To calculate the rate constant k of the reaction, we first need to determine the rate law for the reaction. Since the reaction is second order with respect to A and first order with respect to B, the rate law is:rate = k[A]^2[B]Next, we need to find the change in concentration of A and B over time. The initial concentration of A is 0.2 M and it decreased to 0.1 M after 30 minutes. The change in concentration of A is:[A] = 0.1 MSimilarly, the initial concentration of B is 0.5 M and it decreased to 0.3 M after 30 minutes. The change in concentration of B is:[B] = 0.2 MNow, we can use the integrated rate law for a second order reaction with respect to A and first order with respect to B. The integrated rate law is:1/ [A]_t - [A]_0 = k * t * [B]_0where [A]_t is the concentration of A at time t, [A]_0 is the initial concentration of A, t is the time, and [B]_0 is the initial concentration of B.Plugging in the values, we get:1/ 0.1 - 0.2 = k * 30 * 0.5Solving for k:1/ -0.1 = k * 15k = -10/15k = -2/3 M^-1 min^-1 However, the rate constant should be a positive value. It seems there is an error in the given data or the reaction order. Please check the data and reaction order and try again.