Final answer:
The time it takes for the concentration of A to decrease from 0.500 M to 0.200 M in the given first-order reaction is approximately 0.603 seconds.
Step-by-step explanation:
The given reaction is a first-order reaction, where the reactant A is converting to substance B. We can use the formula for the first-order reaction to calculate the time it takes for the concentration of A to decrease from 0.500 M to 0.200 M.
The formula for a first-order reaction is:
ln([A]₂/[A]₁) = -kt
Where [A]₁ is the initial concentration of A, [A]₂ is the final concentration of A, k is the rate constant, and t is the time required. Rearranging the equation, we get:
t = -(ln([A]₂/[A]₁))/k
Substituting the given values, we get:
t = -(ln(0.200/0.500))/0.800
Using a calculator, we can evaluate this expression to find the required time, which comes out to be approximately 0.603 seconds.