Table of Contents

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

**Expression**

For the response given by:

**aA + bB → cC + dD**

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

Rate ∝ [A]x[B]y ⇒ Rate = k[A]x[B]y

Where,

[A] and [B] denotes the concentrations of the reactants A and B.

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

‘k’ is proportionally constant of the reaction.

It is important to note that the disclosure of the rule of thumb can only be determined by testing. The concept of measurement law cannot be deduced from balanced chemical calculations (since orders that are part of reactants are not exactly the same as stoichiometric coefficients).

**Reaction Order**

The total number of orders that are part of the reactants in the measurement law indicator provides a complete order of reaction.

If Rate = k[A]x[B]y ; overall order of the reaction (n) = x+y

The sequence of a reaction provides insight into the change in the rate of the reaction that can be expected by increasing the concentration of the reactants. for example:

If the reaction may be a zero-order reaction, doubling the concentration of the reactant won’t affect the reaction rate.

If the reaction is first order, doubling the concentration of the reactant will double the reaction rate.

In second-order reactions, doubling the concentrations of the reactants will quadruple the overall reaction rate.

For third-order reactions, when the reactant concentration is doubled, the overall rate increases by eight times.

**Rate constants**

Rearranging the speed equation, the worth of the speed constant ‘k’ is given by:

k = Rate/[A]x[B]y

Therefore, the units of k (assuming that concentration is represented in mol.L-1 or M and time is represented in seconds) are often calculated via the subsequent equation.

k = (M.s-1)*(M-n) = M(1-n).s-1

**Differential rate equation**

Differential rate laws are used to express the rate of a reaction in terms of the change in reactant concentration (D [R]) over a small interval of time (dT). Therefore, the differential sort of the speed expression provided within the previous subsection is given by:

-d[R]/dt = k[A]x[B]y

Differential rate equations can be used to calculate the instantaneous rate of a reaction, which is the reaction rate under very short time intervals. It may be noted that the common rate law is a differential rate equation as it provides insight into the instantaneous rate of the reaction.

**Integrated rate equation**

Integrated rate equations express the concentration of reactants in a chemical reaction as a function of time. Therefore, such rate equations can be employed to test how long a chemical reaction will take to consume a given percentage of reactants. It is important to notice that reactions of various orders have different integrated rate equations.

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**FAQs**

##### What is the Zero-order Reaction?

Reactions in which the concentration of the reactants do not change with respect to time and the concentration rates remain constant throughout are called zero-order reactions.

**Question: Give an Example of a Third-order Reaction.**

**Answer:** 2NO + Cl₂ → 2NOCl

Rate, R = kNONO²Cl₂Cl₂

Here, Order of reaction = Sum exponent of nitric oxide and chloride Order = 2 + 1 = 3

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