According to Lindemann-Hinshelwood mechanism of unimolecular reactions, the observed order at low concentration follows: 

CONCEPT:

Lindemann-Hinshelwood Mechanism of Unimolecular Reactions

• The Lindemann-Hinshelwood mechanism explains the kinetics of unimolecular reactions that involve a single molecule breaking down into products.
• It proposes a two-step process:
  • Step 1: A reactant molecule (A) is activated by collision with another molecule (A or M), forming an excited state (A*).
    A + M → A* + M
  • Step 2: The excited molecule (A*) either decomposes to form products or deactivates back to the ground state by collision.
    A* → Products
    A* + M → A + M
• At low concentrations of the reactant, the activation step (Step 1) becomes the rate-determining step because collisions between molecules are infrequent.

EXPLANATION:

According to Lindemann-Hinshelwood mechanism is given as:

Thus, an activated intermediate (A*) is produced from the reactant after sufficient activation energy is acquired by collision with another molecule M. The activated intermediate (A) gets deactivated through an unimolecular step to give product (P). The first step is bimolecular whereas the second step is unimolecular. Overall rate expression is:

• Rate = K₁K2 [A]2 / K₂+K_₁ [A]

In terms of partial pressure, we have,

• Rate=  K1K2[PA]2/ K₂+K-1[PA]

• The biomolecular step is involved, thus it is true.

At low pressure,

• K-1 [PA] << K₂

• Rate =K₁K₂[PA]² / K₂ = K₁[PA]2
• At low pressure, it is second order.

Thus, according to the Lindemann-Hinshelwood mechanism, the observed order of reaction at low concentration is second order.