Final answer:
The rate constant for the second-order reaction is 0.178 M^-1s^-1.
Step-by-step explanation:
The rate constant for a second-order reaction can be calculated using the equation:
k = (1/t1/2) * (1/[A0])
where t1/2 is the half-life of the reaction and [A0] is the initial reactant concentration. In this case, the half-life is given as 22.5 s and the initial reactant concentration is 0.250 M. Plugging these values into the equation, we get:
k = (1/22.5) * (1/0.250) = 0.178 M-1s-1
Therefore, the rate constant for the reaction is 0.178 M-1s-1.