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 for a chemical reaction is determinable given the value of:

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

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

Where:

• \( k \) represents the rate constant
• \( A \) denotes the pre-exponential factor
• \( E_a \) signifies the activation energy
• \( R \) is the ideal gas constant
• \( T \) indicates the absolute temperature

If the rate constant is known at two distinct temperatures (\( k_1 \) at \( T_1 \) and \( k_2 \) at \( T_2 \)), a modified Arrhenius equation can be employed for activation energy calculation:

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

Rearranging this equation permits solving for \( E_a \):

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

Consequently, the rate constant at two different temperatures is requisite for calculating activation energy.