Order Of Reaction

The overall order of a chemical reaction is determined by summing the exponents of the concentration terms in the rate law expression. Given the rate law for the reaction:

Rate = k[A]^½ [B]^3/2

Here, [A]^½ indicates the reaction is first-order with respect to A but raised to the power of ½, and [B]^3/2 indicates a reaction order of 3/2 with respect to B.

To find the overall reaction order, sum the exponents:

1. Exponent of [A] = ½

2. Exponent of [B] = 3/2

3. Overall order = ½ + 3/2 = 2

Thus, the overall order of the reaction is 2.

In the context of complex reactions, understanding how the order of reaction is determined is crucial. The order of a reaction is typically defined by the rate-determining step, which is the slowest step in a reaction mechanism.

The molecularity of a step in a reaction mechanism refers to the number of molecules participating in that step. In a complex reaction, the molecularity of the slowest step directly influences the order of the reaction. This is because the overall reaction rate is limited by the speed of the slowest step, and thus the order of the overall reaction matches the molecularity of this crucial step.

Therefore, for a complex reaction, the order of reaction is equal to: Molecularity of the slowest step.

The overall order of a reaction is determined by summing the exponents of the concentration terms in the rate expression. Given the rate expression: Rate = k[A] [B] , we identify the exponents for each concentration:

The exponent of [A] is .

The exponent of [B] is .

To find the overall order, add these exponents:

Overall order = + = 2

The order of a reaction can be determined by examining the units of the rate constant. The general formula to determine the order is given by:
Units of rate constant = (mol L^-1)^1-n sec^-1 where n is the order of reaction.
For each option, the order is calculated as follows:

• (A) Units: sec^-1
  Order: 1 (n=1) - This is for a first-order reaction.
• (B) Units: mol L^-1 sec^-1
  Order: 0 (n=0) - This is for a zero-order reaction.
• (C) Units: mol^-1 L sec^-1
  Order: 2 (n=2) - This is for a second-order reaction.
• (D) Units: mol^-1 L² sec^-1
  Order: 3 (n=3) - This is for a third-order reaction.

Arranging the orders in increasing order:
(C) 2nd-order < (A) 1st-order < (B) 0-order < (D) 3rd-order.
The correct arrangement of rate constant units in increasing order is (C) < (A) < (B) < (D).

Inversion of cane sugar is a chemical process where sucrose is hydrolyzed into glucose and fructose in the presence of an acid. The reaction is catalyzed by an acid and is given by the equation:

C₁₂H₂₂O₁₁ + H₂O → C₆H₁₂O₆ + C₆H₁₂O₆

In this reaction, the concentration of water remains constant because it is present in excess. This transforms the reaction's kinetics from being second-order to first-order concerning the concentration of sucrose. Since the reaction behaves kinetically as a first-order reaction when it is actually not, it is termed a pseudo-first-order reaction.

The correct answer is: Pseudo first order reaction

The rate constant for a first-order reaction can be calculated using the formula for half-life: t_1/2 = 0.693/k.

Given: sec.

Substituting in the half-life formula: .

Rearrange to find k: .

Simplifying: .

Therefore, the rate constant is .