Problem 29 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

In a bimolecular reaction, the steric factor \(P\) was experimentally determined to be 4.5. The correct option(s) among the following is(are) (a) The activation energy of the reaction is unaffected by the value of the steric factor (b) Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation (c) Since \(P=4.5\), the reaction will not proceed unless an effective catalyst is used (d) The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally

Step-by-Step Solution

Answer

Both (a) and (b) are true.

Step 1: Recall the definition of steric factor

The steric factor \( P \) is part of the collision theory in kinetics that adjusts for the orientation of molecules during reactions. It modifies the frequency factor in the Arrhenius equation to account for the probability that molecules will collide in the correct orientation.

Step 2: Analyze statement (a)

Option (a) states that the steric factor does not affect the activation energy. Since the activation energy is determined by the energy barrier of the reaction and is independent of the frequency factor or the steric factor, this statement is true.

Step 3: Analyze statement (b)

Option (b) claims that the experimentally determined frequency factor is higher. The Arrhenius equation relates the rate constant \( k \), the activation energy \( E_a \), and the temperature \( T \) with \( A \) (frequency factor) and says: \[ k = A \cdot e^{-E_a/RT} \] The frequency factor accounts for steric and other effects, and since \( P = 4.5 \), this indicates that more collisions are fruitful than predicted, implying that the experimentally determined frequency factor is higher than if \( P = 1 \). Thus, statement (b) is true.

Step 4: Analyze statement (c)

Option (c) suggests that with \( P = 4.5 \), a catalyst is needed to proceed. However, \( P > 1 \) indicates more successful orientations per collision, not less. This makes statement (c) false.

Step 5: Analyze statement (d)

Option (d) suggests the Arrhenius prediction of \( A \) is higher than the experiment. Given \( P = 4.5 \), the experimentally found \( A \) would be higher than the theoretical value assuming \( P = 1 \). Hence, this statement is false, as the experimental value is actually greater due to the factor.

Key Concepts

Steric Factor

The steric factor, denoted as \( P \), plays a crucial role in the collision theory of chemical kinetics. It helps account for the fact that molecules must collide not just with enough energy, but also in the correct orientation to react. In essence, \( P \) modifies the frequency factor in the Arrhenius equation, adjusting for the likelihood that collisions will lead to a chemical reaction.

• If \( P = 1 \), every collision between reactant molecules results in a reaction.
• If \( P > 1 \), it indicates a higher proportion of successful collisions than expected.
• If \( P < 1 \), most collisions are unsuccessful due to incorrect orientations.

This adjustment is critical in calculating the accurate rate of chemical reactions, as molecular orientation can significantly impact whether or not a reaction proceeds.

Activation Energy

Activation energy, often symbolized as \( E_a \), is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that must be overcome for reactants to transform into products. Importantly, the activation energy is an intrinsic property of a reaction itself and is not influenced by external factors like the steric factor.To better understand activation energy:

• It determines the reaction speed; a higher \( E_a \) means a slower reaction at a given temperature.
• It remains constant for a reaction under unchanged conditions.
• It is depicted as a hill that reactants must climb over in the reaction energy profile.

Thus, the activation energy stands apart from factors impacting collision orientation, like the steric factor.

Arrhenius Equation

The Arrhenius Equation is a fundamental formula in chemical kinetics that describes how reaction rates are affected by temperature and activation energy. This equation is:\[k = A \cdot e^{-E_a/(RT)}\]Where:

• \( k \) is the rate constant of the reaction.
• \( A \) is the frequency factor, reflecting the number of times reactants approach the activation barrier per unit time.
• \( E_a \) is the activation energy.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.

This equation demonstrates that as temperature increases, the reaction rate typically increases, primarily because thermal energy helps overcome the activation energy barrier. The steric factor is embedded within the frequency factor \( A \), allowing the equation to account for both energy and orientation considerations.

Frequency Factor

The frequency factor, \( A \), in the context of the Arrhenius Equation, is a measure of the rate at which reactants collide with the proper orientation and energy to cause a reaction. It encompasses both the physical collision frequency and the probability of correct molecular alignment.Key points about the frequency factor:

• It reflects how often molecules collide effectively in a reaction.
• The steric factor is a multiplier within \( A \), affecting the success rate of these collisions.
• When \( P > 1 \), experimental values of \( A \) can be higher than the baseline theoretical values, indicating more opportunistic collisions than expected.

Thus, understanding the frequency factor helps scientists predict and study reaction rates more accurately, considering both kinetic energy and molecular orientation influences. It provides insight into reaction efficiency and helps explain discrepancies between theoretical predictions and experimental findings.