By which activation energy calculate :

Options

A. At a constant temp.
B. At two different temp.
C. For reversible reaction
D. For volatile reaction

Answer

To determine the activation energy (Ea) of a chemical reaction, we can use the Arrhenius equation, which relates the rate constants of a reaction at two different temperatures. Here’s a step-by-step solution:

### Step 1: Understand Activation Energy
Activation energy 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: Recall the Arrhenius Equation
The Arrhenius equation can be expressed as:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) is the rate constant,
- \( A \) is the pre-exponential factor,
- \( E_a \) is the activation energy,
- \( R \) is the gas constant,
- \( T \) is the absolute temperature in Kelvin.

### Step 3: Use the Two-Temperature Form of the Arrhenius Equation
To calculate the activation energy, we can use the form of the Arrhenius equation that involves two different temperatures:
\[ \log \frac{k_2}{k_1} = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \]
where:
- \( k_1 \) and \( k_2 \) are the rate constants at temperatures \( T_1 \) and \( T_2 \), respectively.

### Step 4: Identify the Correct Option
From the options provided:
1. At a constant temperature
2. At two different temperatures
3. For reversible reactions
4. For volatile reactions

The correct option is **"at two different temperatures"** because the activation energy can be calculated by comparing the rate constants at these two different temperatures.

### Conclusion
Thus, the activation energy is calculated using the rate constants at two different temperatures, making option 2 the correct answer.

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