Final answer:
The order of the reaction with respect to [A] is first-order, and the rate law is rate = k[A]. The rate constant (k) of the reaction is 1.247 L mol^-1 s^-1.
Step-by-step explanation:
The order of the reaction with respect to [A] can be determined by comparing the changes in the initial reaction rates with the corresponding changes in the initial concentrations. If the rate doubles when the concentration of A doubles, the reaction is first-order.
If the rate quadruples when the concentration of A doubles, the reaction is second-order. If the rate does not change when the concentration of A doubles, the reaction is zeroth-order. From the given data, we can see that the rate of the reaction doubles when the concentration of A doubles. Therefore, the reaction is first-order with respect to [A]. The rate law for a first-order reaction is expressed as:
rate = k[A], where k is the rate constant.
To find the rate constant (k), we need to use data from one of the experiments. Let's take the first experiment, where [A]initial = 0.170 M and the rate = 0.212 mol L-1 s-1. Plugging these values into the rate law equation, we get:
0.212 = k * 0.170
Solving for k, we find that the rate constant is 1.247 L mol-1 s-1.