 3 Second order reaction Rate of reaction = k[A][B] Rate constant = Litre/mol/s. (litres per mole per second)

Question:What is the integrated form of the Rate Law (in y=mx+b form) for a zero, 1st, and 2nd order reaction?? Any help is appreciated!

Answers:zeroth order: Af = -kt + Ao first order: Ln(Af) = - kt + Ln(Ao) Second order: 1/[Af] = kt + 1/[Ao] Cheers.

Question:Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to N2 and O2 is second order with a rate constant of .0796 M-1s-1 at 737C and .0815 M-1s-1 at 947C. Calculate the activation energy for the reaction.

Answers:use Arrhenius equation k = A exp{ -Ea/(R T) } <=> ln(k) = ln(A) - Ea/(R T) You know the rate constants at two different temperatures, i.e. ln(k ) = ln(A) - Ea/(R T ) ln(k ) = ln(A) - Ea/(R T ) => ln(k ) - ln(k ) = Ea/(R T ) - Ea/(R T ) => Ea = R (ln(k ) - ln(k )) / (1/T - 1/T ) = R ln(k /k ) / (1/T - 1/T ) = 8.3145J/molK ln(0.0815/0.0796) / (1/(737+ 273)K - 1/(947 +273)K) = 1151J/mol