Final answer:
To calculate the rate constant (k) in the given rate law and the concentration of A when the concentration of B is known, we can use the provided values and plug them into the rate law equation. Using the given values, the value of k is approximately 270 M-1sec-1, and the concentration of A when [B] = 0.050 M is approximately 0.992 M.
Step-by-step explanation:
To calculate the value of the rate constant (k) in the given rate law, we can use the values of the concentration of A, the concentration of B, and the reaction rate provided.
a. Using the given values, we can plug them into the rate law equation and solve for k:
Rate = k[A]0[B]2
8.31 x 10-2 M/sec = k x (0.023 M)0 x (0.054 M)2
k = 8.31 x 10-2 M/sec / (0.054 M)2
k ≈ 270 M-1sec-1
b. To calculate the concentration of A when the concentration of B is 0.050 M, we can rearrange the rate law equation and solve for [A]:
Rate = k[A]0[B]2
8.31 x 10-2 M/sec = (270 M-1sec-1) x [A]0 x (0.050 M)2
Simplifying the equation, we get:
[A] ≈ 0.992 M