Question

Activation energy of any chemical reaction can be calculated if one knows the value of

• A. rate constant at standard temperature.
• B. probability of collision
• C. orientation of reactant molecules during collision.
• D. rate constant at two different temperatures

Answer 1

The Correct Option is D

Activation energy of any chemical reaction can be calculated if one knows the value of:

Option 4: rate constant at two different temperatures.

Explanation:

The Arrhenius equation relates the rate constant (k) of a chemical reaction to the temperature (T) and the activation energy (Ea):

$$ k = A e^{-E_a/RT} $$

Where:

• \( k \) = rate constant
• \( A \) = pre-exponential factor
• \( E_a \) = activation energy
• \( R \) = ideal gas constant
• \( T \) = absolute temperature

If you have the rate constant at two different temperatures (\( k_1 \) at \( T_1 \) and \( k_2 \) at \( T_2 \)), you can use a modified form of the Arrhenius equation to calculate the activation energy:

$$ \ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right) $$

By rearranging this equation, you can solve for \( E_a \):

$$ E_a = -R \frac{\ln\left(\frac{k_2}{k_1}\right)}{\left(\frac{1}{T_2} - \frac{1}{T_1}\right)} $$

Therefore, knowing the rate constant at two different temperatures is necessary to calculate the activation energy.