Final answer:
To find the rate equation for the decomposition of substance A, we use the provided data about the concentration change and feed rates in two reactors. By assuming a first-order reaction and applying the first-order rate law, we calculate the residence time in each reactor and the rate constant k to determine the equation.
Step-by-step explanation:
To determine the rate equation for the decomposition of substance A, we need to analyze the given experimental data. Since the color indicator changes when the concentration of A falls below 0.1 M, we know that at the point of color change, the concentration has reached this critical threshold. We're given two scenarios: the color change occurs in the first reactor at a steady-state feed rate of 10 cm³/min and in the second reactor at a feed rate of 50 cm³/min.
Assuming that the decomposition of A is a first-order reaction, the rate of decomposition is proportional to the concentration of A. This can be expressed as rate = -k[A], where k is the rate constant and [A] is the concentration of A.
The volumetric flow rate (F) and the volume of the reactor (V) can be used to determine the residence time (τ) in each reactor, which is τ = V/F. For the first reactor, the residence time would be 400 cm³ / 10 cm³/min = 40 min. For the second reactor at the specified conditions, it would be 400 cm³ / 50 cm³/min = 8 min.
Using the integrated first-order rate law, ln([A]/[A]0) = -kt where [A]0 is the initial concentration and [A] is the concentration at time t, we can solve for the rate constant, k. For the first reactor, t is 40 min and [A]0 = 0.6 M, [A] = 0.1 M; for the second reactor, t is 8 min for the same initial and final concentrations.
Solving for k in each case and comparing the values would then allow us to determine the actual rate equation.