Question

Read the passage carefully and answer the questions that follow.

The rate of a reaction depends on the concentration of reactants. The rate law for a hypothetical reaction \[\ce{aA + bB -> cC + dD}\] is rate = k [A]x[B]y where x and y are calculated experimentally and known as order of reaction. In most cases, the mechanism of a reaction is not straight forward but broken down in simple elementary steps. These steps represent the progress of overall reaction at the molecular level.

1. What will be the order of reaction if the unit of k is mol⁻² L² s⁻¹?
2. State any one difference between order of reaction and molecularity of reaction.
3. For the reaction \[\ce{2A -> B + C}\], the rate law is rate = k[A]^3/2. What is the order and molecularity of the reaction?

Answer 1

i. The order of reaction can be ascertained from the unit of the rate constant (k). The standard formula for the unit of k is:

Unit of k = mol¹⁻ⁿ Lⁿ⁻¹ s⁻¹

Given that the unit of k is mol⁻² L² s⁻¹, we equate it to the general form:

mol¹⁻ⁿ Lⁿ⁻¹ s⁻¹ = mol⁻² L² s⁻¹

Solving for n:

1 − n = −2 

n = 3

Thus, the order of reaction is 3.

ii. The order of a reaction is the sum of the exponents of the concentration variables in the rate law equation, which may be fractional, zero, or an integer. It is ascertained through experimentation and cannot be computed directly.

The molecularity of a reaction refers to the quantity of reactant molecules, atoms, or ions that must collide concurrently in an initial step to produce a reaction. The value is invariably an integer and can be ascertained by summing the molecules involved in the rate-limiting phase.

iii. Given the rate law:

Rate = `k[A]^(3/2)`

The reaction order is determined by summing the exponents of the concentration variables in the rate law. Consequently, the order is `3/2`.

The reaction’s molecularity is ascertained from the stoichiometric coefficients in a unimolecular mechanism. The specified reaction is:

\[\ce{2A -> B + C}\],

Hence, the molecularity is 2.