Steric Factor and Frequency Factor Analysis in Bimolecular Reaction

To determine the correct statements regarding a bimolecular reaction with a steric factor $P = 4.5$, let us analyze the principles of collision theory and the Arrhenius equation.

1. Definition of the Steric Factor ($P$)

According to the modified collision theory for bimolecular reactions, the rate constant $k$ is given by: $k = P \cdot Z_{AB} \cdot e^{-\frac{E_a}{RT}}$

where:

• $Z_{AB}$ is the collision frequency predicted by the simple hard-sphere collision theory (or predicted frequency factor $A_{\text{predicted}}$).
• $P$ is the steric (or probability) factor, which accounts for the orientation requirement of the colliding molecules.
• $E_a$ is the activation energy of the reaction.

Comparing this with the empirical Arrhenius equation, $k = A_{\text{experimental}} \cdot e^{-\frac{E_a}{RT}}$, we get the relationship: $A_{\text{experimental}} = P \cdot A_{\text{predicted}}$ or equivalently: $P = \frac{A_{\text{experimental}}}{A_{\text{predicted}}}$

---

2. Evaluation of Statements

• Statement [A]: "The activation energy of the reaction is unaffected by the value of the steric factor."

  • The activation energy $E_a$ represents the energy barrier that reactants must overcome to form products, which is a property of the potential energy surface of the chemical system.
  • The steric factor $P$ is a measure of the geometrical or orientational probability of the collision leading to a reaction.
  • Therefore, $E_a$ is independent of the magnitude of $P$.
  • Statement [A] is correct.

• Statement [B] & [D]: Frequency Factor Comparison

  • We are given $P = 4.5$. Substituting this into the ratio equation: $A_{\text{experimental}} = 4.5 \times A_{\text{predicted}}$
  • Since $P > 1$, it follows that: $A_{\text{experimental}} > A_{\text{predicted}}$
  • This means the experimentally determined frequency factor is higher than the frequency factor predicted by the theoretical simple collision/Arrhenius equation.
  • Statement [B] is correct.
  • Statement [D] is incorrect.

• Statement [C]: "Since $P = 4.5$, the reaction will not proceed unless an effective catalyst is used."

  • A steric factor greater than 1 ($P > 1$) can occur due to long-range attractive forces or internal degrees of freedom, meaning a higher fraction of collisions lead to product formation than simple hard-sphere collisions predict.
  • This does not imply that a catalyst is required for the reaction to occur.
  • Statement [C] is incorrect.

---

Conclusion

The correct statements are [A] and [B].