A student collected concentration data to determine the rate of the decomposition of N2O5 to NO2 and O2. The data were recorded in the table below. What is the rate law of this reaction?
A. k[NO2]
B. k[N2O5]
C. k
D. k[N2O5]2
[N2O5]M- .5,.44,.39,.34,.30,.27
Time s- 0,200,400,600,800,1000
B.
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To determine the rate law of a reaction, we need to look at how the concentration of the reactants affects the rate of the reaction. We can use the given data to do this.
Let's examine the data for the concentration of N2O5 and the corresponding time:
[N2O5]M: 0.5, 0.44, 0.39, 0.34, 0.3, 0.27
Time (s): 0, 200, 400, 600, 800, 1000
To determine the rate law, we need to compare the changes in concentration with time. One way to do this is to calculate the initial rate of the reaction (the rate at the beginning when time is equal to zero) and compare it to the rate at other points.
To calculate the initial rate, we can consider the change in concentration of N2O5 divided by the change in time for the first two data points:
Initial rate = (0.44 M - 0.5 M) / (200 s - 0 s) = -0.06 M/s
Now let's calculate the rate ratios by comparing the initial rate with the rate at each subsequent time point:
Rate ratio 1 = (-0.3 M/s) / (-0.06 M/s) = 5
Rate ratio 2 = (-0.34 M/s) / (-0.06 M/s) = 5.67
Rate ratio 3 = (-0.39 M/s) / (-0.06 M/s) ≈ 6.5
Rate ratio 4 = (-0.44 M/s) / (-0.06 M/s) ≈ 7.33
Rate ratio 5 = (-0.5 M/s) / (-0.06 M/s) ≈ 8.33
To determine the rate law, we look for consistent rate ratios. In this case, the rate ratios are approximately consistent, indicating a direct relationship between the concentration of N2O5 and the rate of the reaction. Therefore, we can conclude that the rate law of this reaction is:
B. k[N2O5]
The rate of the reaction is proportional to the concentration of N2O5.
To determine the rate law of a reaction, you'll need to use the concentration data and the corresponding time data to calculate the initial rate of the reaction for different trials. The initial rate is the change in concentration per unit time at the beginning of the reaction.
Let's start by calculating the initial rate for each trial. We'll use the formula:
Rate = (Δ[N2O5]) / Δt
where Δ[N2O5] is the change in concentration of N2O5 and Δt is the change in time.
For Trial 1 (0 to 200 seconds):
Δ[N2O5] = 0.44 - 0.5 = -0.06 M
Δt = 200 seconds
Rate1 = (-0.06 M) / (200 seconds)
Repeat this calculation for the rest of the trials:
Trial 2 (200 to 400 seconds):
Δ[N2O5] = 0.39 - 0.44 = -0.05 M
Δt = 200 seconds
Rate2 = (-0.05 M) / (200 seconds)
Trial 3 (400 to 600 seconds):
Δ[N2O5] = 0.34 - 0.39 = -0.05 M
Δt = 200 seconds
Rate3 = (-0.05 M) / (200 seconds)
Repeat the calculation for the remaining trials.
Trial 4 (600 to 800 seconds):
Rate4 = ...
Trial 5 (800 to 1000 seconds):
Rate5 = ...
Now, compare the initial rates for each trial. If the initial rates are constant (within experimental error), the rate law will only depend on the concentration of N2O5. If the initial rates follow a different relationship to the concentration of N2O5, this means there may be other factors affecting the rate of the reaction.
Once you've determined the relationship between the initial rates and the concentration of N2O5, you can determine the rate law. Based on the given answer choices, you'll need to match the relationship to one of the options: k[NO2], k[N2O5], k, or k[N2O5]2.