Arrange the following in the increasing order of rate of the second order reaction
Reactants → products

(A) Reaction at 298 K
(B) Reaction at 298 K with catalyst
(C) Reaction at 500 K with catalyst and double the initial concentration of reactant
(D) Reaction at 500 K with double the initial concentration of reactant

Choose the correct answer from the options given below:

(A), (B), (D), (C)

The correct answer is Option (1) → (A), (B), (D), (C)

For a second-order reaction:

$\text{Rate} \propto k[A]^2$

where

• k increases with temperature (Arrhenius equation)
• Catalyst increases k
• Doubling concentration increases rate by $2^2 = 4$ times

• (When concentration doubles in a second-order reaction, the rate increases four times because the concentration term is squared in the rate law. So doubling concentration gives: 2² = 4 times increase in rate.) 

• (A): 298 K, no catalyst → slowest
• (B): 298 K + catalyst → faster than (A)
• (D): 500 K + double concentration → much faster (higher k and 4× concentration effect)
• (C): 500 K + catalyst + double concentration → fastest

 Increasing order of rate:  (A) < (B) < (D) < (C)