I have no idea where to start with this problem:
A certain reaction has the following general form: aA -> bB
At a particular temperature and (A)o = 2.00(10^-2)M, concentration versus time data were collected for this reaction, and a plot of In(A) versus time resulted in a straight line with a slope value of -2.97(10^-2)min ^-1.
a. Determine the rate law, the integrated law, and the value of the rate constant for this reaction.
b. Calculate the half-life for this reaction.
c. How much time is required for the concentration of A to decrease to 2.50(10^-3)M?
To solve this problem, we need to apply the principles of chemical kinetics and the integrated rate laws. Let's proceed step by step:
a. To determine the rate law, we can use the fact that the plot of In(A) versus time resulted in a straight line with a slope of -2.97(10^-2) min^-1. In general, for a first-order reaction, the integrated rate law is given by the equation:
ln(A) = -kt + ln(Ao)
Where A is the concentration of reactant at time t, Ao is the initial concentration of reactant, k is the rate constant, and t is the time.
Comparing this equation to the given data, we can see that the slope of the line (-2.97(10^-2) min^-1) is equal to -k. Therefore, -k = -2.97(10^-2) min^-1.
Since k is positive (rate constants are always positive), we can write k = 2.97(10^-2) min^-1.
Therefore, the rate law for this reaction is first-order, and the value of the rate constant is 2.97(10^-2) min^-1.
b. To calculate the half-life for a first-order reaction, we can use the following equation:
t1/2 = 0.693 / k
Plugging in the value of k we determined in part a, we get:
t1/2 = 0.693 / 2.97(10^-2) min^-1
Calculating this expression gives us the value of the half-life.
c. To determine the time required for the concentration of A to decrease to 2.50(10^-3) M, we need to use the integrated rate law for a first-order reaction:
ln(A) = -kt + ln(Ao)
Rearranging this equation, we have:
t = (ln(A/Ao)) / -k
Plugging in the given values of A (2.50(10^-3) M), Ao (2.00(10^-2) M), and k (2.97(10^-2) min^-1), we can calculate the time required for the concentration of A to reach the desired value.
By following these steps, we can solve the problem and find the rate law, integrated law, rate constant, half-life, and the time required for the concentration of A to decrease to a specific value.