Final answer:
To determine the relative reaction rate, use the initial rates method. This involves establishing the rate law and calculating the rate constant (k) by examining how changes in reactant concentration influence rate. You then use the rate and concentration data to calculate k.
Step-by-step explanation:
To calculate the relative rate of reaction using an initial rates method, you need to first understand the basics of reaction rates and how they relate to concentration. In the provided examples, the initial rates of the reactions are used to determine the rate law and calculate the rate constant (k). This involves evaluating how changes in concentration affect the reaction rate.
When comparing experiments, if doubling the concentration of a reactant doubles the reaction rate, the reaction is directly proportional to the concentration of that reactant, indicating a first-order reaction. The rate law can be expressed as rate = k[A], where [A] is the concentration of the reactant. To find the rate constant k, you can use the rate and concentration from any one of the experiments. For example, if the rate is 1.60 x 10-8 M/s and the concentration is 0.010 M, the rate constant would be calculated using the formula: rate = k[A], leading to k = rate/[A]. In this case, k = (1.60 x 10-8 M/s) / (0.010 M), giving a rate constant of 1.6 x 10-6 s-1.