Question

According to the Arrhenius equation,

• A. Rate constant increases with increase in temperature. This is
  due to a greater number of collisions whose energy exceeds
  the activation energy
• B. Higher the magnitude of activation energy, stronger is the
  temperature dependence of the rate constant
• C. The pre-exponential factor is a measure of the rate at which
  collisions occur, irrespective of their energy
• D. A high activation energy usually implies a fast reaction

Answer 1

Answer: (A), (B), (C)

The pre-exponential factor is a measure of the rate at which

collisions occur, irrespective of their energy
Rate constant,
$k=A{e}^{\frac{-E_a}{RT}}$
where, $E_a=\text{activation energy and A = pre-exponential factor}$

(a) If $E_a$ is high, it means lower value of $k$ hence, slow reaction. Thus, incorrect.

(b ) On increasing temperature, molecules are raised to higher
energy (greater than $E_a$), hence number of collisions increases. Thus, correct.

(c)
$logk=logA-\frac{E_a}{RT}\Rightarrow \frac{d\left(logk\right)}{dT}=\frac{E_a}{R{T}^2}$
Thus, when $E_a$ is high, stronger is the temperature
dependence of the rate constant. Thus, correct.

(d) Pre-exponential factor $A$ is a measure of rate at which
collisions occur. Thus, correct.