The reaction between NO (nitric oxide) and oxygen is a key step in the formation of
acid rain.
O2(g) + 2NO(g) → 2NO2(g)
A series of experiments were run, each of which starts with a different set of reactant concentrations. From each experiment an initial rate of reaction was obtained.
======Initial concentration=========
==== mol dm-3 ========= == ====Initial rate of reaction=========
======================= = ===(mol dm-3 s-1)
Expt.------- [O2] ======------ [NO]
1) ---- -- 1.10x10-2 === 1.30x10-2 == 3.20 x 10-3
2 --- -- 2.20x10-2 === 1.30x10-2 == 6.40 x 10-3
3 --- -- 1.10x10-2 === 2.60x10-2 == 1.28 x 10-2
4 ----- 3.30x10-2 === 1.30x10-2 == 9.60 x 10-3
5 ----- 1.10x10-2 === 3.90x10-2 == 2.88 x 10-2
a) Using the data from the table, determine the orders of reaction with respect to O2 and NO. Explain your reasoning.
(b) Write a rate equation for this reaction.
(c) Determine the overall order of reaction.
(d) Calculate the rate constant (k) for this reaction, express your answer to the appropriate number of significant and give the units
#1 and #5 will give you the order for NO which I see as 2.
#1 and #2 will give you the order for O2 which I see as 1 so the rate constant expression is
rate = k[NO][O2]2
The overall order is the sum of the individual orders.
Take any one experiment and substitute the number into the rate expression; solve for k.
thank you. I don't understand why the O2 is to the power of two in the rate = k[NO][O2]2 when that is only a first order reaction and the NO is second order.
(a) To determine the orders of reaction with respect to O2 and NO, we can compare the initial rates of reaction for different experiments while keeping one reactant concentration constant and varying the other.
Let's examine the data from Experiments 1 and 2, where the concentration of O2 is constant at 1.10x10^-2 mol dm^-3:
Experiment 1: [O2] = 1.10x10^-2 mol dm^-3, [NO] = 1.30x10^-2 mol dm^-3, initial rate = 3.20x10^-3 mol dm^-3 s^-1
Experiment 2: [O2] = 1.10x10^-2 mol dm^-3, [NO] = 1.30x10^-2 mol dm^-3, initial rate = 6.40x10^-3 mol dm^-3 s^-1
We can see that doubling the concentration of NO (while keeping the concentration of O2 constant) results in doubling the initial rate of reaction. This suggests that the reaction is first order with respect to NO.
Now let's compare the data from Experiments 1 and 3, where the concentration of NO is constant at 1.30x10^-2 mol dm^-3:
Experiment 1: [O2] = 1.10x10^-2 mol dm^-3, [NO] = 1.30x10^-2 mol dm^-3, initial rate = 3.20x10^-3 mol dm^-3 s^-1
Experiment 3: [O2] = 1.10x10^-2 mol dm^-3, [NO] = 2.60x10^-2 mol dm^-3, initial rate = 1.28x10^-2 mol dm^-3 s^-1
Increasing the concentration of NO while keeping the concentration of O2 constant results in quadrupling the initial rate of reaction. This suggests that the reaction is second order with respect to NO.
Therefore, the orders of reaction with respect to O2 and NO are 1 and 2, respectively.
(b) The rate equation can be written as:
Rate = k * [O2]^1 * [NO]^2
(c) The overall order of reaction is the sum of the orders with respect to each reactant. In this case, the overall order of reaction is 1 + 2 = 3.
(d) To calculate the rate constant (k), we can choose any experiment with known initial concentrations and rates to solve for k. Let's use Experiment 1:
[O2] = 1.10x10^-2 mol dm^-3
[NO] = 1.30x10^-2 mol dm^-3
Initial rate = 3.20x10^-3 mol dm^-3 s^-1
Plugging these values into the rate equation, we have:
3.20x10^-3 = k * (1.10x10^-2)^1 * (1.30x10^-2)^2
Simplifying:
3.20x10^-3 = k * 1.43x10^-4
Solving for k:
k = (3.20x10^-3) / (1.43x10^-4)
k ≈ 22.38 mol^-2 dm^6 s^-1
Therefore, the rate constant (k) for this reaction is approximately 22.38 mol^-2 dm^6 s^-1.
To determine the orders of reaction with respect to O2 and NO, we need to analyze the given data.
(a) The order of reaction with respect to a particular reactant can be determined by observing how changes in the concentration of that reactant affect the initial rate of reaction. Let's compare the experiments and their corresponding rates of reaction:
Experiment 1: [O2] = 1.10x10^-2 mol dm^-3, [NO] = 1.30x10^-2 mol dm^-3, Initial rate = 3.20x10^-3 mol dm^-3 s^-1
Experiment 2: [O2] = 2.20x10^-2 mol dm^-3, [NO] = 1.30x10^-2 mol dm^-3, Initial rate = 6.40x10^-3 mol dm^-3 s^-1
As we double the concentration of O2 while keeping the NO concentration constant, the initial rate doubles (3.20x10^-3 mol dm^-3 s^-1 to 6.40x10^-3 mol dm^-3 s^-1). This indicates that the reaction is first order with respect to O2.
Experiment 3: [O2] = 1.10x10^-2 mol dm^-3, [NO] = 2.60x10^-2 mol dm^-3, Initial rate = 1.28x10^-2 mol dm^-3 s^-1
As we double the concentration of NO while keeping the O2 concentration constant, the initial rate quadruples (3.20x10^-3 mol dm^-3 s^-1 to 1.28x10^-2 mol dm^-3 s^-1). This indicates that the reaction is second order with respect to NO.
Therefore, the reaction is first order with respect to O2 and second order with respect to NO.
(b) The rate equation represents the relationship between the initial rate of reaction and the concentrations of the reactants. Based on the determined orders of reaction, we can write the rate equation:
Rate = k[O2]^1[NO]^2
(c) The overall order of the reaction is the sum of the individual orders. In this case, the overall order is 1 (from O2) + 2 (from NO) = 3.
(d) To calculate the rate constant, we can use the information from any of the experiments. Let's choose Experiment 1:
[O2] = 1.10x10^-2 mol dm^-3, [NO] = 1.30x10^-2 mol dm^-3, Initial rate = 3.20x10^-3 mol dm^-3 s^-1
Using the rate equation, we can rearrange it to solve for the rate constant (k):
k = Rate / ([O2]^1[NO]^2)
= 3.20x10^-3 mol dm^-3 s^-1 / [(1.10x10^-2 mol dm^-3)^1(1.30x10^-2 mol dm^-3)^2]
= 3.20x10^-3 mol dm^-3 s^-1 / (1.13x10^-4 mol^3 dm^-9)
= 2.83x10^1 dm^3 mol^-2 s^-1
The rate constant (k) for this reaction is 2.83x10^1 dm^3 mol^-2 s^-1, expressed to the appropriate number of significant figures and with the appropriate units.