Understanding the Arrhenius Equation and Activation Energy

The Arrhenius equation describes how the rate constant (k) of a reaction depends on temperature (T) and activation energy (E_a). It is given by:

$k=A{e}^{-\frac{E_a}{RT}}$

where:

• k is the rate constant
• A is the pre-exponential factor (frequency factor)
• E_a is the activation energy
• R is the gas constant
• T is the temperature in Kelvin

Step-by-Step Analysis of the Given Statements:

Step 1: Evaluate the statement: "higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant."

From the Arrhenius equation, the term $e^{-\frac{E_a}{RT}}$ shows that a higher E_a makes the exponent more negative, meaning k is more sensitive to changes in T. Thus, this statement is correct.

Step 2: Evaluate the statement: "a high activation energy usually implies a fast reaction."

A high E_a means a larger energy barrier, so fewer molecules have sufficient energy to react at a given temperature, leading to a slower reaction. Therefore, this statement is incorrect.

Step 3: Evaluate the statement: "rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy."

As T increases, the exponential term $e^{-\frac{E_a}{RT}}$ becomes larger because the negative exponent becomes less negative. This corresponds to a higher fraction of molecules with energy ≥ E_a, increasing k. This statement is correct.

Step 4: Evaluate the statement: "the pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy."

The pre-exponential factor A represents the frequency of collisions with the correct orientation. It is indeed related to the collision rate and is independent of the energy of collisions. This statement is correct.

Final Answer:

The correct statements are:

• Higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant.
• Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
• The pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.

The incorrect statement is: "a high activation energy usually implies a fast reaction."

Related Topics:

• Chemical Kinetics
• Collision Theory
• Temperature Dependence of Reaction Rates
• Maxwell-Boltzmann Distribution

Key Formulae and Theory:

Arrhenius Equation: $k=A{e}^{-\frac{E_a}{RT}}$

Activation Energy (E_a): The minimum energy required for a reaction to occur. It is the energy barrier that must be overcome.

Pre-exponential Factor (A): Also called the frequency factor, it represents the number of collisions per unit time with the proper orientation for reaction.

Effect of Temperature: Increasing temperature increases the rate constant because it increases the fraction of molecules with energy greater than or equal to E_a.

Arrhenius Plot: Plotting ln(k) vs 1/T gives a straight line with slope = -E_a/R and intercept = ln(A). This is used to determine E_a and A experimentally.