For 2NO2 + O3 -> N2O5 + O2: Doubling [NO2] doubles the rate, doubling [O3] doubles the rate. What is the rate law?

Step 1: Write the general form of the rate law. For the reaction 2NO_2 + O_3 → N_2O_5 + O_2, the general rate law can be written as: rate = k[NO_2]^x[O_3]^y where k is the rate constant, x is the order of reaction with respect to NO_2, and y is the order of reaction with respect to O_3. Step 2: Determine the reaction order with respect to NO_2. The problem states that "Doubling [NO_2] doubles the rate". If we double [NO_2] while keeping [O_3] constant, the rate becomes 2 × rate. 2 × rate = k(2[NO_2])^x[O_3]^y Dividing this by the original rate law: 2 × raterate = k(2[NO_2])^x[O_3]^yk[NO_2]^x[O_3]^y 2 = (2)^x Therefore, x = 1. The reaction is first-order with respect to NO_2. Step 3: Determine the reaction order with respect to O_3. The problem states that "doubling [O_3] doubles the rate". If we double [O_3] while keeping [NO_2] constant, the rate becomes 2 × rate. 2 × rate = k[NO_2]^x(2[O_3])^y Dividing this by the original rate law: 2 × raterate = k[NO_2]^x(2[O_3])^yk[NO_2]^x[O_3]^y 2 = (2)^y Therefore, y = 1. The reaction is first-order with respect to O_3. Step 4: Write the complete rate law. Substitute the determined orders x=1 and y=1 into the general rate law: rate = k[NO_2]^1[O_3]^1 rate = k[NO_2][O_3] Step 5: Compare the derived rate law with the given options. The derived rate law is rate = k[NO_2][O_3]. The visible options are: (a) rate = k[NO_2] (b) rate = k[NO_2]^2[O_3] Neither of the visible options matches the derived rate law. Assuming there are other options not shown in the image, the correct rate law based on the experimental data is: rate = k[NO_2][O_3] 3 done, 2 left today. You're making progress.