The following initial rate data apply to the reaction
F2(g) + 2Cl2O(g) ----> 2FClO2(g) + Cl2(g)
Expt. # [F2](M) [Cl2O](M) Initial rate (M/s)
1 0.05 0.010 5.0 x 10^–4
2 0.05 0.040 2.0 x 10^–3
3 0.10 0.010 1.0 x 10^–3
Which of the following is the rate law (rate equation) for this reaction?
You didn't give any choices but it appears to be first order with respect to F2 and first order with respect to Cl2O
To determine the rate law for the reaction, we need to analyze how the initial rates change with the concentrations of reactants. By comparing Experiments 1 and 2, we can focus on how the concentration of Cl2O affects the rate of reaction, while keeping the concentration of F2 constant. Similarly, by comparing Experiments 1 and 3, we can examine the effect of F2 concentration on the reaction rate, while keeping the Cl2O concentration constant.
Let's start by comparing Experiments 1 and 2:
[F2] is constant: 0.05 M
[Cl2O]
Experiment 1: 0.010 M
Experiment 2: 0.040 M
The concentration of Cl2O quadruples while the initial rate increases by a factor of 4 as well. This suggests that the rate of the reaction is directly proportional to the concentration of Cl2O. Therefore, the rate law will include Cl2O as a factor, possibly to the first power.
Next, let's compare Experiments 1 and 3:
[Cl2O] is constant: 0.010 M
[F2]
Experiment 1: 0.05 M
Experiment 3: 0.10 M
The concentration of F2 doubles, while the initial rate also doubles. This indicates that the rate of the reaction is directly proportional to the concentration of F2. Therefore, the rate law will include F2 as a factor, possibly to the first power.
Combining the observations from both comparisons, the rate law for this reaction can be expressed as:
rate = k × [F2]^a × [Cl2O]^b
where a is the order with respect to F2 and b is the order with respect to Cl2O.
Based on our comparisons, we determined that a = 1 and b = 1. Thus, the rate law (rate equation) for this reaction is:
rate = k × [F2] × [Cl2O]
To determine the rate law for a reaction, you need to analyze how the initial rates change with changes in the concentrations of reactants. In this case, we have data from three experiments with different initial concentrations of [F2] and [Cl2O], and their corresponding initial rates.
Let's start by comparing the initial rates in experiments 1 and 2. The concentrations of [F2] are the same in both experiments (0.05 M), while the concentration of [Cl2O] is 0.010 M in experiment 1 and 0.040 M in experiment 2. Based on this information, we can determine how the variation in [Cl2O] affects the initial rate.
Comparing the initial rates:
Experiment 1: [F2] = 0.05 M, [Cl2O] = 0.010 M, initial rate = 5.0 x 10^–4 M/s
Experiment 2: [F2] = 0.05 M, [Cl2O] = 0.040 M, initial rate = 2.0 x 10^–3 M/s
Looking at the data, we can see that when the concentration of [Cl2O] increases by a factor of 4 (0.010 M to 0.040 M), the initial rate increases by a factor of 4 (5.0 x 10^–4 to 2.0 x 10^–3). This indicates that the reaction is directly proportional to the concentration of [Cl2O].
Next, let's compare the initial rates in experiments 1 and 3. The concentration of [Cl2O] is the same in both experiments (0.010 M), while the concentration of [F2] is 0.05 M in experiment 1 and 0.10 M in experiment 3.
Comparing the initial rates:
Experiment 1: [F2] = 0.05 M, [Cl2O] = 0.010 M, initial rate = 5.0 x 10^–4 M/s
Experiment 3: [F2] = 0.10 M, [Cl2O] = 0.010 M, initial rate = 1.0 x 10^–3 M/s
Looking at the data, we can see that when the concentration of [F2] doubles (0.05 M to 0.10 M), the initial rate also doubles (5.0 x 10^–4 to 1.0 x 10^–3). This indicates that the reaction is directly proportional to the concentration of [F2].
Based on our analysis, we can conclude that the rate law for the given reaction is:
Rate = k[F2][Cl2O]
The rate law is first order with respect to both [F2] and [Cl2O].