Integrated Rate Law Expression of Zero Order Reaction | Physical Chemistry PDF Download

Integrated Rate Law Expressions

Integrated rate law expression provides the predicted temporal evolution in reactant and product concentrations for reactions having an assumed order dependence.

Zero-Order Reaction

• The rate of reaction is independent of the concentration of the reactants in these reactions.
• A change in the concentration of the reactants has no effect on the speed of the reaction
• Examples of these types of reactions include the enzyme-catalyzed oxidation of CH₃CH₂OH (ethanol) to CH₃CHO (acetaldehyde).

Consider the following elementary reaction

 
For zero-order reaction, the rate law is

k is rate constant.

⇒ –d[A] = k dt

If at t = 0, the initial concentration is [A]₀ and the concentration at t = t, is [A], then integration yields

⇒ [A]₀ – [A] = kt
This is an integrated rate equation for a zero-order reaction in terms of reactant.

= k d[P] = k dt
at              t = 0,  [P] = 0
and at        t = t, [P] = [P]
then integration yields

[P] = kt
This is an integrated rate law equation for a zero-order reaction in terms of product.
i.e. [A]₀ – [A] = kt = [P]

Graphical Representation of Zero-Order Reaction

Graph of Reactant vs Time.

[A]₀ – [A] = kt
[A] = –kt + [A]₀
y = mx + c

Graph of Product vs Time.

[P] = kt

y = mx

Concentration of Product vs Time.

[A]₀ – [A] = 2kt …(i)

When t = 0 then [P] = 0 and t = t then [P] = [P]

[P] = 3kt     …(ii)

          …(iii)

Problem. Find the integrated rate law expression for an elementary zero-order reaction given below.

Sol.

The rate law of the above elementary reaction is given below

⇒

⇒  – [[A] – [A]₀] = kt
        [A]₀ – [A] = kt    …(i)

⇒


   …(ii)
⇒

[P] = kt      …(iii)

From equation (i), (ii) & (iii) we get