The following kinetic data were obtained for the reaction: NO2(๐)+O3(๐)โNO3(๐)+O2(๐)
Experiment: Initial [NO2](M): Initial [O3](M): Initial Rate(M/s):
1 0.21 0.70 6.3
2 0.21 1.39 12.5
3 0.38 0.70 11.4
Find the reaction order for each reactant and the overall reaction order?
Thia is difficult to answer on the computer but here goes. You can follow up if there is something you don't understand but remember to state your question clearly and concisely. You get the exponents by substituting concentrations that are the same. You will see that. First, however, I will copy your data and try to make it more readable.
Experiment # Initial [NO2](M) Initial [O3](M) Initial Rate(M/s)
......1....................... 0.21.................... 0.70...................... 6.3
......2........................ 0.21..................... 1.39................... 12.5
......3........................ 0.38...................... 0.70.....................11.4
The reaction is NO2(๐) + O3(๐) โ NO3(๐) + O2(๐)
so rate = k(NO2)^a(O3)^b and it's a and b that we want to determine. So we pick for NO2 trials that are the same and that will give us b, the order for (NO3). I see that experiment # 1 and 2 are the same; we substitute.
rate 1 = k1(NO2)^a(O3)^b or
6.3 = k1(0.21)^a(0.70)b. Do the same for experiment 2.
12.5 = k2(0.21)^a(1.39)^b. Now you divide the second eqn by the first like so. I havve used the dots for spacing to make a fraction on both sides of the equal sign.
12.5......k2(0.21)^a(1.39)^b
------ = ------------------------- and solve that equation for b.
6.3 ..... k1(0.21)^a(0.70)b
Since we know rate constant k is constant then k2/k1 will cancel and you can see that (NO2)^a in the numerator and denominator cancel and we have this
.............(O3)^b
,,,,,,,,,,,,,,,(1.39)^b
1.98 = ---------------- or
...............(0.70)^b
1.98 = (1.98)^b we see that the exponent b, which is the order of the reaction for component O3 is 1.
Follow the same procedure using experiment 1 and 3 where the (O3) is constant and will cancel which allows you to determne the exponent a.
Post your work if you get stuck.
The overall order is the sum of a and b
To determine the reaction order for each reactant and the overall reaction order, we can use the method of initial rates.
The rate of a chemical reaction can be expressed using the rate law equation:
Rate = k [A]^m [B]^n
Where:
- Rate is the reaction rate,
- k is the rate constant,
- [A] and [B] are the concentrations of the reactants A and B, and
- m and n are the reaction orders for reactants A and B, respectively.
To find the reaction orders, we need to compare the initial rates for different experiments while keeping one reactant concentration constant and varying the other. By observing how the initial rate changes with changing concentration for a specific reactant, we can determine its reaction order.
In Experiment 1 and Experiment 2, the concentration of NO2 is constant while the concentration of O3 is changing. Comparing the initial rates for these two experiments:
(Initial Rate for Experiment 2) / (Initial Rate for Experiment 1) = (12.5 M/s) / (6.3 M/s) โ 1.98
Since the concentration of NO2 (the reactant with constant concentration) does not change, the change in initial rate can be attributed to the change in the concentration of O3. From the ratio above, it is clear that when the concentration of O3 doubles (from 0.70 M to 1.39 M), the initial rate approximately doubles as well. This indicates a first-order dependence on O3.
Now, let's compare the initial rates of Experiment 1 and Experiment 3, where the concentration of O3 is constant, and the concentration of NO2 is changing:
(Initial Rate for Experiment 3) / (Initial Rate for Experiment 1) = (11.4 M/s) / (6.3 M/s) โ 1.81
Similar to the previous comparison, the change in the initial rate can be attributed to the change in the concentration of NO2. When the concentration of NO2 doubles (from 0.21 M to 0.38 M), the initial rate approximately doubles as well. This indicates a first-order dependence on NO2.
Based on the analysis above, the reaction order for NO2 is 1, and the reaction order for O3 is also 1. Therefore, the overall reaction order is the sum of the individual reaction orders:
Overall reaction order = 1 + 1 = 2
So, the reaction is second-order overall.