Q.Match the statements given in Column I and Column II.
Column I:

The key idea is Average Rate of Reaction and the factors that govern it — catalysts, molecularity, half-life, activation energy, and molecular orientation.

Reasoning:

1. A catalyst works by providing an alternative path with lower activation energy → (i) matches (c).
2. Molecularity is the number of reacting species in an elementary step; it is always a positive integer — cannot be a fraction or zero → (ii) matches (a).
3. For a first-order reaction, each successive half-life is identical → (iii) matches (d).
4. The Boltzmann factor $e^{-E_a/RT}$ gives the fraction of molecules with energy $\geq E_a$ → (iv) matches (f). …

Let's go through each statement one by one, building the reasoning from first principles.

1. (i) Catalyst alters the rate of reaction → (c) by lowering the activation energy

A catalyst provides an alternative reaction pathway with a lower activation energy ($E_a$). This means a larger fraction of molecules have enough energy to cross the barrier at the same temperature. The catalyst itself is not consumed — it simply changes the route. The rate increases because more molecules can react per unit time.

2. (ii) Molecularity → (a) cannot be fraction or zero

Molecularity is the number of molecules (or atoms) that collide in an elementary step. It is always a positive integer: 1 (unimolecular), 2 (bimolecular), or rarely 3 (termolecular). It can never be zero (no reaction without at least one molecule) or a fraction (you can't have half a molecule colliding). This is a fundamental definition — molecularity is a theoretical concept, not an experimentally determined number like order.

3. (iii) Second half life of first order reaction → (d) is same as the first

For a first order reaction, the half-life ($t_{1/2}$) is independent of the initial concentration:

Since $k$ is constant at a given temperature, every successive half-life is identical. The second half-life equals the first, the third equals the second, and so on. This is a unique property of first order kinetics — no other order has constant half-lives.

4. (iv) $e^{-E_a/RT}$ → (f) refers to the fraction of molecules with energy equal to or greater than activation energy

This expression comes directly from the Arrhenius equation:

The exponential term $e^{-E_a/RT}$ represents the fraction of molecules that have energy $\geq E_a$ at temperature $T$. It is derived from the Maxwell-Boltzmann distribution — only molecules in the high-energy tail of the distribution can overcome the activation barrier.

5. (v) Energetically favourable reactions are sometimes slow → (b) proper orientation is not there always …

Method: Concept Matching by Definition & Principle

This method works by identifying the core definition, formula, or physical principle behind each statement in Column I, then matching it to the precise description in Column II.

Steps:

1. Analyze each statement in Column I for its defining characteristic.
2. Recall the exact meaning of the term or concept (no guesswork).
3. Find the corresponding description in Column II that matches that meaning exactly.
4. Eliminate mismatches by checking if the description fits the concept’s definition.

Step-by-step matching:

• (i) Catalyst alters the rate of reaction

  Principle: A catalyst works by providing an alternative pathway with lower activation energy.

  Match: (c) by lowering the activation energy

• (ii) Molecularity

  Definition: The number of molecules taking part in an elementary step. It is always a positive integer (1, 2, 3…) — never a fraction or zero.

  Match: (a) cannot be fraction or zero

• (iii) Second half life of first order reaction

  Key fact: For a first order reaction, the half-life is constant — every half-life is the same.

  Match: (d) is same as the first

• (iv) $e^{-E_a/RT}$

  Meaning: This is the fraction of molecules having energy equal to or greater than the activation energy $E_a$ (from the Arrhenius equation).

  Match: (f) refers to the fraction of molecules with energy equal to or greater than activation energy …

Here are the most common mistakes students make when matching these statements, along with the correct reasoning to avoid them.

Mistake 1: Confusing "Catalyst" with "Molecularity"

• The Error: Students often match (i) Catalyst alters the rate of reaction with (b) proper orientation is not there always because they think a catalyst "fixes" orientation problems.
• Why it's wrong: A catalyst changes the pathway of the reaction, specifically by lowering the activation energy ($E_a$). Orientation is a factor for effective collisions, not for catalyst function.
• How to avoid: Remember the definition: A catalyst provides an alternative mechanism with lower $E_a$. The correct match is (i) → (c).

Mistake 2: Forgetting that Molecularity is an Integer

• The Error: Matching (ii) Molecularity with (f) refers to the fraction of molecules... because both involve "molecules."
• Why it's wrong: Molecularity is the number of reacting species (atoms, ions, molecules) that collide in the rate-determining step. It is always a positive integer (1, 2, 3) and cannot be zero or a fraction.
• How to avoid: Link "Molecularity" directly to "number of molecules." The only option describing a number property is (a) cannot be fraction or zero. So, (ii) → (a).

Mistake 3: Misunderstanding "Second Half-Life" of a First-Order Reaction

• The Error: Thinking the second half-life is different (longer or shorter) because the concentration is lower.
• Why it's wrong: For a first-order reaction, the half-life ($t_{1/2}$) is independent of concentration. Therefore, the second half-life is exactly the same as the first.
• How to avoid: Memorize the key property: $t_{1/2} = \frac{0.693}{k}$ for first order. Since $k$ is constant, $t_{1/2}$ is constant. The correct match is (iii) → (d).

Mistake 4: Confusing the Exponential Term with the Area Under the Curve

• The Error: Matching (iv) $e^{-E_a/RT}$ with (e) total probability is one because both involve "probability."
• Why it's wrong: The term $e^{-E_a/RT}$ is the fraction of molecules that have energy equal to or greater than the activation energy. It is not a total probability; it is a specific fraction (always less than 1).
• How to avoid: Recognize the Arrhenius equation factor. $e^{-E_a/RT}$ directly gives the fraction of molecules with sufficient energy. So, (iv) → (f).

Mistake 5: Ignoring the "Energetically Favorable" vs. "Kinetic Barrier" Distinction

• The Error: Matching (v) Energetically favourable reactions are sometimes slow with (c) by lowering the activation energy.
• Why it's wrong: A reaction can be thermodynamically favorable (spontaneous, negative $\Delta G$) but still slow because of a high activation energy barrier. The reason it's slow is that molecules lack proper orientation during collisions, not because the catalyst is missing.
• How to avoid: "Energetically favourable" = thermodynamics (spontaneous). "Slow" = kinetics (high $E_a$ or poor orientation). The statement directly implies that even if energy is sufficient, orientation may be wrong. So, (v) → (b).

Mistake 6: Misinterpreting the "Constant Area" of the Maxwell-Boltzmann Curve …