Final answer:
The rate law for the reaction A + B → C + D can be determined by comparing the initial rates of different trials while keeping the concentration of one reactant constant. In this case, the reaction is second order with respect to A, and the rate law is rate = k[A]²[B]. The rate constant (k) can be calculated using any of the trials by substituting the values of [A], [B], and the initial rate into the rate law equation.
Step-by-step explanation:
The rate law for the reaction A + B → C + D can be determined by analyzing the experimental data. In this case, we have four trials with different initial concentrations of A, B, and the corresponding initial rates. By comparing the initial rates for different trials while keeping the concentration of one reactant constant, we can determine the order of the reaction with respect to that reactant.
Let's analyze the data:
Trial[A][B]Initial Rate (M/min)10.400.200.1220.200.200.03030.400.400.2440.600.400.54
Let's analyze the data for Trial 1 and Trial 2:
Trial 1: [A]o = 0.4 M, [B]o = 0.2 M, Initial Rate = 0.12 M/min
Trial 2: [A]o = 0.2 M, [B]o = 0.2 M, Initial Rate = 0.03 M/min
Since the concentration of B is constant while comparing the rates of these two trials, we can determine the order of the reaction with respect to A by taking the ratio of the initial rates:
Rate ratio = Initial Rate(Trial 1) / Initial Rate(Trial 2) = (0.12 M/min) / (0.03 M/min) = 4
This indicates that doubling the concentration of A leads to a four-fold increase in the rate of the reaction. Therefore, the reaction is second order with respect to A. The rate law for the reaction can be expressed as:
Rate = k[A]²[B]
We can now determine the rate constant (k) by using any of the trials and substituting the values of [A], [B], and the initial rate into the rate law equation. Let's use Trial 1 to calculate k:
k = Initial Rate / ([A]²[B]) = 0.12 M/min / (0.4 M)²(0.2 M) = 0.75 M⁻²min⁻¹