Question

Define molecularity and order of a reaction. Derive the integrated rate equation for the rate constant of first-order reaction.

Hint:

Molecularity is a theoretical concept for elementary steps, while reaction order is experimentally determined.

Answer 1

Step 1: Definitions: - Molecularity: The number of reactant molecules participating in an elementary reaction. - Order of Reaction: The sum of powers of reactant concentrations in the rate law. 

Step 2: Derivation of First-Order Rate Equation: \[ \text{Rate} = k[A] \] 

Step 3: Separating Variables: \[ \frac{d[A]}{[A]} = -k dt \] 

Step 4: Integrating Both Sides: \[ \int \frac{d[A]}{[A]} = - \int k dt \] \[ \ln [A] = -kt + C \] 

Step 5: Applying Initial Conditions: \( [A] = [A]_0 \) at \( t = 0 \): \[ \ln [A]_0 = C \] \[ \ln [A] = -kt + \ln [A]_0 \] \[ [A] = [A]_0 e^{-kt} \] Thus, the first-order rate equation is: \[ [A] = [A]_0 e^{-kt} \]