The following kinetic data were obtained for the reaction: NO2(𝑔)+O3(𝑔)→NO3(𝑔)+O2(𝑔)

Question

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?

Answer 1

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(𝑔) + O3(𝑔) → NO3(𝑔) + O2(𝑔)
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