Question

According to Collision Theory, the rate constant of a chemical reaction depends on activation energy. If the activation energy of a reaction increases, then the value of the rate constant \(k\) will:

• A. Increase exponentially
• B. Remain unchanged
• C. Decrease exponentially
• D. Become zero

Hint:

Remember: \[ k = A e^{-E_a/RT} \]
• Larger activation energy \(\Rightarrow\) smaller rate constant
• Higher temperature \(\Rightarrow\) larger rate constant

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
According to collision theory and chemical kinetics, reactants must overcome an energy barrier to transform into products. This minimum threshold energy is the activation energy ($E_a$). The rate constant ($k$) quantifies the speed of this chemical reaction. The Arrhenius equation mathematically formalizes how the rate constant depends on both the activation energy and temperature.
Step 2: Key Formula or Approach:
The dependency is modeled by the Arrhenius equation: $$ k = A e^{-\frac{E_a}{RT}} $$ Where: - $k$ is the reaction rate constant. - $A$ is the pre-exponential or frequency factor (representing collision frequency with proper orientation). - $E_a$ is the activation energy of the reaction. - $R$ is the universal gas constant. - $T$ is the absolute temperature in Kelvin.
Step 3: Detailed Explanation:
Let's analyze the mathematical behavior of the exponent when the activation energy ($E_a$) increases: 1. The term $E_a$ sits inside a negative exponent: $-\frac{E_a}{RT}$. 2. If $E_a$ grows larger, the value of the fraction $\frac{E_a}{RT}$ increases. 3. Because of the negative sign in front, the overall exponent $-\frac{E_a}{RT}$ becomes more negative (smaller). 4. Evaluating a base with a larger negative exponent ($e^{-\text{larger value}}$) causes the value to shrink rapidly. Therefore, an increase in activation energy results in an exponential decrease in the value of the rate constant $k$. Physically, this happens because a taller energy barrier means a much smaller fraction of colliding molecules possess the required kinetic energy to react successfully. This corresponds to option (C).
Step 4: Final Answer:
The value of the rate constant $k$ will decrease exponentially.