Question

Explain the difference between molecularity and order of reaction. Show that the time taken to complete three-fourth of the first-order reaction is doubled to its half-life.

Hint:

Molecularity is theoretical while order is experimentally determined. First-order reactions follow exponential decay.

Answer 1

Step 1: Difference Between Molecularity and Order: \begin{center} \begin{tabular}{|c|c|} \hline Molecularity & Order of Reaction
\hline It is the number of molecules colliding in an elementary step. & It is determined experimentally from rate law.
\hline Always a whole number. & Can be fractional or whole.
\hline \end{tabular} \end{center} Step 2: First-Order Reaction Derivation: \[ t = \frac{2.303}{k} \log \frac{[A]_0}{[A]} \] For three-fourth completion: \[ t_{3/4} = \frac{2.303}{k} \log \frac{4}{1} = 2 t_{1/2} \] Thus, the time taken for 75% completion is twice the half-life.