For a second-order reaction, the rate law is given by:rate = k[A]^2where rate is the reaction rate, k is the rate constant, and [A] is the concentration of the reactant.We are given the rate 0.025 M/s and the initial concentration of the reactant 0.10 M . We can now solve for the rate constant k :0.025 M/s = k 0.10 M ^2To solve for k, divide both sides by 0.10 M ^2:k = 0.025 M/s / 0.10 M ^2k = 0.025 M/s / 0.01 M^2 k = 2.5 M^-1 s^-1 So, the rate constant k at 300 K for this gas phase reaction is 2.5 M^-1 s^-1 .