The rate law for the given reaction A(g) + 3 B(g) → C(g) + 2 D(g) is determined to be Rate = k[B]^2. Here option B is correct.
To determine the rate law for the given reaction A(g) + 3 B(g) → C(g) + 2 D(g), we can use the method of initial rates and compare the rates for different experiments.
Let's use the data from the table to find the rate order with respect to A and B:
Experiment 1: [A] = 0.300 M, [B] = 0.180 M, Rate = 0.0234 M/min
Experiment 2: [A] = 0.300 M, [B] = 0.360 M, Rate = 0.0934 M/min
Experiment 3: [A] = 0.150 M, [B] = 0.180 M, Rate = 0.0234 M/min
Now, let's compare the effect of changing the concentration of A and B on the rate.
When [A] is doubled (compare Experiments 1 and 3), the rate remains the same. Therefore, the reaction rate is independent of [A].
When [B] is doubled (compare Experiments 1 and 2), the rate increases by a factor of 4 (0.0934 / 0.0234 = 4). This indicates that the rate is proportional to [B]^2.
Based on the above analysis, the rate law is Rate = k[B]^2.
So, the correct option is b) Rate = k[B]^2
Complete question:
Using the information in the table, the rate law for the reaction A(g) + 3 B(g) → C(g) + 2 D(g) is
[A0] (M) [B0] (M) Rate (M/min)
0.300 0.180 0.0234
0.300 0.360 0.0934
0.150 0.180 0.0234
Options:
a) Rate K[A][B]^3
b) Rate k[B]^2
c) Rate k[A]^2[B]
d) Rate k[A][B]^2