Rate law and specific rate constant

Introduction

In chemistry, reaction rate refers to the pace at which a chemical reaction occurs. It is frequently described in terms of either the concentration (amount per unit volume) of a product generated in a unit of time or the concentration of a reactant consumed in a unit of time, depending on the application. 

It may also be expressed in terms of the number of reactants consumed or products created in a certain amount of time. The rate law of a chemical reaction is an equation that defines the correlation between the reaction rate and the concentrations of reactants in the reaction.

Expression

Let’s consider a reaction in which the rate equation of a reaction in which b, a, c and d are the various stoichiometric coefficients is expressed as 

Rate ∝ [A]x[B]y ⇒ Rate = k[A]x[B]y;

Here, the primary equation that we considered was 

aA + bB → cC + dD. 

Where,

• The quantities of the reactant molecules A and B are denoted by [A] and [B].
• The partial reaction orders for reactants A and B are denoted by x and y. (which may or may not be equal to their stoichiometric coefficients a & b).
• The rate constant of the reaction is the proportionality constant ‘k’.

The difference between the rate law and the specific rate constant may seem obscure, but it’s really quite simple. The rate law is a general statement that describes how the speed at which a chemical reaction occurs varies with respect to a variety of factors such as temperature and pressure. However, the specific rate constant considers only one factor: the concentration of the reactants.

Reaction Orders

Reaction order is the power to which concentration is raised in a rate law equation. The order explains how and why the proportion of a reaction rate influences the rate law numerically.

There are several ways to express the rate law equation, so let’s begin with the most basic one: R = k[A]n

As a result, when the order is one, or when n = one, it indicates that the correlation between Reactant A concentration and the rate of the reaction is precisely proportional. When A rises, R rises in tandem. R doubles if A doubles.

Rate Constants

The rate constants for zero, first, second, and nth-order reactions are listed below in their units.

• For reaction with order 0, the unit of rate constant is M s-1 (or) mol L-1 s-1.
• For reaction with order 1, the units of the rate constant is s-1.
• For reaction with order 2, the unit of rate constant is M-1 s-1 (or) L mol-1 s-1 .
• For reaction with order n, the unit of rate constant is M1-n s-1 (or) L(-1+n) mol(1-n) s-1.

In a rate equation, each reaction has its own constant. The particular rate constant (k) is indeed a proportionality constant that will be distinct to each experimentation. This implies that its value is influenced by other parameters in the experiment, such as temperature, that affect the response rate. When other rate-altering variables vary, k may change even when the same molecules are utilized in the reaction.

Differential Rate Equations

Reactant concentration changes (d[R]) are utilized by differential rate law to represent reaction rate as a function of short-term variations (dt) in reactant concentrations. As a result, the differential form of the rate expression in the preceding subsection is:

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

By putting a rate and the appropriate concentrations into a variable rate law and solving for k, we may get a rate constant.

Calculating the instantaneous rate of a reaction, which is the rate of a reaction occurring within a very short period of time, may be accomplished using differential rate equations.

Integrated Rate Equations

The concentration of the reactants in a chemical reaction is expressed as a function of time using integrated rate equations. As a result, rate equations may be used to determine how long a certain percentage of the reactants will be consumed in a chemical process. It’s worth noting that integrated rate equations for reactions of various orders differ.

• For a zero-order reaction, the integral rate equation is:

k.t = [R0] – [R] 

(or) 

k = ([R0] – [R])/t

• For first-order reactions, the integrated rate law is:

k.t = 2.303log([R0]/[R]) 

(or)

 k = (2.303/t).log([R0]/[R])

• The integral rate equation for second-order reactions is:

k.t = (1/[R]) – (1/[R0])

Conclusion

In this article, we studied the rate law and the specific rate constant in detail. The rate of a reaction is affected by temperature, pressure, and the number of reactants involved in the reaction. Because the reactants are depleted over time, reactions normally slow down. A catalyst, which is a material that is not itself a reactant, can sometimes speed up a process.