Question

define rate law with mathematical expression. ​

Answer 1

ANSWER

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• The rate law or rate equation for a chemical reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders).[1] For many reactions, the initial rate is given by a power law such as

${\displaystyle v_{0}\;=\;k[\mathrm {A} ]^{x}[\mathrm {B} ]^{y}} {\displaystyle v_{0}\;=\;k[\mathrm {A} ]^{x}[\mathrm {B} ]^{y}}$

• where [A] and [B] express the concentration of the species A and B, usually in moles per liter (molarity, M). The exponents x and y are the partial orders of reaction for A and B and the overall reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The constant k is the reaction rate constant or rate coefficient of the reaction. Its value may depend on conditions such as temperature, ionic strength, surface area of an adsorbent, or light irradiation. If the reaction goes to completion, the rate equation for the reaction rate

${\displaystyle v\;=\;k[\mathrm {A} ]^{x}[\mathrm {B} ]^{y}} {\displaystyle v\;=\;k[\mathrm {A} ]^{x}[\mathrm {B} ]^{y}}$

applies throughout the course of the reaction.

• Elementary (single-step) reactions and reaction steps have reaction orders equal to the stoichiometric coefficients for each reactant. The overall reaction order, i.e. the sum of stoichiometric coefficients of reactants, is always equal to the molecularity of the elementary reaction. However, complex (multi-step) reactions may or may not have reaction orders equal to their stoichiometric coefficients. This implies that the order and the rate equation of a given reaction cannot be reliably deduced from the stoichiometry and must be determined experimentally, since an unknown reaction mechanism could be either elementary or complex. When the experimental rate equation has been determined, it is often of use for deduction of the reaction mechanism.

• The rate equation of a reaction with an assumed multi-step mechanism can often be derived theoretically using quasi-steady state assumptions from the underlying elementary reactions, and compared with the experimental rate equation as a test of the assumed mechanism. The equation may involve a fractional order, and may depend on the concentration of an intermediate species.

• A reaction can also have an undefined reaction order with respect to a reactant if the rate is not simply proportional to some power of the concentration of that reactant; for example, one cannot talk about reaction order in the rate equation for a bimolecular reaction between adsorbed molecules:

${\displaystyle v_{0}=k{\frac {K_{1}K_{2}C_{A}C_{B}}{(1+K_{1}C_{A}+K_{2}C_{B})^{2}}}.\,} </p><p>{\displaystyle v_{0}=k{\frac {K_{1}K_{2}C_{A}C_{B}}{(1+K_{1}C_{A}+K_{2}C_{B})^{2}}}.\,}</p><p></p><p> </p><p>$

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Answer 2

Defination:

The rate law (also known as the rate equation) for a chemical reaction is an expression that provides a relationship between the rate of the reaction and the concentrations of the reactants participating in it.

Expression :

For a reaction given by:

aA + bB → cC + dD

Where a, b, c, and d are the stoichiometric coefficients of the reactants or products, the rate equation for the reaction is given by:

Rate ∝ [A]x[B]y ⇒ Rate = k[A]x[B]y

Where,

[A] & [B] denote the concentrations of the reactants A and B.

x & y denote the partial reaction orders for reactants A & B (which may or may not be equal to their stoichiometric coefficients a & b).

The proportionality constant ‘k’ is the rate constant of the reaction.

It is important to note that the expression of the rate law for a specific reaction can only be determined experimentally. The rate law expression cannot be obtained from the balanced chemical equation (since the partial orders of the reactants are not necessarily equal to the stoichiometric coefficients).

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