WordNet

be worthy of or have a certain rating; "This bond rates highly"
amount of a charge or payment relative to some basis; "a 10-minute phone call at that rate would cost $5" (同)charge per unit
a magnitude or frequency relative to a time unit; "they traveled at a rate of 55 miles per hour"; "the rate of change was faster than expected"
a quantity or amount or measure considered as a proportion of another quantity or amount or measure; "the literacy rate"; "the retention rate"; "the dropout rate"
assign a rank or rating to; "how would you rank these students?"; "The restaurant is rated highly in the food guide" (同)rank, range, order, grade, place
estimate the value of; "How would you rate his chances to become President?"; "Gold was rated highly among the Romans" (同)value
give (hair) the appearance of being fuller by using a rat
a pad (usually made of hair) worn as part of a womans coiffure
any of various long-tailed rodents similar to but larger than a mouse
catch rats, especially with dogs
desert ones party or group of friends, for example, for ones personal advantage
employ scabs or strike breakers in
steadfast in purpose or devotion or affection; "a man constant in adherence to his ideals"; "a constant lover"; "constant as the northern star"
a number representing a quantity assumed to have a fixed value in a specified mathematical context; "the velocity of light is a constant"
a quantity that does not vary (同)constant quantity, invariable
standing or position on a scale
a local tax on property (usually used in the plural)

PrepTutorEJDIC

〈C〉『割合』,『率』 / 〈C〉《the~,a~》『速度』(speed),進度 / 〈C〉『値段』,『相場』;料金 / 〈U〉等級(class),(…)等 / 《複数形ぃ》《英》地方税 / (…の金額に)…‘の'『値段を決める』,見積もる《+『名』+『at』+『名』》 / …‘を'『評価する』,みなす / 《米話》…‘に'値する,‘の'価値がある / 『評価される』;みなされる
…‘を'どなりつける
『ネズミ』 / ひきょう者,裏切り者 / ネズミをつかまえる / 《話》(人を)裏切る,密告する《+『on』+『名』〈人〉》
『不変の』,一定の / 『絶え間のない』,不断の,繰り返される / 《文》〈人が〉心変わりしない;(…に対して)誠実な,貞節な《+『to』+『名』》 / (数学で)常数;(化学・物理分析などにおける)定量
〈C〉〈U〉（品質・技量などによる）格づけ,評価 / 〈C〉（個人・会社の経済的な）信用度 / 〈C〉(トン・馬力による)(船舶・車)の等級 / 〈C〉(テレビ・ラジオの)視聴率

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/06/01 22:08:14」(JST)

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In chemical kinetics a reaction rate constant, k or , quantifies the rate of a chemical reaction.^[1]

For a reaction between reactants A and B to form product C

the reaction rate is often found to have the form:

Here k(T) is the reaction rate constant that depends on temperature. [A] and [B] are the concentrations of substances A and B 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 one would use instead moles of A or B per unit area).

The exponents m and n are called partial orders of reaction and are not generally equal to the stoichiometric coefficients a and b. Instead they depend on the reaction mechanism and can be determined experimentally.

Temperature dependence

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

and the reaction rate by

where E_a is the activation energy, and R is the gas constant. Since at temperature T the molecules have energies according to a Boltzmann distribution, one can expect the proportion of collisions with energy greater than E_a to vary with e^−E_a/RT. A is the pre-exponential factor, or frequency factor (not to be confused here with the reactant A).

Units

The units of the rate constant depend on the global order of reaction:^[2] If concentration is measured in units of mol·L⁻¹ (sometimes abbreviated as M), then

For order (m + n), the rate coefficient has units of mol^1−(m+n)·L^(m+n)−1·s⁻¹
For order zero, the rate coefficient has units of mol·L⁻¹·s⁻¹ (or M·s⁻¹)
For order one, the rate coefficient has units of s⁻¹
For order two, the rate coefficient has units of L·mol⁻¹·s⁻¹ (or M⁻¹·s⁻¹)
And for order three, the rate coefficient has units of L²·mol⁻²·s⁻¹ (or M⁻²·s⁻¹)

Plasma and gases

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

Rate constant calculations

Rate constant can be calculated for elementary reactions by molecular dynamics simulations. One possible approach is to calculate the mean residence time of the molecule in the reactant state. Although this is feasible for small systems with short residence times, this approach is not widely applicable as reactions are often rare events on molecular scale. One simple approach to overcome this problem is Divided Saddle Theory.^[3] Other methods as Benett Chandler procedure,^[4]^[5] Milestoning are also developed for rate constant calculations.

Divided Saddle Theory

The theory is based on the assumption that the reaction can be described by a reaction coordinate, and that we can apply Boltzmann distribution at least in the reactant state. A new, especially reactive segment of the reactant, called the saddle domain, is introduced, and the rate constant is factored:

where is the conversion factor between the reactant state and saddle domain, while is the rate constant from the saddle domain. The first can be simply calculated from the free energy surface, the latter is easily accessible from short molecular dynamics simulations ^[3]

References

^ http://www.chem.arizona.edu/~salzmanr/480a/480ants/chemkine.html
^ Blauch, David. "Differential Rate Laws". Chemical Kinetics.
^ ^a ^b János Daru and András Stirling; J. Chem. Theory Comput., 2014, 10 (3), pp 1121–1127 http://pubs.acs.org/doi/abs/10.1021/ct400970y
^ Chandler, David (1978). "Statistical mechanics of isomerization dynamics in liquids and the transition state approximation". The Journal of Chemical Physics 68 (6): 2959. doi:10.1063/1.436049.
^ Bennett, C. H. (1977). Christofferson, R., ed. Algorithms for Chemical Computations, ACS Symposium Series No. 46. Washington, D.C.: American Chemical Society. ISBN 978-0-8412-0371-6.

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NAID 130005093556

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