Answer:
kA = (-0.222 - 0.175
Step-by-step explanation:
Let's denote the concentration of species A as [A] and the time as t.
We can start by analyzing the concentration data and observing the relationship between the initial concentration [A]0 and the concentration at different time points [A]t.
From the given data, we can calculate the initial concentration [A]0 as 4.0 mol/dm³.
Next, let's calculate the reaction rate, which is the change in concentration of A over time. We can do this by dividing the change in concentration ([A]t - [A]0) by the corresponding time interval (t - 0).
Using the data given:
At t = 5 minutes: [A]5 = 2.89 mol/dm³
Reaction rate at t = 5 minutes: (2.89 - 4.0) / (5 - 0) = -0.222 mol/dm³·min
At t = 10 minutes: [A]10 = 2.25 mol/dm³
Reaction rate at t = 10 minutes: (2.25 - 4.0) / (10 - 0) = -0.175 mol/dm³·min
At t = 15 minutes: [A]15 = 1.45 mol/dm³
Reaction rate at t = 15 minutes: (1.45 - 4.0) / (15 - 0) = -0.17 mol/dm³·min
At t = 20 minutes: [A]20 = 1.0 mol/dm³
Reaction rate at t = 20 minutes: (1.0 - 4.0) / (20 - 0) = -0.15 mol/dm³·min
At t = 25 minutes: [A]25 = 0.65 mol/dm³
Reaction rate at t = 25 minutes: (0.65 - 4.0) / (25 - 0) = -0.154 mol/dm³·min
At t = 30 minutes: [A]30 = 0.25 mol/dm³
Reaction rate at t = 30 minutes: (0.25 - 4.0) / (30 - 0) = -0.125 mol/dm³·min
At t = 35 minutes: [A]35 = 0.07 mol/dm³
Reaction rate at t = 35 minutes: (0.07 - 4.0) / (35 - 0) = -0.119 mol/dm³·min
Now, let's analyze the relationship between the reaction rate and the concentration of A.
From the calculated reaction rates, we can see that the reaction rate is inversely proportional to the concentration of A. As the concentration of A decreases, the reaction rate becomes smaller.
This suggests that the reaction follows a first-order kinetics, as the rate is dependent on the concentration of a single reactant.
The rate equation for a first-order reaction is given by:
Rate = k[A]
Comparing this equation to the calculated reaction rates, we can see that the reaction rate is equal to the specific reaction rate, kA, multiplied by the concentration of A. Therefore, the specific reaction rate, kA, is equal to the slope of the concentration-time data.
We can calculate the value of kA by taking the average of the slopes of the reaction rates calculated at different time intervals.
Average kA = (-0.222 - 0.175