For a first-order reaction, the integrated rate law is given by:ln [A]t/[A]0 = -ktwhere [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, k is the rate constant, and t is the time.In this case, the initial concentration of hydrogen peroxide, [A]0, is 0.1 M. After 5 minutes 300 seconds , 80% of the hydrogen peroxide has decomposed, so the remaining concentration, [A]t, is 20% of the initial concentration, which is 0.02 M.Now we can plug these values into the integrated rate law equation:ln 0.02/0.1 = -k * 300Solving for k:k = - ln 0.02/0.1 / 300 k 0.00796 sSo, the rate constant for the first-order decomposition of hydrogen peroxide under these conditions is approximately 0.00796 s.