Rate Expression and Rate Constant

Whenever you deal with a reaction, and you need to calculate the relationship between reactants and products, then rate law and rate constant is the only way out. Suppose you are experimenting with adding two chemicals and want to know the amount of product made after a specific amount of time. Then, you have to use the rate law expression. 

In the same way, if you wish to calculate the amount of reactant after a specific amount of time, then rate expression is your one-stop destination.

Rate Law

The expression which provides the relationship between the concentration of reactants and the rate of reactants is termed as rate law. Let us understand the rate law with the help of a rate law expression. 

Rate Law Expression

Let us assume that a reaction occurs between the reactants A and B with the coefficients a and b, respectively. The products formed in the reaction are C and D, where the coefficients are c and d, respectively. 

aA + bB —–> cC + dD

Where,

a is the stoichiometric coefficient of the reactant A

b is stoichiometric coefficients of the reactant B

c is stoichiometric coefficients of the product C

d is stoichiometric coefficients of the product D

Then, the rate law expression will be

Rate ∝ [A]x[B]y

Rate = k[A]x[B]y

Where,

[A] is the concentration of reactant A

[B] is the concentration of the reactant B.

x is the partial reaction orders for reactants A

y is the partial reaction orders for reactants B

k is the constant of proportionality, also known as the rate constant of the reaction

An important note that should be kept in mind is that you cannot theoretically calculate the rate law. The only way to calculate the rate law is through experiments. 

Characteristics of Rate Constant

• As the name suggests, the rate constant does not depend upon the concentration of reactants or products. It is independent of the concentration of reactants and products. That is why it is a constant. 
• The rate constant varies with the temperature of the reaction. 
• The order of any reaction can be determined by the unit of the rate constant, which is discussed later in this article.

Order of a reaction

The order of the reaction is known as the sum of powers of the overall reactant and products. 

Let us suppose that there is a reaction taking place:

aA + bB —> cC + dD

Where,

a is the stoichiometric coefficient of the reactants

b is stoichiometric coefficients of the reactants

c is stoichiometric coefficients of the products

d is stoichiometric coefficients of the products

Then, the rate law would be

Rate = k[A]x[B]y

Then, the order of the reaction would be (n) = x+y

The order of the reaction is denoted by n.

Rate Constants

Once you rearrange the rate equation, then the rate constant is defined by “k”. 

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

There’s also a way to calculate the unit of k for different units of rate constants

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

Where,

s is the time in seconds

n is the order of the reaction

M is the mass

The rate constants for different orders of reaction are:

If the order of a reaction is 0, then the unit of rate constant will be mol.L-1.s-1

If the order of a reaction is 1, then the unit of rate constant will be s-1

If the order of a reaction is 2, then the unit of rate constant will be L.mol-1.s-1

If the order of a reaction is n, then the unit of rate constant will be L(-1+n).mol(1-n).s-1

Conclusion

The article consists of the rate law and its expression. Here, you will find the discussion of the order of the reaction and the rate constant. All these things are necessary to calculate the number of reactants and products left or produced in a reaction. By proper experiments, you can calculate the rate law and have a look at the beautiful experiments of nature. You will wonder after seeing the reaction process and the formation of bonds between two compounds. Let’s enjoy chemistry.