Activation energy is ______ to rate of reaction

Options

A. directly proportional
B. inversely proportional
C. equal
D. not related

Explanation

To answer the question "Activation energy is ______ to rate of reaction," we can follow these steps:

### Step 1: Understand Activation Energy
Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It is a crucial factor in determining the rate of a reaction.

### Step 2: Introduce the Arrhenius Equation
The relationship between the rate of a reaction and activation energy is described by the Arrhenius equation:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.

### Step 3: Analyze the Equation
From the Arrhenius equation, we can see that the rate constant \( k \) is affected by the exponential term \( e^{-\frac{E_a}{RT}} \). As the activation energy \( E_a \) increases, the term \( -\frac{E_a}{RT} \) becomes more negative, which means that \( e^{-\frac{E_a}{RT}} \) decreases.

### Step 4: Establish the Relationship
Since the rate constant \( k \) is directly related to the rate of reaction, if \( k \) decreases due to an increase in \( E_a \), it implies that the rate of reaction also decreases. Therefore, we can conclude that the rate of reaction is inversely proportional to the activation energy.

### Step 5: Final Answer
Thus, we can fill in the blank in the question: "Activation energy is **inversely proportional** to the rate of reaction."