For a second-order reaction, the half-life t1/2 is related to the rate constant k and the initial concentration A0 by the following equation:t1/2 = 1 / k * A0 Given the half-life t1/2 is 5 minutes and the initial concentration A0 is 0.5 M, we can solve for the rate constant k :5 minutes = 1 / k * 0.5 M Now, we can rearrange the equation to solve for k:k = 1 / 5 minutes * 0.5 M k = 1 / 2.5 M*minutesk = 0.4 M^-1 minutes^-1 So, the rate constant k for this second-order reaction is 0.4 M^-1 minutes^-1 .