For the reaction A to products}, the following data were obtained: t=0 s, A}]=0.715 M; 22 s, 0.605 M; 74 s, 0.345 M; 132 s, 0.055 M.
What is the half-life of the reaction?
To find the half-life of the reaction, we need to determine the time it takes for the concentration of A to decrease to half of its initial value.
Given the data, we can calculate the initial rate of reaction by comparing the change in concentration of A over time intervals. Let's calculate the rate of reaction for the first interval:
Initial rate = (0.605 M - 0.715 M) / (22 s - 0 s)
Initial rate = -0.11 M / 22 s
Initial rate = -0.005 M/s
To find the time taken for the concentration to reduce to half, we can use the formula for first-order reactions:
ln(A_t / A_0) = -kt
where A_t is the concentration at time t, A_0 is the initial concentration, k is the rate constant, and t is time.
Rearranging the equation, we get:
t_1/2 = ln(2) / k
We can now calculate the rate constant k using the initial rate:
k = -ln(A_t / A_0) / t
k = -ln(0.605 M / 0.715 M) / 22 s
k ≈ 0.0123 s^-1
Now, we can calculate the half-life using the rate constant:
t_1/2 = ln(2) / k
t_1/2 = ln(2) / 0.0123 s^-1
t_1/2 ≈ 56.4 s
Therefore, the half-life of the reaction is approximately 56.4 seconds.